Equivalence of Product Tax Changes and Public Enterprise Price Changes
  • 1 0000000404811396https://isni.org/isni/0000000404811396International Monetary Fund

The generation of operating surpluses by nonfinancial public enterprises is one technique by which domestic resources can be mobilized for use by the public sector (the enterprises themselves or some governmental unit). Assuming that the enterprises are operated in a manner consistent with X-efficiency and allocative efficiency, the pricing policies and practices that would be consistent with the generation of operating surpluses (or losses) are almost certainly regarded by many as a substitute in some sense for taxation (or subsidization) measures in the mobilization of domestic resources. 1 For example, Musgrave and Musgrave noted that, in the case of government monopolies, “if the government does not follow this [marginal cost pricing] rule but charges a higher price, this may be considered equivalent to imposing an excise tax on the product.” 2


The generation of operating surpluses by nonfinancial public enterprises is one technique by which domestic resources can be mobilized for use by the public sector (the enterprises themselves or some governmental unit). Assuming that the enterprises are operated in a manner consistent with X-efficiency and allocative efficiency, the pricing policies and practices that would be consistent with the generation of operating surpluses (or losses) are almost certainly regarded by many as a substitute in some sense for taxation (or subsidization) measures in the mobilization of domestic resources. 1 For example, Musgrave and Musgrave noted that, in the case of government monopolies, “if the government does not follow this [marginal cost pricing] rule but charges a higher price, this may be considered equivalent to imposing an excise tax on the product.” 2

The generation of operating surpluses by nonfinancial public enterprises is one technique by which domestic resources can be mobilized for use by the public sector (the enterprises themselves or some governmental unit). Assuming that the enterprises are operated in a manner consistent with X-efficiency and allocative efficiency, the pricing policies and practices that would be consistent with the generation of operating surpluses (or losses) are almost certainly regarded by many as a substitute in some sense for taxation (or subsidization) measures in the mobilization of domestic resources. 1 For example, Musgrave and Musgrave noted that, in the case of government monopolies, “if the government does not follow this [marginal cost pricing] rule but charges a higher price, this may be considered equivalent to imposing an excise tax on the product.” 2

It has been contended that prices above marginal costs in nationalized industries should be employed as a means of imposing indirect taxation, since “the collection of general taxation involves costs and the social cost of a sufficiently small rise in the price of goods will be less.” 3 Others are more cautious, contending only that the pricing policies of nonfinancial public enterprises bear many of the characteristics of taxation. This author has examined cases in which state-owned trading enterprises were regarded as little more than quasi-taxing authorities. 4 A slightly different but closely related study reviewed the equivalence of the pricing and output decisions of state trading enterprises with the instrument of ad valorem trade taxes. Equivalence was found to obtain in many cases, but it did not obtain under certain circumstances, principally when monopolistic elements or fixed prices were present. 5

With the growth in relative importance of public enterprises in many countries in recent years, increased attention should be given to the possible use of a price increase as an alternative technique of resource mobilization. The purpose of the present study is to analyze the equivalence or lack of equivalence with regard to resource mobilization and allocation of (a) an increase in nonfinancial public enterprises’ prices, and (b) the application of a tax to certain transactions and/or enterprises. In the course of the analysis, the advantages and disadvantages of pricing measures, as contrasted with certain taxation measures, will be noted.

The main findings of the analyses and the principal conclusions to be drawn from them are summarized in Section I. The analytical portion of the paper begins with the development of a conceptual framework for the analyses (Section II). Section III includes various partial equilibrium analyses of alternative tax and pricing measures, and Section IV presents a general equilibrium analysis applicable to a broader scope of government ownership. Some concluding remarks are given in Section V.

I. Summary of Principal Findings and Conclusions

This paper finds that in a variety of partial and general equilibrium settings, when the concept of equivalence is defined to include the levels of government and public sector revenues as well as real economic variables such as the levels of production and consumption, an excise or product tax is not often found to be equivalent to an increase in the price of a public enterprise’s output. 6

From the point of view of public sector and government revenues, there may be sharp differences between the two actions. Both partial and general equilibrium analyses indicate that only a tax could always be expected to raise government revenues. If the nonfinancial public enterprise is facing competition in output markets, an effort to increase prices independently will probably result in a reduction in profits and public sector revenues. If a monopoly nonfinancial public enterprise is already maximizing profits, both a price increase and a tax increase will result in lower profits, but a tax increase will ensure the transfer of some revenues to the government.

Equivalence between excises and pricing actions by particular nonfinancial public enterprises seems most likely to occur when the enterprise has previously constrained its profit maximization and is able to shift the tax fully into higher output prices. Even in this case equivalence does not fully obtain. As long as demand is elastic, a tax is more likely than a price increase to have a greater impact on government revenues, even though both devices may have identical effects on public sector revenues and on the dependent variables of the economy. This result derives from the assumption that the dividend is generally not determined in the same manner as the tax. For example, if a dividend is composed of the incremental profits following a price increase, the tax will always generate more government revenues than an equal price increase will. To have an equal impact on the government’s budget, therefore, the price increase required would in general need to be greater than the tax increase, which in turn would mean a greater impact on the economy’s real variables.

These results are generally confirmed by the general equilibrium analysis. However, numerical simulations indicate that under certain circumstances—in particular when demand is elastic and when the private sector is relatively larger than the public sector and its output is relatively more capital intensive and when capital is immobile between the two sectors—the imposition of a relative price increase for public sector goods will yield more incremental profits than an equal tax increase will yield incremental tax receipts. However, the general equilibrium analysis also indicates that only a tax increase can always be expected to yield positive incremental revenues to either government or public sector revenue. Furthermore, there is less variation between the highest and lowest simulated effective yields from taxes than from price increases. Taxes appear to be generally less sensitive to changes in parametric values, except for the sensitivity of government (that is, tax) revenues to changes in the elasticity of demand when capital is immobile between the two sectors.

In general, and in particular from the viewpoint of raising revenues for the government’s budgetary purposes, the tax would appear to be more reliable and more predictable than a price increase and is likely to raise equal government revenues with fewer distortions. Furthermore, if noncapital factors and material inputs are paid more than the value of their marginal product (as is often suspected of labor in many nonfinancial public enterprises), some part of higher sales receipts resulting from a price increase might be paid to already overpriced factors. Since tax revenues would not be shared with the factors, the tax might seem the more appropriate instrument. Also, a tax would probably be the preferred method of levying a charge aimed at reflecting social costs not included in the financial costs of production, because the use of a price increase might have the undesired result that some of the proceeds would accrue to noncapital factors and material inputs. Finally, tax increases are more likely than price increases to be uniform across firms and consequently might introduce fewer distortions into the pricing system.

However, in some circumstances and for some purposes, pricing action may be preferred. This would be most likely when public sector revenues, rather than only government revenues, are of concern. For example, if the nonfinancial public enterprise were operating at a loss, a price increase would increase the receipts of the enterprise whereas a tax might reduce its receipts and profits further. If the government had been financing the enterprise’s deficit by budgetary subsidies, a price increase might result in reduced government expenditures and a smaller budget, as well as a public sector, deficit. Furthermore, only a price increase could reduce the level of implicit subsidies that do not require the transfer of financial resources from the government to the enterprise. Thus, although the tax may be generally preferable, there are circumstances that are not uncommon in which a price increase may be the preferred instrument.

II. Conceptual Framework

Definition of Equivalence

In a narrow sense, equivalence might be taken to mean that the two alternative instruments (that is, a price increase and a tax increase) would have the same effect on only one objective variable—for example, the public sector’s revenue. However, this would ignore the problem of whether and how the incremental revenue would be shared between the government and the nonfinancial public enterprises, and it would imply that tax revenue accruing to the government would be regarded as interchangeable for public purposes with the retained profits of the enterprises. Consequently, in this paper, equivalence in a narrow sense is taken to mean that two alternative instruments would have the same effect on the government’s revenue and that all incremental profits of public enterprises resulting from the price increase would be transferred to the government by means of a dividend. 7

With regard to resource allocation, a broader concept of equivalence is required because variables other than revenue yield might be relevant to the analysis and differentially affected by the two instruments. Equivalence between the policy instruments can be said to obtain in a broad sense when in the market for a commodity the solution for all endogenous variables obtained for one instrument can be duplicated by a unique setting of the second instrument. 8 It is not particularly useful at this point to specify precisely the variables that will be used to determine broad equivalence, as the determination of whether two instruments are equivalent may be affected by a variety of circumstances. Actions that may be equivalent in some sense in the short run may not be equivalent in the long run. Effects may differ in open and closed economies. The extent of competition in output and input markets and numerous institutional factors are also likely to affect equivalence. Even if a particular price increase is equivalent in some sense to a tax for an individual enterprise, it does not necessarily follow that equivalence would obtain if the analysis is extended to a large number of enterprises with general equilibrium implications. For example, for an individual trading enterprise a price increase to its customers might be equivalent to a tariff, but for several trading enterprises it may more nearly resemble the effects of a change in the exchange rate.

Both partial and general equilibrium analytical techniques are employed in this paper. The partial equilibrium analysis contrasts both tax and price changes of equal rates (or amounts) and of equal yields. For the general equilibrium analysis, equal rate changes are assumed to facilitate the analysis. In the case of the partial equilibrium analysis, the object variables are essentially the government revenue generated, domestic prices, supply and demand, and exports or imports of the good or service in question. In the general equilibrium analysis, the allocation of and returns to factors of production are also analyzed. When equal yields are assumed, the analysis may be thought of as employing the differential incidence technique; that is, each tax is substituted for a pricing action of equal real yield in order to finance a given level of real government expenditure. 9 When equal rates are assumed, equal yields need not obtain, and an analytical technique similar to that of balanced budget incidence analysis is employed. While the answers to an equal rate analysis may differ quantitatively from those to an equal yield analysis, they do not differ qualitatively, and the conclusions are not significantly altered.

Types of Tax

In general, the following types of tax are of interest. For an individual enterprise an excise tax on its output, with or without an accompanying border tax adjustment for traded goods, is most relevant. 10 If the enterprise is engaged solely in state trading and has little domestic production or value added, comparisons of pricing actions with import taxes and export taxes are relevant. Furthermore, a distinction must also be made between selective excise taxes that affect only a single enterprise or commodity and a broadly based product tax that may have significant implications for other general equilibrium variables. Other types of tax are of less interest to the analysis. Profits or capital taxes are less likely to be used as a substitute for pricing actions. However, they may indeed be used to transfer profits resulting from pricing actions and under certain restrictive circumstances may be equivalent to dividends and even certain pricing measures. Most other taxes, such as individual income taxes and property taxes, have little relevance to the analysis. 11

Competitive Environment

Public enterprises are not always monopolies, and the government’s policies with respect to them cannot always be considered in isolation from the effects of the environment in which they function. For example, suppose that the public enterprise is faced with substantial competition from other domestic firms so that it is in effect a price taker. In this case, independent pricing action by the public enterprise is simply not possible, and it could not be used as an alternative to taxation. Furthermore, all sales proceeds generated by its operations would be fully utilized by cost payments for resource inputs and factors of production. Since it is assumed that the public enterprise must compete with other enterprises for factor and resource inputs and pay to each factor the value of its marginal product, then the enterprise could not, through monopsony buying practices, generate profits other than normal cost payments for the purchase or use of capital. Consequently, an individual nonfinancial public enterprise in a competitive industry could not from its own operations be expected to generate resources for the government, except in the form of the normal return to invested capital.

The only other way that individual firms in a competitive industry might provide substantial revenues for the government would be through the imposition of an excise tax on the output of the entire industry. An excise on only the nonfinancial public enterprises’ sales could not affect either the output price (assuming that output levels are maintained) or the payments to noncapital factors, and any receipts would subsequently represent a reduction in the return to the government-owned capital. Consequently, the excise tax would in effect be a tax on the nonfinancial public enterprises’ profits. 12

The mobilization of resources for the public sector appears to require that an individual nonfinancial public enterprise enjoy some form of monopoly position or that the public enterprise sector be of such importance that changes in it can have significant repercussions in the whole economy. The remainder of this paper is devoted to a comparative analysis of pricing and taxation measures based on certain assumptions of possible conditions in output markets. First, partial equilibrium analyses of a monopolistic nonfinancial public enterprise are presented with various assumptions about pricing and profit-maximizing behavior. Then a general equilibrium analysis is presented, in which the scope of the nonfinancial public enterprise sector is broad and the effects of alternative pricing and taxation measures may impinge on the private sector as well.

III. Partial Equilibrium Analysis of Monopolistic Nonfinancial Public Enterprises

Pricing and taxation measures are probably most nearly equivalent when a nonfinancial public enterprise faces neither domestic nor foreign competition in the market for its output and when it is not sufficiently large for its actions to have significant ramifications in other industries in the economy. In this situation, a price in excess of marginal cost would be equivalent to an excise tax on the output with respect to production, consumption, prices, and, perhaps, the government’s revenue. 13 The market description is probably most applicable, however, to municipal public utilities and may not be very relevant to many nonfinancial public enterprises of a commercial or industrial character. The remainder of the partial equilibrium analysis is devoted to some alternative market conditions that might be encountered.

Domestic Monopoly With Import Competition

Consider first a nonfinancial public enterprise that has a monopoly in domestic production but confronts strong competition from private sector imports over which it has no control. The enterprise, even though it has a domestic production monopoly, would not be able to raise its output prices unilaterally because of the constraints of foreign competition. Any such attempt would merely divert domestic customers to foreign suppliers. Consequently, there can be no equivalence between unilateral pricing action and any form of taxation.

The situation is illustrated in Chart 1. Assuming that there are no divergences between private and social costs, the supply curve for the domestic, import-competing monopolist may be represented by the curve SS, which may be thought of as representing the long-run marginal cost (private and social) of production for various levels of output in the domestic industry (or firm, in this case). The domestic demand curve is represented by DD. Employing the small-country assumption, imports are assumed to be infinitely available at the price OB, which, assuming that the exchange rate is in equilibrium, represents the marginal and average social cost of imports. If the government levied a tax equal to AB per unit of output, it would in effect be taxing domestic production. Since the market price is fixed by international considerations, the price received by domestic producers would be reduced by AB to OA. Domestic producers would regard this as a shift in their supply curve to S’S’, and they would be willing to produce only OM. Domestic consumption would remain unchanged at OR, and imports consequently would rise by MN to equal MR. In this case, a unilateral price increase would be impossible because of international competition, and the imposition of a tax on the domestic nonfinancial public enterprise would be more nearly equivalent to a producer price decrease than to a consumer price increase. If the enterprise’s supply is elastic, the tax will both reduce public sector revenues and guarantee to the government a certain share of those revenues. If the enterprise’s supply is inelastic, so that payments to noncapital factors cannot be reduced, the excise will be equivalent to a profits tax on the normal return to equity invested in the enterprise.

Chart 1.
Chart 1.

Domestic Monopoly with Import Competition

Citation: IMF Staff Papers 1981, 002; 10.5089/9781451946871.024.A004

A consumer price increase could be accomplished in conjunction with a tariff measure. For example, suppose that a tariff in the amount of BC (or rate of BC/OB) is imposed. The price to consumers would rise from OB to OC, and consumption would fall from OR to OQ. If no domestic tax is imposed, domestic producers would receive BC more per unit of output and would expand their output to OP, and would have receipts totaling OCJP. Imports would fall to PQ, and the proceeds of the tariff would equal IJKL.

If both a tariff and a tax are imposed on domestically produced goods, so that all consumption is taxed, domestic consumers will continue to pay a price equal to OC, but domestic producers will receive only OB. 14 Consequently, domestic production would remain at ON, but imports would bear the full brunt of the adjustment in consumption and would fall to NQ. However, the increase in the domestic price is possible only because of the tariff or border tax adjustment on imports. As a domestic price increase cannot occur independently, pricing and taxation measures cannot be considered as substitutes in these circumstances.

Much the same considerations apply if it is assumed that the government subsidizes, rather than taxes, domestic production. If the unit subsidy is equal to BC, for example, domestic production will expand to OP. Domestic consumption and the product price would remain constant at OR and OB, respectively. The cost of the subsidy to the government would equal BCJI. The government may wish to subsidize production, for example, if it is believed that the marginal social cost of production as represented by S”S” is less than the marginal private cost. A subsidy equal to BC will raise domestic output to OP, where the marginal social cost of domestic production and the marginal cost of imports are equal. The net domestic social gain would be represented by the triangular area GG’I. 15

Profit-maximizing Nonfinancial Public Enterprise Without Import Competition

To this point it has been assumed that the nonfinancial public enterprise could not maximize profits as a privately owned monopoly could. In general, it is probably not reasonable to expect that unconstrained profit maximization is characteristic behavior for all nonfinancial public enterprises. On the other hand, it is reasonable to expect that the government may encourage fiscal monopolies that engage in producing and/or trading goods for which demand is thought to be highly inelastic (such as tobacco, sugar, salt, and alcoholic beverages), as well as other monopoly public enterprises (such as oil companies), to maximize their mobilization of resources.

A nonfinancial public enterprise with a monopoly on domestic sales can either produce its output in domestic productive facilities or import some or all of the commodity for sale. Thus, it can be either a manufacturing or a trading enterprise. Such a domestic monopoly could probably be sustained only through artificial means, such as refusal by the government to grant import licenses to potential competitors. If only profit motives and no social costs or benefits are involved, a profit-maximizing nonfinancial public enterprise will produce domestically at a level of output for which the domestic marginal revenue and marginal costs are equal as long as the cost of domestic production is below that of importing. If imported costs are lower, it will import a level of output for which the marginal foreign costs equal the marginal domestic revenue. In either case, the price charged would be what the market would bear, and profits would be maximized.

Consider first a profit-maximizing nonfinancial public enterprise that produces domestically and has a monopoly import license. In Chart 2, the enterprise’s long-run supply curve may be represented by MC and its average costs by AC in the absence of any tax and by the curves denoted by primes for the imposition of a tax. In the absence of any tax or subsidy, the monopolist produces an amount OE and sells it at a price OB. As long as the world market price, for example price OW, is higher than domestic costs, all production will be local. The monopolist’s receipts will equal OBCE, and profits will be ABCF.

Suppose that an excise tax equal to A’A” (or F’F or F’G’) is imposed. As there is no international trade in the good, it is immaterial whether the tax is levied under the origin or the destination principles. The nonfinancial public enterprise would continue to maximize after-tax profits by equating MC’ with its marginal revenue. Output would fall to OE’, and the price including tax would rise to OB’. Gross sales receipts would equal OB’C’E’, of which tax proceeds would account for A’A”G’F’. Since a profit-maximizing monopolist always operates in the elastic portion of his demand curve, gross receipts would be less than in the absence of a tax. If the monopolist is initially in a long-run equilibrium position in which average costs are minimized, the imposition of the tax will result in an increase in average costs. As the sales price rises by less than the tax, average receipts net of tax would fall, and unit profits would decline. Total profits would fall to A’B’C’F’.

Chart 2.
Chart 2.

Profit-Maximizing Nonfinancial Public Enterprise Without Import Competition

Citation: IMF Staff Papers 1981, 002; 10.5089/9781451946871.024.A004

Suppose that the government attempted to raise an equal amount of revenue by simply requiring the monopolist to increase the price from OB to OB plus A’A’’ so that the absolute amount of price increase was equal to the tax (that is, if dP = dT = A’A”). In this case, output, sales receipts, and both total and unit profits would be even less under the price increase than under the tax as long as demand was elastic. Dividends could not be related to increases in profits, which would have fallen. If the dividend is determined to be equal to the amount of price increase times the number of units of output, then the amount of the dividend would be less than the tax receipts, since the output level would have fallen more sharply. Alternatively, if a price increase of only BB’ (dP = BB’ < dT) is imposed, output levels and sales receipts would fall to the same levels as in the case of the tax, but dividend receipts of government would be less and the retained profits of the nonfinancial public enterprise greater than with the tax.

Both broad and narrow equivalence will obtain between dP = BB’ and alternatively dT = A’A”, when all monopoly profits of the enterprise are transferred to the government by means of either a tax or a dividend or both. This may be a reasonable expectation for fiscal monopolies whose profits are often transferred essentially in entirety to the government. 16 Similarly, the profits of many government-owned oil exporting or other mineral resource exporting companies turn over essentially all of their profits after excluding funds sufficient to finance expenditures for capital expansion. However, in many nonfinancial public enterprises not all profits are transferred to the government, in which case whether or not there is equivalence depends on how the dividend is determined. In particular, broad equivalence requires that the price increase be less than the alternative tax increase and that the dividend be determined in the same manner as, and be equal to, the alternative tax (per unit or ad valorem). However, dividends are seldom determined in relationship to the quantity or value of output; more commonly, they are likely to be related to changes in profits and perhaps receipts or prices. In this event, equivalence with respect to government revenue would not obtain, and a tax and pricing measure would be equivalent with respect to the real variables only in a qualitative sense. Furthermore, if the enterprise is a profit maximizer, profits and receipts will fall as a result of any price increase, and no revenues will be obtained from a dividend based on either of these variables.

Alternatively, if, owing to lower costs in international markets, the profit-maximizing enterprise imports goods for resale in domestic markets rather than producing them domestically, much the same conclusions can be obtained. However, in these circumstances it would not be possible to impose an excise tax under the origin principle, since there is no domestic production and such a tax would not apply to imports. Consequently, the tax would have to be levied under the destination principle and would in the absence of domestic production be equivalent to a tariff.

Constrained, Profit-maximizing Monopoly With Control Over Imports

In nonfinancial public enterprises, constrained behavior may result in a market solution somewhere between the solutions that would result from competitive and profit-maximizing behaviors. Although there may be no orthodox economic explanations for such behavior, several plausible explanations can be imagined. 17 For example, managers of nonfinancial public enterprises, especially those that are not fiscal monopolies, may wish to avoid maximizing profits in order to satisfy other objectives of a social nature, such as the desire to generate more output or employment than would be generated under the reduced output of a profit-maximizing monopolist. Alternatively, prices may be held below maximum levels for political reasons. In addition, various considerations may suggest that social benefits (costs) may exceed (be less than) private benefits (costs). Any of these considerations may result in the enterprise earning profits that are somewhat less than the maximum attainable, but other considerations may result in profits that are in excess of a normal return to capital being earned. For example, managers of nonfinancial public enterprises for whom growth of the enterprise is an important objective may find it advantageous and easier to expand their operations through sufficient, yet socially acceptable, levels of profits. Indeed, in some countries internally financed capital expenditures of these enterprises escape the government’s planning processes entirely. Such behavior may be referred to as constrained profit maximization.

A constrained monopolist may either produce domestically or import his goods for resale. As shown in Chart 3, the monopolist initially chooses to buy at the world price OW imports equal to OE for resale at the price OA, which is somewhat lower than his profit-maximizing price. His sales proceeds would equal OACE, and profits would be WACB. If the enterprise’s decision to import is due to the lower costs of imports, the only effect of introducing a tax based on the origin principle would be to reduce the likelihood of any domestic production, because the tax would not apply to imports and would lower their relative price even further. If a tax based on the destination principle and equal to AA’ is applied to both imports and domestic production, if there is any, the outcome will depend on the degree of forward shifting by the enterprise. Since, by assumption, profits were constrained, the enterprise can restore them by increasing its price. If the monopolist chooses to pass on the full tax to consumers in the form of a price increase equal to the tax increase, the amount sold will fall to OE’. Gross receipts will fall to OA’C’E’, but gross profits (or public sector revenues) will rise (as long as the price increase does not exceed the level consistent with maximum profits) to WA’C’B’. Tax proceeds would amount to AA’C’C”. However, profits net of tax would be WAC”B’, which would be unambiguously less than profits had been before imposition of the tax as long as the domestic price increase does not exceed the tax increase. To maintain its own level of profits, the enterprise would need to increase its price by more than the tax increase, that is, to practice shifting in excess of 100 per cent.

Chart 3.
Chart 3.

Constrained, Profit-Maximizing Monopolist with Control over Imports

Citation: IMF Staff Papers 1981, 002; 10.5089/9781451946871.024.A004

Suppose, alternatively, that no tax is levied but that the domestic price is raised by C”C’ and the additional profits are transferred to the government. The effects on the domestic price, domestic consumption, imports, and gross profits would be the same as in the case of the forward shifted tax. However, the distribution of profits between the enterprise and the government would differ. Profits would rise by AA’C’C”-CC”B’B, which is unambiguously less than the proceeds of an alternative, equal tax increase. Since demand is elastic, the government, by taking only the incremental profit, definitionally prevents the enterprise from bearing any reduction in profits due to a reduction in sales and absorbs all such losses itself.

If the constrained monopolist produces domestically, the same conclusions obtain, with only minor modifications. Again, much depends on by how much the enterprise raises its price in response to the imposition of a tax. In addition, with domestic production, since profits were not initially maximized, a reduction in output may lead to somewhat lower average costs, whereas with imports average costs are assumed to be constant. Thus, the reduction in public sector revenues resulting from lower output may be somewhat offset by both lower unit costs and higher prices. 18

Monopoly Nonfinancial Public Enterprise With Control Over Exports

A nonfinancial public enterprise may be both a monopoly supplier in domestic markets and an exporter to world markets. Such an enterprise might be an export marketing board that purchases all, or effectively all, of the output of numerous small producers for further resale or export, or alternatively, the enterprise may be assumed to be the actual monopolistic producer. In either case the enterprise’s supply curve can be represented by the industry’s long-run marginal cost curve. In the absence of barriers to trade, domestic prices in excess of those prevailing in world markets could only be achieved in conjunction with tax or tariff measures aimed at supporting a higher domestic price. Furthermore, price increases could be achieved only if there were pre-existing artificial constraints of domestic prices to levels below those in world markets or in conjunction with a tax or tariff increase. For example, many governments impose pricing ceilings on domestic transactions in some export commodities, particularly agricultural export commodities. In the absence of artificial constraints, taxation measures must be considered as complements to, rather than substitutes for, pricing measures, but with pre-existing constraints, both pricing measures and taxes may be feasible.

Consider initially a situation in which the nonfinancial public enterprise does not discriminate between its domestic and foreign buyers by exercising its domestic monopoly power (Chart 4). However, assuming that the world market price is OW and that as much domestic output as is available can be sold at that price, the combined domestic demand (DD) and foreign demand (WD’) curves would appear as DD’ to the enterprise. If the enterprise exercises no monopoly power and there is no government intervention, the international price OW would prevail in domestic markets and domestic consumption would be OF. Output would total OF’, of which FF’ would be exported.

If the enterprise could divide its market and sell to domestic consumers at prices above the international levels, profits on domestic sales would be maximized at output OF’’ and price OC. However, in the range of outputs between OF” and OF, the enterprise could behave as a constrained profit maximizer. Price discrimination in domestic markets would require some barrier to trade that would permit the enterprise to exercise monopoly power, such as quotas or perhaps a monopoly import license. Alternatively, a tariff of at least a magnitude of CW can be imposed to ensure that the enterprise does not face import competition in the range up to its maximum profit position. As there would be no imports in practice, all public sector revenues would accrue initially in the form of receipts or profits of the enterprise. In Chart 4, with constrained profit maximization practiced by the enterprise initially, OE might be produced and sold domestically at the price OB, yielding domestic receipts of OBGE and profits of ABGH. Additionally, the enterprise could produce EF’ for sale in international markets, yielding additional receipts of EIJF’ and profits of HIJK. If the enterprise autonomously raised its price to domestic consumers to OB’, total output would remain unchanged, but domestic consumption would fall to OE’ and exports would rise to E’F’. Profits on domestic consumption, which had been constrained, would increase to AB’G’H’ and profits on foreign sales would increase to H’I’JK. Total profits would increase by BB’G’G’’-II’G’’G.

Chart 4.
Chart 4.

Monopolist with Control over Exports

Citation: IMF Staff Papers 1981, 002; 10.5089/9781451946871.024.A004

If an excise tax equal to G’G” is levied in accordance with the destination principle, and if the full tax is passed on by the enterprise in the form of a higher price to domestic consumers, the effects on production, consumption, and trade will be the same as in the case of the price increase. As in the previous cases, however, the tax proceeds (BB’G’G”) exceed the incremental profits (BB’G’G”-II’ G”G) resulting from a price increase as long as demand is elastic. Consequently, if government revenues are to be equivalent, the price increase with dividend would have to exceed the forward shifted tax and in turn would have to lead to a greater reduction in domestic demand and therefore to a greater expansion of exports.

If the tax is levied under the origin principle, it is usually assumed that the price to domestic consumers will not rise. Since no compensating tax would be levied against imports in the absence of barriers to trade, the threat of substitute imports would act to prevent a forward shifting of the tax. In that case, the imposition of the tax would have no effect in domestic markets. However, since the tax would be seen by producers as a reduction in the price they receive, exports and total output would fall to EE” and OE”, respectively. Profits per unit of sales would fall by the amount of the tax, in addition to whatever increase or decrease may occur in average costs as a result of the change in the level of output. In Chart 4, profits would fall to the area bounded by A’BGIJ’K’.

Even if the tax is levied in accordance with the origin principle, the enterprise may be able to exercise monopoly power and to shift the tax forward fully to domestic consumers but not to foreign consumers. In this case, the effects on domestic consumption would be the same as for a tax based on the destination principle. However, the effects on overall output, profits from domestic and export sales, and the level of exports would differ. Since the net receipts per unit of international sales would also fall (or alternatively, average production costs would rise) by the amount of the tax, total output would decline to OE”. However, whether exports rise or fall will depend on whether the slope of the supply curve is more or less than the slope of the demand curve. If the slopes are equal there will be no change in the level of exports. Furthermore, profits derived from both domestic and export sales will be affected by changes in the average cost per unit of output resulting from changes in the level of output. As shown in Chart 4, these costs decline, thus somewhat offsetting the negative impact of the tax on average costs and profits. However, if the industry output of OF’ had represented the low point of its long-run average cost curve, then average costs would have risen with the output reduction and would have further reduced the profitability of international sales. Profits on domestic sales would equal A’B’G’H”, and on international sales they would total H’’TJ’K’.

Finally, to raise equal amounts of revenue, the tax rate (or unit tax) based on the origin principle would be lower than the rate based on the destination principle if the nonfinancial public enterprise is an exporter. Consequently, with equal yields, a price with dividend measure would have the greatest impact on domestic demand, and a tax based on the origin principle would have the least impact. With regard to overall output, only the tax based on the origin principle would have any impact. 19

Assuming that market conditions are such that autonomous pricing actions by the nonfinancial public enterprise would generate additional profits, the results of the partial equilibrium analysis indicate that, as long as demand is elastic, the equivalence of a price change to the tax would depend on how the amount of the dividend was determined, but if the dividend were set as equal to the change in either receipts or profits, it would not be equivalent to either tax. A “per unit” or “ad valorem” dividend would be equivalent to an excise levied in accordance with the destination principle but not the origin principle. The results obtained will depend on whether the enterprise is an importer, exporter, or nontrader. Thus, if dividends are determined in a more common manner—for example, as some function of incremental profits—broad equivalence would not obtain for the individual enterprise.

IV. General Equilibrium Analysis of Broadly Based Taxes and Policies for Nonfinancial Public Enterprises

Conceptual Framework

The analysis thus far has been confined to the context of a single public enterprise or monopolistic industry. However, in many countries, the scope of government ownership of business is so broad that nonfinancial public enterprises in a variety of industries face direct competition in output markets from private enterprises, or at least strong indirect competition from private producers of near substitutes. Furthermore, even if there is no competition in product markets, there is always competition in the markets for factors of production.

In such circumstances, partial equilibrium analysis may not fully, or even adequately, reveal the equivalence or nonequivalence of public enterprise pricing measures and taxes; general equilibrium techniques may be better suited for such an analysis. In this section a general equilibrium model of a competitive economy is employed to study the equivalence of taxation and pricing measures in public enterprises. In particular, the model employed is an adaptation of the model developed by Harberger for use in tax incidence analysis. 20

No effort will be made in the text to repeat in detail all of the equations and algebraic formulations of either the basic Harberger model or subsequent modifications to it. However, some discussion of the analysis is necessary. Four formulations of the model are developed in order to analyze taxes and price changes under two basic assumptions: (a) that capital is mobile between the public and private enterprise sectors, and (b) that capital is immobile between the public and private enterprise sectors. It is assumed that there is no international trade. Therefore, there are the following four systems of equations depicting the four formulations: (1) mobile capital with tax change; (2) immobile capital with tax change; (3) mobile capital with price change; and (4) immobile capital with price change. The equations composing the four systems are contained in Table 3, in the Appendix; the solutions to the systems with regard to product and factor prices and the allocation of factors of production appear in Table 4, in the Appendix. 21

In each of the four systems it is assumed that two factors of production—capital and labor (K and L)—are fixed in total supply but are fully employed in producing two goods (X and Y) under conditions of constant returns to scale. In all the formulations, relative prices are assumed to be fully flexible. The first and third systems (with the exception that the price of good Y, rather than that of labor, is used as the numeraire) employ the original Harberger formulation, in which both factors of production are fully mobile. The second and fourth systems assume that capital is not mobile between the public and private enterprise sectors. 22 The results of the analysis of the equivalence of taxation and pricing measures with regard to product and factor prices, output, and factor allocation will reflect in a large measure the assumptions that underlie equations 1 through 4. The assumption that labor is fully mobile but that capital invested in public enterprises is not mobile is particularly critical. As long as the government’s investment decision is based on considerations other than those affected by changes in the rate of return to its capital, capital invested in public enterprises in each industry may be assumed to be fixed exogenously. For example, the government may establish, solely for national prestige, an automobile plant. Alternatively, the variables in the model might be thought of as depicting financial returns, while the government’s decision-making process, which takes into account social considerations, is excluded from the model. With immobility assumed, capital invested in public and private enterprises may earn different rates of return, because capital flows will not result in an equalization of the rates of return.

Systems 1 and 3 each contain nine equations and nine unknowns, while systems 2 and 4 contain ten equations and ten unknowns. In systems 1 and 3, there is a common rate of return to capital; in systems 2 and 4, as a result of the immobility of capital, there are two rates of return to capital and an additional equation to depict the assumed immobility of capital. Five equations are common to all four systems. All systems include the same demand equation, in which demand depends only on changes in relative product prices and taxes under the assumption that all consumer groups, including the government, spend their incomes in the same way at the margin and have the same income-compensated elasticity of demand. 23 In each of the four systems, production functions are assumed to be linear homogeneous and are depicted by the same equation. 24 The assumptions of full employment of both factors are represented by the same equations in all formulations, as is the choice of the price of the private sector good as the numeraire.

The assumptions about capital mobility taken in conjunction with the assumption about relative product prices result in some differences between the systems in the equations for the product/factor price relationships and the equations for factor substitution in the public and private sectors and for the relationship between relative factor prices and factor intensities in production. In systems 1 and 2, relative product and factor prices are assumed to be flexible, and free market forces are assumed to determine how they would respond to the imposition of a tax on the output of the public enterprise sector. Consequently, in each of these systems there are two equations in which relative factor prices and factor proportions in production in each sector are related by the elasticity of factor substitution in that sector. Similarly, there are two equations for the relationship between product and factor prices in the public and private sectors.

In systems 3 and 4, the price of public sector output is assumed to exceed (or fall short of) the price of the private sector output by an exogenously determined amount (or rate) A. This assumption could reflect a policy decision to raise (or to lower) the prices of nonfinancial public enterprises’ output relative to the prices of private enterprises’ output by A and to maintain that differential. Analytically, such a pricing policy must imply that the link between output prices and production costs in the public sector is broken. Consequently, the prices of these enterprises’ outputs are related to output prices in the private sector, and both are in turn determined by production costs in the private sector. Consequently, the product/factor price relationship in the public enterprise sector is replaced by an equation based on the assumption made about the output price differentials. The product/factor price relationship in the private enterprise sector is the same as in systems 1 and 2. In system 3, since both factors of production are mobile between the two sectors and factor prices uniform between the two sectors, factor prices and the distribution of factor incomes in the public sector are simultaneously determined and are equated with those in the private sector.

In system 4, the same output price assumption is made, but it is also assumed that capital employed in the public sector is fixed and unresponsive to changes in its rate of return. In this system, the return to labor is simultaneously determined for both industries, and the return to capital is determined by market forces in the private sector. However, the return to capital in the public sector is a residual, and, furthermore, factor substitution in the public sector is no longer a function of relative factor prices; that is, the capital employed is exogenously fixed, and labor employed in the industry must vary in order to accommodate any change in output necessary to equate supply and demand. Under these assumptions there are two product/ factor price relationships (one of which determines residually the return to capital in public sector enterprises) but only one relationship between factor substitution and factor returns (that for private sector enterprises). The other substitution equation is replaced by the equation for the assumed difference in output prices between the two sectors.


In the remaining discussion, it will be convenient to adopt the following assumptions and denotations. Good X is assumed to be produced by public sector enterprises and good Y by privately owned enterprises. The prices of goods and factors are denoted by P, with a subscript to indicate the relevant good or factor. Thus, Px, Py, PL, and PK represent the prices of goods X and Y, the wages of labor, and the return to capital, respectively. In systems 2 and 4, a second subscript indicates whether the return to capital represents the X or the Y industry. Taxes are represented by T with an appropriate subscript. 25 The amounts of capital and labor are represented by K and L, respectively, with subscripts to indicate the industry of its employment. Changes in variables are indicated by differential notation.

As in the partial equilibrium analysis, revenues raised from a tax on the public enterprise sector’s output are assumed to be an alternative to additional profits resulting from increases in the prices of those products. Profits (including the normal return to capital) may be represented by PKKx, tax revenues by TxX and TyY, and total government revenues by R. Assuming that nonfinancial public enterprises disburse all profits as dividends, government revenues become




Assuming that taxes on the output of public and private enterprises are initially equal (Tx = Ty) and that dTy = 0, and since in the first approximation dX = -dY


It can also be shown that


where fK and fL are the initial shares of capital and labor, respectively, in the production of good X. 27 Alternative pricing and taxation measures would yield equal revenues (i.e., dPKxKx = dTxX, or alternatively, dPKxfK = dTx), as indicated by equation (1), only in the short run, when factors of production are not mobile. Furthermore, equation (2) indicates that equal yields would obtain for both a tax increase or a price increase only if labor (and other factors and material inputs) did not share in the increased sales receipts resulting from the price increase and if there were no induced changes in factor prices in the case of a tax increase. 28

In any time frame other than the short run, equal yields would require that labor be prevented from sharing in the increased sales proceeds by artificial market imperfections. Ordinarily, one would expect that the incremental profits would be less than the incremental sales proceeds due to the following factors. First, labor would, through a normal bargaining process, expect to receive some share of the increased value of the output through wage increases and would not normally be expected to allow the full increment to accrue to capital. Second, if consumer demand is elastic, one would expect some decline in demand and in the value of output if the price of output were raised.

Under various sets of assumptions other than the short run, the relationships between an autonomous change in the price of the output and the tax change required to generate equal revenue yields can be ascertained. In general, these relationships vary according to the assumptions made about factor mobility and market competition. As noted earlier, it is less complicated and equally enlightening to employ a balanced budget technique in the general equilibrium analysis; this eliminates the need to compute these complicated relationships. That is, one may assume that the price change and the alternative tax measure are equal (equal either in amount or in rate) and that any differences in their revenue yields can be made up through changes in the level of government expenditure or, if a differential incidence technique is assumed, in the revenue yield of a third, neutral tax such as a general sales or ad valorem tax. In practice, it is likely that for most purposes a comparison of an equal rate (or amount) change is quite relevant; that is, most policymakers would at least initially tend to regard a 10 per cent ad valorem tax as a substitute for a 10 per cent increase in the output’s price. Consequently, the remainder of the general equilibrium analysis will concern itself with equal rate (or amount) changes.

Throughout the remainder of the analysis it is useful to use the following slightly different definitions of government and public sector revenues. Using numerical superscripts to indicate the system under consideration and subscripts g and p to indicate government and public sector revenues, respectively, the change in government revenues for systems 1 and 2 is defined as


Thus, it is assumed that the government receives only the proceeds of the tax after adjusting for any tax-induced changes in output levels. In systems 3 and 4, it is assumed that the government takes all the profits of the nonfinancial public enterprise, and the change in government revenues is defined as


Public sector revenues consist of both the tax proceeds and the enterprise’s profits and are defined as




By substituting into these equations the solutions contained in Table 4, in the Appendix, expressions for the changes in government and public sector revenues can be obtained.

For purposes of this paper it is relevant to contrast system 1 with system 3 and system 2 with system 4. This will contrast a tax with an equal price increase under conditions of mobile capital and exogenously fixed capital in the public sector industry. Focus first on the case of mobile capital. Assuming that demand is inelastic, the enterprise’s output price would rise by the same amount (dPx = A = Tx) for either an autonomous price change or a tax increase. There would be no change in either factor prices (dPK = dPL = 0) or factor allocation (dKx = dLx = 0). This does not imply that absolute factor prices do not change, since all variables are expressed relative to the price of good Y. Instead, it suggests that the relative command of capitalists and laborers over resources is unchanged. All share in the increased income from X sales and increased costs of purchases of X in accordance with their initial shares in income or consumption. Since the solutions are the same for the two systems, if demand is inelastic, equal price and tax increases would be equivalent alternatives with respect to all real variables of the system. Furthermore, they would also be equivalent with respect to both public sector and government revenues.

If it is assumed that demand is elastic, the solutions for all dependent variables in system 3 will be a constant proportion greater than those in system 1. Consequently, a pricing measure would have a proportionally greater impact on all the dependent variables than would the imposition of an equal tax. Thus, the impacts of the two actions on the real dependent variables differ only in a fixed proportion, and if the price increase is set as an appropriate proportion of the alternative tax increase, either action will have the same impact on the real dependent variables.

However, the two actions would differ in their revenue impact. Indeed, whereas in system 1 the tax increase will almost certainly result in an increase in government revenues for reasonable ranges of demand elasticities, in system 3 government revenues will fall as a result of the decline in demand and the flight in capital out of the X industry. Similar conclusions hold with regard to public sector revenues. The presumptive signs for the revenue impacts, as well as the per unit return to public enterprise capital, of taxation and of pricing measures are given in Table 1. 30

When the solutions to systems 2 and 4, in which capital is immobile, are considered, much the same conclusions are reached, with two important exceptions. That is, equal tax or price changes would result in proportional differences between all dependent variables of the system, with the exception of the return to capital in public sector enterprises. Conversely, equal changes in all dependent variables except the return to public sector capital could be achieved by a price increase that is smaller than the similar tax increase. However, as a result of a tax increase in system 2, the return to capital in the public sector enterprises declines, whereas as a result of a price increase in system 4, the return rises. The differing signs attached to the returns to public sector capital in systems 2 and 4 result mainly from the impact on net receipts of producers in the two systems that are available for distribution to factors of production. In the case of system 2, the change in net receipts per unit of output to public sector producers is dPx - Tx, which is unambiguously negative. In the case of system 4, all the additional proceeds accrue to the producer; this amounts to dPx per unit of output, which is unambiguously positive.

Table 1.

Presumptive Signs of Changes in Government and Public Sector Revenues and Return to Capital in Public Enterprises

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notationRg = government revenuesRp = public sector revenuesPKx = return to capital invested in public enterprisesfk = initial share of capital in the production of the output of public enterprisesgk = initial share of capital in the production of the output of private enterprises

See text for explanation of systems 1 through 4.

With both the tax and price increase, the return to private capital rises, the wages of labor fall, the demand for public sector output falls, and the amount of labor employed in its production falls. The price of the public sector output rises relative to private sector output in both cases, but it rises by relatively less in the case of a tax than for an equal (amount or rate) price increase. In both systems (since capital in public sector enterprises is fixed), if demand is elastic, public sector output can be reduced only by reducing the labor input. Consequently, with the increase in demand in the private sector the capital to labor ratio falls, but the ratio rises in the public sector. However, the return to labor is largely influenced by what the private sector is prepared to pay to accept workers leaving the public sector. Since the marginal input to the private sector is more labor intensive than the previous factor mix, the return to labor must fall. The return to the fixed private sector capital rises as demand is diverted into private sector goods from public sector goods.

In the extreme case in which demand is completely inelastic, the following nonzero solutions obtain:

dPx=Tx in system 2, anddPx=A anddPKx=AfK in system 4

All other variables have zero solutions.

With inelastic demand in system 2, all factors share the tax in proportion to their initial contribution to national income, and factor shares remain unchanged. 31 In system 4, all the proceeds of the increased output price accrue to the profits of the public enterprise. Since demand is not elastic, there are no changes in output levels or in factor allocation and consequently no change in the returns to factors that are determined in the marketplace (i.e., dPKy and dPL). All the additional proceeds accrue residually to public sector capital.

Numerical Example

Data are not available to quantify these relationships for any particular country. However, it is possible to review the sensitivity of the results to various conditions by assuming certain reasonable values for some relevant parameters and substituting them into the solutions for government and public sector revenues. Table 2 has been compiled to show the sensitivity of these revenues to variations in the elasticity of demand, the extent of public ownership, and the relative capital intensity of the outputs of public and private enterprises.

Table 2.

Government and Public Sector Revenues1

(As ratio of value of nonfinancial public enterprises’ output)

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notationE = elasticity of demand for X with respect to the price of X in terms of YKy/Kx = ratio of capital in private sector to capital in public sectorLx/Ly = ratio of public sector wage bill to private sector wage bill (residually determined)fK = initial share of capital in production of XgK = initial share of capital in production of YSx,Sy = elasticities of factor substitution in the X and Y industriesTx = rate (amount) of tax on XA = rate (amount) of price increase for good XdRg = change in government revenuesdRp = change in public sector revenues

See text for explanation of systems 1 through 4.

No effort is made in Table 2 to insert observed or estimated parametric values, since the values may vary greatly between countries and between industries and since the table is mainly for illustrative purposes. Columns A through H in the table give the value of government and public sector revenues as a ratio of the value of public enterprises’ output under the assumed parametric values also indicated in the same columns. All columns essentially indicate the effective rate of taxation resulting from an assumed tax or relative price increase of 10 per cent (i.e., Tx = A = 0.1). 32 The elasticity of demand is alternatively assumed to be 0.5 or 1.0. Differences in the size of the public sector relative to the private sector are indicated by the ratio of private to public sector capital, which is assumed to be either 2.0 or 0.5. In four cases, the output of nonfinancial public enterprises is assumed to be more capital intensive than output of private enterprises (fK = 0.2; gK = 0.1), and the assumption is reversed in the other four cases. 33 Cobb-Douglas production functions, in which the elasticities of substitution are unity, are assumed in all cases. 34

The highest effective yield is for dRg4=dRp4=12.3 per cent. From the viewpoint of revenues, a pricing measure would produce the highest yield under the assumptions characterized in column F. With the private sector good relatively capital intensive, demand relatively elastic, capital fixed, and the private sector relatively larger, the reduction in demand in response to the price increase would be more than fully absorbed by the shift of labor to the private sector and the fall in labor’s wages. The residual return to capital consequently increases. In contrast, the lowest effective yield, which is negative, also results from a pricing measure when dRg3=dRp3=2 per cent. In this case, demand is elastic and capital is fixed, but the public sector good is relatively capital intensive. The highest yield from a tax is about 9.6 per cent and occurs when capital is immobile and demand is least elastic (dRg2 for columns A, C, E, and G). The lowest effective tax yield is only 9.0 per cent (dRg1), when demand is elastic and capital is mobile. However, if public sector revenues are considered, the highest tax yield will be lower and the lowest tax yield will be higher than is the case with government revenue.

These results suggest that the greatest revenues for the public sector result from pricing measures when capital is not mobile, but the lowest revenues result when capital is mobile. Thus, if one is concerned with the financing requirements of the public sector, the degree of capital mobility and responsiveness to the rate of return in nonfinancial public enterprises may be crucial to the expected revenue from pricing measures. The capital mobility assumption is also important to the expected government revenues from a tax increase, but it is much less important if public sector revenues are considered.

Rg3 andRp3 show the greatest sensitivity to differences in elasticity. Revenues are negatively affected by increases in elasticity in all cases except for pricing measures when capital is fixed. If capital is mobile, revenues from pricing measures are more sensitive to elasticity increases. If capital is fixed, government revenues are more sensitive to elasticity if they are raised by taxes than by prices, but for public sector revenues there is little difference between the sensitivity to elasticity of revenues from taxation or pricing actions.

In general, the results indicate that revenues are not very sensitive to differences in the relative sizes of the public and private sectors. Only Rg4 andRp4 vary by more than a percentage point with differences in the relative size, and in this case they fall by only 1.7 per cent. The same two revenue categories show the greatest sensitivity to differences in the relative capital intensity of private and public sector goods. The variation in this case is only 2.1 percentage points. Overall, revenues raised by taxation measures would appear to be less sensitive to these two factors than would revenues from pricing actions.

V. Concluding Remarks

The preceding analyses indicate that, when the mobilization of domestic resources is taken into account, as well as the allocation of resources, equivalence between an excise or product tax and an increase in the price of a public enterprise’s output may not obtain under a variety of realistic circumstances. In particular, a tax appears to be more reliable and predictable than a price increase for the purpose of raising budgetary revenues for the government, and a tax is likely to raise equal revenues with less distortion. Nevertheless, equal price increases may, in some circumstances, generate more resources for the public sector as a whole. Consequently, the objectives of public policy should be clearly defined and taken into account when determining whether a tax increase or a public enterprise price increase would be the preferred instrument to achieve a policy objective.


E = income-compensated elasticity of demand for X with respect to price of X in terms of Y (E > 0)

Sx, Sy = elasticities of factor substitution in X and Y industries (Sx > 0; Sy > 0)

fL,fK, gL, gK = initial shares of labor and capital, respectively, in production of X and Y, respectively (fL > 0, fK > 0, gL > 0, gK > 0)

Kx, Ky = capital employed in X and Y industries, respectively

Lx, Ly = labor employed in X and Y industries, respectively

Px, Py = prices of goods X and Y, respectively

PL, PK = returns to labor and capital, respectively


Table 3.

General Equilibrium Systems1

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In the table, equations are referred to by the number of the column and the row in which they appear. For example, equation 1.2 refers to the equation that appears in the second row of the first column.

The notation used is defined on p. 372.

Table 4.

Solutions to General Equilibrium Systems1

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notationE, Sx, and Sy 0Z=SxKxfL+SyKygL+XE(gLfL)(gLfL)W=Sy(EfK+fLSx)+ESxgKLxLy

For the case of E = 0, dPKy = 0 and dPKx = AfK


Mr. Floyd, Senior Economist in the Tax Policy Division of the Fiscal Affairs Department, received his doctorate from Rice University.


The analysis throughout this paper is confined to nonfinancial public enterprises. Consequently, it should not necessarily be construed as applying to either private or public financial enterprises.


Richard A. Musgrave and Peggy B. Musgrave, Public Finance in Theory and Practice (New York, 1973), pp. 678-79.


A. M. Henderson, “Prices and Profits in State Enterprise,” Review of Economic Studies, Vol. 16 (1948-49), p. 18.


Robert H. Floyd, “Income Taxation of State Trading Enterprises,” in State Trading in Industrialized and Developing Countries, ed. by M. M. Kostecki. (It is scheduled to be published by Macmillan Press Limited in 1981.)


Peter J. Lloyd, “State Trading and the Theory of International Trade,” in State Trading in Industrialized and Developing Countries, ed. by M. M. Kostecki. (It is scheduled to be published by Macmillan Press Limited in 1981.)


Many of the conclusions relating to tax and price increases and their revenue effects are essentially the opposite to conclusions that would obtain with respect to tax and price decreases, or alternatively subsidy increases, and their effects on revenues or expenditures.


An alternative means of transferring the profits to the government would be through income taxation. For an analysis of an income tax on public enterprises and its equivalence to a dividend, see Robert H. Floyd, “Some Aspects of Income Taxation of Public Enterprises,” Staff Papers, Vol. 25 (June 1978), pp. 310-42.


For additional discussions of the concept of equivalence, see Lloyd, “State Trading and the Theory of International Trade” (cited in footnote 5); and Jagdish Bhagwati, “On the Equivalence of Tariffs and Quotas,” in Trade, Growth, and Balance of Payments: Essays in Honor of Gottfried Haberler, by Robert E. Baldwin and others (Chicago, 1965), pp. 53-67.


For a complete discussion on incidence concepts, see Richard A. Musgrave, The Theory of Public Finance: A Study in Public Economy (New York, 1959), pp. 211-17.


Border tax adjustments consist of a tax or surcharge levied on imports in compensation for and equal to or less than taxes levied on similar products produced and consumed domestically. Similarly, taxes levied on exported goods are rebated or simply never charged. When border tax adjustments are applied to compensate for a domestic tax, products carry the tax burden of their country of destination, and the tax is said to be levied under the destination principle. Since all consumption of the good is taxed regardless of its place of production, the tax is essentially a tax on consumption. If border tax adjustments are not applied, products carry the tax burden of their country of origin, and the tax is said to be levied under the origin principle. In this case the tax is essentially a tax on production.


From the analysis of certain taxes and the use of tax equivalence theorems, the effects of other taxes on the dependent variables can be ascertained. For a detailed statement of the tax equivalence propositions for a closed economy, see Musgrave, The Theory of Public Finance (cited in footnote 9).


Throughout this paper it is assumed that the internal operations of nonfinancial public enterprises are X-efficient. Thus, it would not be possible to increase profits through reductions of inefficient managerial practices, such as employment of excess labor or payment of wages in excess of levels prevailing in the private sector. While such practices are thought to be common, especially in nonfinancial public enterprises in many developing countries, there would seem to be little reason to expect that the choice between a tax and a price increase would alter these practices.


The equivalence with regard to revenue depends on the method of determining the dividend. This consideration is discussed in more detail in the following analyses.


In this case, the tax on imports might represent a border tax adjustment for a domestic tax rather than a separate tariff.


See Warner Max Corden, Trade Policy and Economic Welfare (Oxford, 1974), pp. 9-12, for a fuller discussion of the possible social gains from subsidization and implicit assumptions of the analysis.


For a discussion of the revenue of fiscal monopolies, see Sijbren Cnossen, Excise Systems; A Global Study of the Selective Taxation of Goods and Services (Johns Hopkins University Press, 1977).


For an essential economic explanation, see Murray Brown and Nagesh Revankar, “A Generalized Theory of the Firm: An Integration of the Sales and Profit Maximization Hypotheses,” Kyklos, Vol. 24 (No. 3, 1971), pp. 427-43.


No diagram is provided for this case. A relevant diagram would be similar to Chart 2 except that the output levels would initially exceed the levels consistent with maximum profits.


Although it is not presented specifically in the text, the same analytical technique could be applied to a monopoly nonfinancial public enterprise that sells in the domestic market at a price below the world market level, thus subsidizing domestic consumption. Any effort to reduce the subsidy by means of a price increase or the imposition of a tax would yield the same results.


The following discussion is derived from the standard Harberger model by including public ownership of some capital and public production of one good. The basic model on which this discussion is founded can be found in Arnold C. Harberger, “The Incidence of the Corporation Income Tax,” Journal of Political Economy, Vol. 70 (June 1962), pp. 215-40. The uses to which the model and its subsequent variations have been put may be found in Charles E. McLure, Jr., “General Equilibrium Incidence Analysis: The Harberger model after ten years,” Journal of Public Economics, Vol. 4 (February 1975), pp. 125-61. Since factors of production are both mobile and fixed in supply, the context of the Harberger model is neither strictly short run nor long run, but rather somewhere in between. Thus, while it can demonstrate the effects of taxes on factor allocation, the model can be used only to infer their long-run effects on such variables as the growth rates of capital and labor.


The modifications required to incorporate international trade into the basic Harberger model are complicated and are not likely to alter quantitatively the conclusions concerning the differential effects of pricing and taxation measures on the domestic object variables of either the partial or general equilibrium analyses. Furthermore, the more important effects on international trade are most likely to occur as a result of measures related to particular state trading enterprises with monopolies over certain imports or exports. Consequently, since it seems that little would be gained, no extension of the general equilibrium model to include international trade is attempted. For one of the few extensions of the Harberger model to an international context, see Robert H. Floyd, “Some Long-Run Implications of Border Tax Adjustments for Factor Taxes,” Quarterly Journal of Economics, Vol. 91 (November 1977), pp. 555-78.


The adaptation employed for these formulations was originally developed for other purposes by Charles E. McLure, Jr., “The Theory of Tax Incidence with Imperfect Factor Mobility,” Finanzarchiv, Vol. 30 (No. 1, 1971), pp. 27-48. The McLure formulation can be reinterpreted and adapted without modification to the purposes of this paper.


While this is admittedly a substantial simplification, it in no way distorts the results of the analysis. Since the primary objective is to contrast a tax with a pricing measure, any constant spending pattern may be assumed, and the analytically simplest pattern is one with equal marginal rates.


As a result of the assumptions about factor mobility and full employment, only one supply equation is needed in each nation. The use of only one supply and demand equation means that the model is confined to infinitesimally small movements along a price line tangent to the transformation curve.


Harberger assumed that units of goods and factors were defined so that all prices were initially at unity. In addition to simplifying the algebraic computations, this convention has the effects that any change in price (dP) is also a fractional change in that price and that the tax term can represent both unit and ad valorem taxes.


With full employment, a movement along the transformation curve would imply PxX + PyY = k, where k is a constant. Since Px = Py = 1 initially by assumption, as a first approximation base we have dX = -dY. However, when distortions are present in factor markets, the equality may not hold because of possible losses in real income. See Harry G. Johnson, “Factor Market Distortions and the Shape of the Transformation Curve,” Econometrica, Vol. 34 (July 1966), pp. 686-98.


The assumptions of competition and linear homogeneous production functions ensure that factor payments and tax bills exhaust total receipts in each industry and may be used to derive the text’s formulation of Euler’s theorem. A similar formulation for the Y industry yields dPy = dPLgL + dPKgK + Ty, where gK and gL represent the initial factor shares in the production of good Y.


More precisely, if the superscript t is used to designate revenue changes resulting from a tax, and variables with no superscript indicate variables related to a price change, we have in the short run dPKxtKx+dTxX=dPKxKx ordTx=(dPKxdPKxt)fK. Thus, it is implicitly assumed in the text that dPxtK = 0.


The first definition most closely corresponds to the definition employed on p. 363.


In some cases, the signs represent the changes in revenues that would occur under assumed, but reasonable, parametric values.


The zero solutions for the factor prices also reflect the assumption of no change in the price of the numeraire good. That is, their relative purchasing power over good Y does not change, even though it would have declined if it had been defined in terms of good X.


Since the definitions of government and public sector revenues in systems 1 and 2 are nonlinear, changes in nominal and effective rates would not be proportional. Doubling the nominal rate therefore would not exactly double the effective rate.


The values of the ratio Lx/Ly can be derived from the assumed values of Ky/Kx,fK, and gK. Furthermore, it can be shown that if fK = 0.2 and gK = 0.1, then Ky/Kx = 2 implies X/Y = 0.25, or the value of nonfinancial public enterprise output is only a fourth of that of private enterprises or 20 per cent of GNP. If Ky/Kx = 0.5, then X/Y = 1.


The effects of differences in the elasticity of demand can be seen from comparisons of columns A with B, C with D, E with F, and G with H. The importance of the relative size of the public sector can be seen from comparisons of A with C, B with D, E with G, and F with H, and the importance of the relative capital intensity of public and private sector outputs from comparisons of A with E, B with F, C with G, and D with H.

IMF Staff papers: Volume 28 No. 2
Author: International Monetary Fund. Research Dept.