I. Fundamental Structure of Applied General-Equilibrium Models

General-equilibrium models have four essential ingredients. There must be a specification of (1) the endowments of consumers, (2) their preferences, (3) the production technology, and (4) the conditions of equilibrium.

In general, consumers may possess endowments of any or all of the commodities in the economy. Often, in practice, consumers are endowed only with factors of production (capital and labor). The preferences of consumers are specified with the demand function for each commodity. Commodity demands are nonnegative and depend on all prices in a continuous manner. They are homogeneous at degree zero in prices, meaning that only relative prices matter. Market demands are the sum of individual household demands, and they satisfy Walras’s law. If some notation is introduced, the consumer side of the model can be specified. Let N be the number of commodities (including factors), W_i be the total endowments of commodity i, and D_i ($\overrightarrow{P}$), i = 1,…, N be the market demand functions. With this notation, Walras’s law now states

The value of market demands must equal the value of market endowments at all prices. This condition automatically holds if market demands are simply the sum of individual demands when the individuals are subject to their budget constraints.

On the production side of a general-equilibrium model, technology is usually described by a set of constant-returns-to-scale activities or by production functions that exhibit nonincreasing returns to scale. The advantage of the activity-analysis approach is that the conditions for equilibrium are very simple when production is modeled in this way. On the other hand, production functions are more convenient to use in applied work. They are easily given parameters, since most of the relevant econometric literature involves their estimation.

With the activity-analysis approach, the J activities available to the economy can be listed in an (N × J) matrix A, where the aij elements are negative for inputs and positive for outputs. The first N columns

of this matrix are disposal activities. Joint products are possible; however, activities are restricted to satisfy the condition of boundedness that A$\overrightarrow{X}$+$\overrightarrow{W}$ is bounded from above at any nonnegative set of J activity levels $\overrightarrow{X}$ The interpretation of this condition is that the production possibility is finite in all dimensions.²

In the activity-analysis modeling of production, equilibrium is characterized by a nonnegative vector of N prices and J activity levels (P^*, X^*) so that

(1) demand equals supplies for all commodities

and

(2) activities in use break even, with those not used having negative economic profits.

A simplified numerical example may illustrate the general-equilibrium structure. For expositional purposes, consider a model with two final goods (manufacturing and nonmanufacturing), two factors of production (capital and labor), and two classes of consumer. Consumers have initial endowments of factors but no initial endowments of goods. The “rich” consumer group owns capital, while the “poor” group owns labor. Production of each good takes place according to a constant elasticity of substitution (CES) production function, and each consumer class has demands that are derived from maximizing a CES utility function subject to its budget constraint.

The production functions are given by

where Q_i denotes output of the ith industry, Φ_i is the scale or units parameter, δ_i is the distribution parameter, K_i and L_i are the factor inputs, and σ_i is the elasticity of factor substitution.

The CES utility functions are given by

where $X_i^q$ is the quantity of good i demanded by the qth consumer, af are share parameters, and ${\alpha }_i^q$ is the substitution elasticity in consumer class q’s CES utility function.

If consumers maximize these utility functions subject to the constraint that expenditures not exceed income derived from the sale of endowments, the resulting demand functions are

where I^q is individual q’s income level.

With this structure, a “toy” model can be specified, with the following values of the parameters.

		Production
		ϕ	δ		σ
Manufacturing (1)		1.5	0.6		2.0
Nonmanufacturing (2)		2.0	0.7		0.5
	Consumption
	Endowments		Preference parameters
	K	L	α1	α2	σ
Rich households	25	0	0.5	0.5	1.5
Poor households	0	60	0.3	0.7	0.75

View Table

		Production
		ϕ	δ		σ
Manufacturing (1)		1.5	0.6		2.0
Nonmanufacturing (2)		2.0	0.7		0.5
	Consumption
	Endowments		Preference parameters
	K	L	α1	α2	σ
Rich households	25	0	0.5	0.5	1.5
Poor households	0	60	0.3	0.7	0.75

This model has been solved using Merrill’s (1971) algorithm, which is an advanced variant of Scarf’s method. The results are shown in Table 1. At the prices computed, total demand for each output exactly matches the amount produced. It follows that producer revenues equal consumer expenditures. It also is true, to a high degree of approximation, that the labor and capital endowments are fully employed and that consumer factor incomes equal producer factor costs. The cost per unit of output in each sector matches the price, which means that economic profits are zero. The expenditure of each household exhausts its income. Thus, the solution closely approximates all the properties of an equilibrium for this economy. The closeness of the approximation can be enhanced by increasing the amount of computation time allowed for the algorithm used in the solution.

Table 1.

Equilibrium Solution: General Equilibrium for Illustrative Simple Model

Table 1.

Equilibrium Solution: General Equilibrium for Illustrative Simple Model

Equilibrium prices
	Manufacturing output			1.399
	Nonmanufacturing output			1.093
	Capital			1.373
	Labor			1.000
			Production
			Quantity	Revenue	Capital	Capital Cost
Manufacturing			24.992	34.898	6.212	8.532
Nonmanufacturing			54.378	59.439	18.788	25.805
		Total		94.337	25.000	34.337
			Labor	Labor Cost	Total Cost	Cost Per Unit of Output
Manufacturing			26.366	26.366	34.898	1.399
Nonmanufacturing			33.634	33.634	59.439	1.093
		Total	60.000	60.000	94.337
			Demand
			Manufacturing	Nonmanufacturing		Expenditure
Rich households			11.514	16.674		34.337
Poor households			13.428	37.704		60.000
		Total	24.942	54.378		94.337
			Labor Income	Capital Income		Total Income
Rich households			0	34.337		34.337
Poor households			60	0		60.000
		Total	60	34.337		94.337

View Table

Table 1.

Equilibrium Solution: General Equilibrium for Illustrative Simple Model

Equilibrium prices
	Manufacturing output			1.399
	Nonmanufacturing output			1.093
	Capital			1.373
	Labor			1.000
			Production
			Quantity	Revenue	Capital	Capital Cost
Manufacturing			24.992	34.898	6.212	8.532
Nonmanufacturing			54.378	59.439	18.788	25.805
		Total		94.337	25.000	34.337
			Labor	Labor Cost	Total Cost	Cost Per Unit of Output
Manufacturing			26.366	26.366	34.898	1.399
Nonmanufacturing			33.634	33.634	59.439	1.093
		Total	60.000	60.000	94.337
			Demand
			Manufacturing	Nonmanufacturing		Expenditure
Rich households			11.514	16.674		34.337
Poor households			13.428	37.704		60.000
		Total	24.942	54.378		94.337
			Labor Income	Capital Income		Total Income
Rich households			0	34.337		34.337
Poor households			60	0		60.000
		Total	60	34.337		94.337

This illustrative example shows the kind of models that can be solved with the relatively new computer-based algorithms. However, it does not indicate how data are collected and incorporated and how taxes and other policy variables are introduced. Also, it is necessary to develop techniques of welfare economics to compare the equilibria that result from alternative policies.

II. Specification of Policy Models

Data Requirements and Parameter Specification

In applying general-equilibrium models, a complete equilibrium data set must be assembled. This includes factor usage by industry, an input/output table, consumer expenditures by commodity and incomes by source, government expenditures and tax collections, and information on foreign trade and investment. The normal practice is to gather this data from available sources for a particular year. In general, such data are inconsistent. For example, total labor payments by employers do not match total labor income. To be useful, the data must be adjusted for consistency. This adjustment requires some judgment as to which data are most reliable and which should be changed so as to be consistent.

The consistent data represents what is often referred to as the “benchmark” equilibrium. The strong assumption is made that the data represent an equilibrium of the economy. The construction of data sets of this type is described in St. Hilaire and Whalley (1980), Piggott and Whalley (1983), and Ballard, Fullerton, Shoven, and Whalley (1983). Since the benchmark data are usually presented in value terms, units must be chosen for goods and factors to obtain separate price and quantity observations. A commonly used type of unit conversion, originally adopted by Harberger, is to choose units for both goods and factors that have a price of unity in the benchmark equilibrium.

With the benchmark observation at hand, parameters are then chosen so that the solution to the model explicitly replicates the benchmark data. This procedure is termed model calibration. Values of the parameters thus generated can then be used to solve for a different equilibrium under alternative policy regimes. This is usually termed a counterfactual or policy replacement equilibrium.

The typical calibration procedure involves only one year’s data or one single observation, which may be an average over a number of years. Depending on the complexity of functional forms used, the data may not uniquely identify the parameters. With Cobb-Douglas functions, a single benchmark observation serves to uniquely identify the values of the parameters, since expenditure and factor shares by sector are known. With other functions, it is typically true that an infinite number of combinations of parameters can replicate the data in the required manner. In such cases, extraneously specified elasticities usually serve as identifying restrictions. Once specified, these allow the other parameters to be determined uniquely from the equilibrium observation.

The extraneous specification of elasticities can be thought of as determining the curvature and position of isoquants and indifferent surfaces. If Cobb-Douglas preference functions are chosen, a single observation of a point and slope at that point of an indifference curve is sufficient to uniquely determine the parameters of the function. If CES functions are used, extraneous values of substitution elasticities are required, since the curvature of indifference curves, described by the single elasticity parameter, is not given by benchmark data. For demand functions of a linear expenditure system, income elasticities are determined, once the origin coordinates for utility measurement are known. The current procedure in setting the additional parameters is to scan empirical literature to select appropriate values of substitution elasticities for the underlying utility and production functions. The primary role of calibration is thus to determine the shares and unit parameters in these functions, once elasticities are known. No statistical test of the chosen model specification is involved, since a deterministic procedure is employed for calculating the values of the parameters from the equilibrium observation. This entire procedure is clearly dependent on both the accuracy of the assembled data and the assumption that it represents an equilibrium. Also, the key role played by elasticities used in these models becomes immediately apparent.

Once the calibration procedure is completed, a full model is available and can be used for policy analysis. As indicated in Figure 1, any policy change can be specified, and a counterfactual equilibrium for a new policy regime can be computed. Policy appraisal then proceeds on the basis of paired comparisons of counterfactual and benchmark equilibria. If further policy changes are to be evaluated, the specification of policy changes is repeated.

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Flow Chart for Typical Applied General-Equilibrium Model

Citation: IMF Staff Papers 1983, 002; 10.5089/9781451946895.024.A005

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There are a number of reasons why this calibration approach, rather than a more direct econometric approach, is so widely used in setting the parameters for applied models. First, in some of the models, many thousands of parameters are involved; to estimate all these parameters of the model simultaneously by using time-series methods would require an unrealistically large number of observations. Second, the way in which benchmark data sets are used to generate the values of the parameters under calibration involves taking an observation in value terms and then decomposing it into separate price and quantity observations. Benchmark equilibrium prices, by construction, represent unity in each benchmark equilibrium, making it difficult to sequence equilibrium observations with consistent units through time, as would be required for time-series estimation. These problems, combined with the difficulty of incorporating equilibrium restrictions into a satisfactory estimation procedure, have thus far largely excluded complete econometric estimation of general-equilibrium systems, although some progress in this direction has been made in recent work by Mansur (1981). Mansur, for instance, notes the difficulties in simply writing down a likelihood function for a maximum-likelihood procedure incorporating full-equilibrium restrictions. He suggests a partitioning approach, using segmented production and demand systems, with a third segment incorporating their equilibrium interdependence. Other attempts at econometric estimation of complete-equilibrium systems occur in the work of Allingham (1973) and Jorgenson (1983).

III. Applications

In this section, let us review some of the applications that have been completed using the U.S. model. It should be stated at the outset that a large number of other models have been used for policy evaluation in other countries. These include Whalley’s (1975) evaluation of the major U.K. tax reform package of 1973, Miller and Spencer’s (1977) assessment of the United Kingdom’s entry into the European Economic Community, Piggott’s (1979) evaluation of Australian tax policy, Feltenstein’s (1980) analysis of trade restrictions in Argentina, Whalley’s (1982 b) examination of the effects of the Tokyo Round trade agreement, and Serra-Puché’s (1983) policy model for Mexico. Similar models are being used for energy economics (Hudson and Jorgenson (1978) and Borges and Goulder (1983)), development policy (Derviş, de Melo, and Robinson (1981)), and even economic history (James (1981)).

The U.S. model consists of 19 production sectors, 16 consumer goods, and 12 consumer groups. It is a dynamic model incorporating the complete tax system (federal, state, and local personal income taxes, corporate taxes, sales and excise taxes, social security taxes, etc.). The benchmark data set represents the 1973 economy. The model’s development was financed by the U.S. Treasury Department; it is currently in use there, most recently in evaluating flat-tax proposals.

The policy that has received the most attention in the United States from general-equilibrium modelers is the integration of the U.S. corporate and personal income tax, probably because Harberger originally examined the incidence and efficiency consequences of the corporate income tax with his two-sector model. Corporate equity capital is taxed twice in the United States in that the earnings of firms are subject to the 46 percent corporate income tax. Aftertax earnings are either distributed as dividends and taxed at the personal level or retained. If retained, the earnings may lead to partially taxable capital gains. Capital income from other sectors, particularly real estate and to some extent agriculture, is lightly taxed. The result is an inefficient allocation of capital across sectors and, quite possibly, a distortion of the consumption/saving decision.

Another policy that has been evaluated with the U.S. general-equilibrium model is the possibility of taxing consumption rather than income at the personal level. This result could be accomplished by first establishing the household’s income and then allowing a deduction for all saving. As the tax would be direct, special exemptions could be granted the blind, the elderly, those with large families, etc., and the tax could have increasing marginal rates. The advocates of a consumption tax argue that it does not distort the consumption/saving decision, as does an income tax, and that it is better to base taxes on a household’s withdrawals from the social product (consumption) than on a rough approximation of their contribution to it (income).

Before evaluating the consumption tax, it is important to recognize that the United States already has a partial consumption tax, since roughly half of saving is not subject to tax: 30 percent through retirement plans and life insurance, where the tax is deferred until withdrawal (as with a consumption tax), and 20 percent in the form of new housing construction. Housing must be purchased with aftertax dollars (i.e., the saving/investment is not deductible), but the return on it, imputed or otherwise, is very lightly taxed. Thus, it is not taxed twice, as with an income tax; its treatment is more nearly analogous to a consumption tax.

Table 2 presents the dynamic efficiency gains for a consumption tax and corporate tax integration. The figures are in 1973 dollars. The key parameters of the model are set at 0.4 for the saving elasticity and 0.15 for the labor supply elasticity. The elasticity for factor substitution in value added varies by industry, but it is generally slightly less than unity. The gain in efficiency depends on how the lost revenue is compensated for. For example, if a consumption tax is instituted by making 80 percent of saving deductible (over and above the 20 percent currently saved through new housing acquisition), row (1) of Table 2 shows the gain to be $686 billion if the revenue shortfall was made up with lump-sum tax increases. However, if marginal tax rates are increased in a multiplicate manner (everyone’s ratio is multiplied by a common X > 1.0), the gain is $621 billion, while if they increased in an additive manner (t’ = t + X), the welfare measure increases by $636 billion. These numbers are about 1.25 percent of the present value of future national income, expanded to include the value of leisure. The discount rate used is each consumer’s aftertax rate of return to capital before the tax change, which averaged a real rate of return of 4 percent.

Table 2.

United States: Dynamic Welfare Effects in Present Value of Compensating Variations over Time

(In billions of 1973 dollars) ¹

¹The numbers in parentheses represent the gain as a percentage of the present discounted value of consumption plus leisure in the base sequence. This number is $49,863 trillion for all comparisons and accounts for only the initial population.

Table 2.

United States: Dynamic Welfare Effects in Present Value of Compensating Variations over Time

(In billions of 1973 dollars) ¹

		Types of Scaling to Preserve Tax Yield
Tax Replacement		Lump sum	Multiplicative	Additive
(1)	Consumption tax	686.167	620.652	636.002
	(80 percent savings deduction)	(1.376)	(1.245)	(1.275)
(2)	Corporate tax integration	731.550	338.858	448.541
	with indexation of capital gains	(1.467)	(0.680)	(0.889)
(3)	Consumption tax with	1,429.503	999.813	1,135.083
	integration	(2.867)	(2.005)	(2.276)
(4)	Pure consumption tax	1,500.881	1,344.423	1,388.410
	with integration	(3.010)	(2.696)	(2.784)
(5)	Partial consumption tax	328.268	289.999	298.180
	(55 percent savings deduction)	(0.658)	(0.582)	(0.598)
(6)	Full savings deduction	991.704	962.633	964.370
	with housing preference	(1.989)	(1.931)	(1.934)
(7)	Pure income tax without	–579.177	–471.653	–496.861
	integration	(–1.162)	(–0.946)	(–0.996)
(8)	Pure income tax with	128.298	–22.596	21.422
	integration	(0.257)	(–0.045)	(0.043)

¹The numbers in parentheses represent the gain as a percentage of the present discounted value of consumption plus leisure in the base sequence. This number is $49,863 trillion for all comparisons and accounts for only the initial population.

View Table

Table 2.

United States: Dynamic Welfare Effects in Present Value of Compensating Variations over Time

(In billions of 1973 dollars) ¹

		Types of Scaling to Preserve Tax Yield
Tax Replacement		Lump sum	Multiplicative	Additive
(1)	Consumption tax	686.167	620.652	636.002
	(80 percent savings deduction)	(1.376)	(1.245)	(1.275)
(2)	Corporate tax integration	731.550	338.858	448.541
	with indexation of capital gains	(1.467)	(0.680)	(0.889)
(3)	Consumption tax with	1,429.503	999.813	1,135.083
	integration	(2.867)	(2.005)	(2.276)
(4)	Pure consumption tax	1,500.881	1,344.423	1,388.410
	with integration	(3.010)	(2.696)	(2.784)
(5)	Partial consumption tax	328.268	289.999	298.180
	(55 percent savings deduction)	(0.658)	(0.582)	(0.598)
(6)	Full savings deduction	991.704	962.633	964.370
	with housing preference	(1.989)	(1.931)	(1.934)
(7)	Pure income tax without	–579.177	–471.653	–496.861
	integration	(–1.162)	(–0.946)	(–0.996)
(8)	Pure income tax with	128.298	–22.596	21.422
	integration	(0.257)	(–0.045)	(0.043)

¹The numbers in parentheses represent the gain as a percentage of the present discounted value of consumption plus leisure in the base sequence. This number is $49,863 trillion for all comparisons and accounts for only the initial population.

Row (2) of Table 2 shows the welfare gains of integrating the two income tax systems. The results are more sensitive to the replacement tax used for maintaining government revenues, both because integration involves the loss of more tax receipts and because it does not stimulate saving, capital formation, and growth as much as does the consumption tax. Row (3) combines the policies of the first two systems and shows that the efficiency improvement is approximately additive.

Since 80 percent of total savings is deductible under the plans of rows (1) and (3) and 20 percent of total savings flow into tax-favored housing, these plans capture the intertemporal effects of a full consumption tax. However, since any savings can be used for housing, these plans leave an intersectoral distortion in favor of owner occupancy. The plan of row (4) allows full deductibility of savings and eliminates the preference for housing. Gains are larger, as expected. The efficiency gain of the plan in row (4) relative to the current tax system is roughly $1.5 trillion with lump-sum revenue replacement, $1,350 billion with multiplicative marginal rate surcharges, and $1,390 billion with additive marginal rate surcharges. Row (5) examines a partial move toward a consumption tax—halfway between the current 30 percent sheltering of retirement plans and the 80 percent of row (1)—while row (6) exempts all saving from taxation, leaves the housing preference unchanged, and results in a personal income tax subsidy to saving. However, since this subsidy offsets the corporate income tax, which is left in place, total efficiency is enhanced relative to the plan shown in row (1).

The results shown in rows (7) and (8) indicate that the United States could move to a pure income tax and integrate the corporate tax with no loss in efficiency, but that a pure income tax alone would lose efficiency. For row (7), the tax base is increased, since imputed income from housing is included and existing savings deductions are eliminated. Thus, the tax rate can be lowered, rather than raised, to maintain government revenues. Results in row (7) show that moving to a pure income tax alone involves an efficiency loss of $579 billion if marginal tax rates are not lowered—primarily because the intertemporal distortions of the current system are worsened. However, if the marginal rates are reduced, the efficiency loss to the economy is lowered to roughly $470 billion. The improvement in the interindustry allocation of capital (resulting primarily from the taxation of the return to owner-occupied housing) tends to offset the deterioration in the intertemporal efficiency (now reduced by the marginal rate adjustments). Row (8) shows the results from a comprehensive single-level income tax plan involving corporate tax integration as well. Such a tax system lowers revenues and thus necessitates a rate increase to maintain the yield. When the rates are adjusted either multiplicatively or additively, the net efficiency impact of the package is negligible.

The results in Table 2 are sensitive to the elasticities incorporated in the model. For example, the $621 billion from row (1), with a multiplicative scaling of the marginal tax rates, becomes $411 billion if the uncompensated saving elasticity is zero and $1,279 billion if this elasticity is 2.0. A more thorough evaluation of these results appears in Fullerton, Shoven, and Whalley (1983).

Table 3 provides information on how long the economy takes to resettle into a steady-state growth path after a tax change occurs. Once the economy has completely adjusted to the new policy regime, all relative prices will again remain constant. For consumption tax proposals, the new steady state is characterized by a higher capital intensity and a lower relative return to capital. The results of Table 3 indicate that, for the cases with a savings elasticity of 0.4, roughly 40 percent of the adjustment is completed after 10 years and 80 percent after 30 years. The economy then asymptotically approaches the new steady-state growth path. The transition is accomplished much more rapidly with a savings elasticity of 2.0, despite the fact that the total adjustment is larger. Adjustments in capital/labor ratios proceed in patterns similar to the adjustments of the price ratios in Table 3.

Table 3.

United States: Time Path for Ratio of Rental Price of Capital to Wage Rate

¹Refers to the number of the row in Table 2.

Table 3.

United States: Time Path for Ratio of Rental Price of Capital to Wage Rate

Plan Number1	Savings Elasticity	Revenue Replacement	Prechange	Years
				0	10	20	30	40	50
				Factor price ratios
(1)	0.4	Lump sum	1.00	1.00	0.93	0.89	0.86	0.84	0.83
(1)	0.4	Additive	1.00	0.99	0.92	0.88	0.85	0.84	0.83
(3)	0.4	Additive	1.00	1.19	1.04	0.96	0.92	0.89	0.88
(1)	0.0	Additive	1.00	0.99	0.94	0.91	0.89	0.87	0.86
(1)	2.0	Additive	1.00	0.99	0.80	0.79	0.79	0.79	0.79
(7)	0.4	Additive	1.00	0.97	1.00	1.02	1.04	1.06	1.07

¹Refers to the number of the row in Table 2.

View Table

Table 3.

United States: Time Path for Ratio of Rental Price of Capital to Wage Rate

Plan Number1	Savings Elasticity	Revenue Replacement	Prechange	Years
				0	10	20	30	40	50
				View Expanded Factor price ratios View Expanded
(1)	0.4	Lump sum	1.00	1.00	0.93	0.89	0.86	0.84	0.83
(1)	0.4	Additive	1.00	0.99	0.92	0.88	0.85	0.84	0.83
(3)	0.4	Additive	1.00	1.19	1.04	0.96	0.92	0.89	0.88
(1)	0.0	Additive	1.00	0.99	0.94	0.91	0.89	0.87	0.86
(1)	2.0	Additive	1.00	0.99	0.80	0.79	0.79	0.79	0.79
(7)	0.4	Additive	1.00	0.97	1.00	1.02	1.04	1.06	1.07

¹Refers to the number of the row in Table 2.

Interestingly, Ballard and Goulder (1982) find that the adjustment to a new steady state is slightly slower with perfect foresight and the institution of a consumption tax, since consumers are deterred from additional saving by the recognition that future capital deepening will depress the rate of return to capital.

In previous literature, estimates of the length of the long run have varied widely. Sato (1963) finds the adjustment to be extremely long (more than 100 years), while Hall (1968) and Summers (1981) find it to be surprisingly short (about 5 years). It is difficult to reconcile these various findings completely, but it is clear that a prime determinant is the strength of substitution effects in the model used for the analysis.

Ballard, Shoven, and Whalley (1982) made another set of computer runs, asking a question of more theoretical interest: What are the efficiency costs of the entire U.S. tax system? This question is of interest because efficiency issues are often treated as minor ones, relative to those of economic stability. The aim here was also to estimate the marginal cost of a government dollar raised by increasing taxes. In the past, efficiency costs have frequently been quoted as fractions of gross national product or as the deadweight loss relative to the revenue raised. The former measure is ridiculous if the question is whether a tax on automobile tires or restrictions on steel imports are inefficient. The latter measure—the average distortion per dollar raised—does not often give the right answer either (average figures seldom do in economics). What has been computed, therefore, is the marginal distortionary cost per marginal dollar raised for each of the major tax systems in the United States.

The estimate here for the hypothetical experiment of removing the entire tax system and replacing it with a set of lump-sum levies (proportional to income and with sales taxes actually paid so as to minimize income and wealth transfers) is that the present value of welfare would increase by $3.3 trillion, which is roughly 6.7 percent of national income plus leisure, or 10 percent of national income. The primary result of removing all marginal taxes is tremendous capital deepening. The net of tax rental/wage ratio immediately climbs by 113 percent and gradually sinks from there to become 30 percent higher than its present value in the new steady-state growth path. The capital/labor ratio is 50 percent higher after 50 years. The labor supply also grows, being 19 percent higher in the first period, because leisure is no longer the ultimate tax shelter that it is under the current system.

These results are sensitive to the values of the key elasticity parameters, as shown in Table 4, although the general picture is preserved. The standard case is shown in row (2). The total loss represents 3.55 percent of expanded national income, even when both the uncompensated labor supply and saving elasticities are zero.

Table 4.

United States: Sensitivity Analysis with Respect to Key Parameters of Deadweight Loss of Total Tax System

¹The figures in parentheses express the welfare gains as a percentage of the total present value of welfare from consumption and leisure, which is $49,863 trillion.

Table 4.

United States: Sensitivity Analysis with Respect to Key Parameters of Deadweight Loss of Total Tax System

Labor Supply Elasticity	Saving Elasticity	Welfare Gain1 (trillion 1973 dollars)
(1) 0.15	0.0	2.231
		(4.48)
(2) 0.15	0.4	3.338
		(6.69)
(3) 0.15	2.0	8.236
		(16.52)
(4) 0.0	0.0	1.772
		(3.55)
(5) 0.0	0.4	2.709
		(5.43)
(6) 0.0	2.0	7.017
		(14.07)

¹The figures in parentheses express the welfare gains as a percentage of the total present value of welfare from consumption and leisure, which is $49,863 trillion.

View Table

Table 4.

United States: Sensitivity Analysis with Respect to Key Parameters of Deadweight Loss of Total Tax System

Labor Supply Elasticity	Saving Elasticity	Welfare Gain1 (trillion 1973 dollars)
(1) 0.15	0.0	2.231
		(4.48)
(2) 0.15	0.4	3.338
		(6.69)
(3) 0.15	2.0	8.236
		(16.52)
(4) 0.0	0.0	1.772
		(3.55)
(5) 0.0	0.4	2.709
		(5.43)
(6) 0.0	2.0	7.017
		(14.07)

¹The figures in parentheses express the welfare gains as a percentage of the total present value of welfare from consumption and leisure, which is $49,863 trillion.

Table 5 contains the results of computing the marginal distortionary costs of the U.S. tax system. If all marginal tax rates were multiplied by 1.01, the effect would be to raise government receipts by $3,331 billion. Transfers to consumers amount to just under one third of government revenues; the question is whether this fraction of a marginal tax increase would also be returned to households as transfers. Table 5 computes the marginal cost of funds for exhaustive expenditures under the assumptions that transfers are adjusted when receipts increase and that they are held fixed.

Table 5.

United States: Relationship Between First-Period Marginal Tax Revenue Collections and Marginal Change in Welfare (Annualized to First Period) for Various Parts of Tax System

Table 5.

United States: Relationship Between First-Period Marginal Tax Revenue Collections and Marginal Change in Welfare (Annualized to First Period) for Various Parts of Tax System

Marginal Rates Increased by 1 Percent	Increase in Total Tax Revenues	Increase in Transfers	Increase in Government Tax Payments on Labor Use	Net Increase Revenue (col. (2)-(3)-(4))	Decrease in Utility	Marginal Welfare Loss per Dollar of Revenue (col. (6)÷(5)–1)	Marginal Welfare Loss, Holding Transfers Fixed
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
Billion dollars
(1) All marginal rates	3.331	1.101	0.233	1.997	3.520	0.763	0.52
(2) Capital taxes by industry	0.615	0.205	0.021	0.389	0.694	0.784	0.51
(3) Labor taxes by industry	0.767	0.242	0.156	0.369	0.475	0.287	0.19
(4) Consumer purchase taxes	0.330	0.108	0.010	0.212	0.398	0.877	0.63
(5) Output taxes	0.131	0.043	0.004	0.084	0.129	0.536	0.43
(6) Motor vehicle taxes	0.013	0.003	0.000	0.010	0.013	0.300	0.23
(7) Marginal income taxes	1.895	0.633	0.055	1.207	2.209	0.830	0.57

View Table

Table 5.

United States: Relationship Between First-Period Marginal Tax Revenue Collections and Marginal Change in Welfare (Annualized to First Period) for Various Parts of Tax System

Marginal Rates Increased by 1 Percent	Increase in Total Tax Revenues	Increase in Transfers	Increase in Government Tax Payments on Labor Use	Net Increase Revenue (col. (2)-(3)-(4))	Decrease in Utility	Marginal Welfare Loss per Dollar of Revenue (col. (6)÷(5)–1)	Marginal Welfare Loss, Holding Transfers Fixed
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
View Expanded Billion dollars View Expanded
(1) All marginal rates	3.331	1.101	0.233	1.997	3.520	0.763	0.52
(2) Capital taxes by industry	0.615	0.205	0.021	0.389	0.694	0.784	0.51
(3) Labor taxes by industry	0.767	0.242	0.156	0.369	0.475	0.287	0.19
(4) Consumer purchase taxes	0.330	0.108	0.010	0.212	0.398	0.877	0.63
(5) Output taxes	0.131	0.043	0.004	0.084	0.129	0.536	0.43
(6) Motor vehicle taxes	0.013	0.003	0.000	0.010	0.013	0.300	0.23
(7) Marginal income taxes	1.895	0.633	0.055	1.207	2.209	0.830	0.57

If transfers increase, then $1,101 billion is returned to households. Further, of the $3,331 billion raised, the government itself pays $0,233 billion. Netting out the transfers and the government’s own tax payments, the funds available for a public project are $1,997 billion, shown in column (5). The decrease in consumer welfare is $3,520 billion, 1.76 times as much as the money available for the government project. Column (7) reflects this distortionary cost ($0.76) per dollar transferred to the public sector. If transfer payments are not increased, the government ends up with more net revenue and households have a larger decrease in utility, with the net result that consumers lose 1.52 times as much as the government raises. This fact is reflected in column (8).

The implications of these numbers, if accepted, are great. The $1.76 or $1.52 private cost of a marginal government dollar means that cost-benefit studies that use unity as the critical benefit/cost ratio support projects that are socially inefficient. They do this by not taking into account the resource waste caused by the distortionary taxes that are used to raise the additional revenues. The correct critical ratio would be 1.76 or 1.52, depending on how transfer payments react to the enlarged government budget. At a more theoretical level, the results indicate that Paul Samuelson’s conditions for the optimal provision of public goods should include

where λ is 1.76 or 1.52. Public goods not only use up resources in their manufacture but also are a cost to economic welfare in the distortionary taxes that they necessitate.

Rows (2)–(7) of Table 5 compute the marginal cost of each major type of tax. If these tax types were used in a third-best optimal manner, they would each have the same marginal distortionary cost per dollar raised. This cost would minimize the total deadweight loss for a given revenue using this given set of instruments. The results of columns (7) and (8) show that the U.S. tax system is far from this condition of optimality. An additional flat tax on labor by industry (payroll tax) could raise one dollar for as little as $1.19 in private welfare, whereas increasing the 1973 personal income tax rates would result in government dollars that cost $1.57 each at the margin, even if transfer payments are frozen.

The results of this table are elaborated on in Ballard, Shoven, and Whalley (1982). They illustrate a kind of analysis that cannot be carried out appropriately with partial equilibrium techniques.

IV. Conclusion

General-equilibrium analysis has developed from an abstract economic theory to a computational procedure and now to a tool that can be used for policy purposes. It is not always the appropriate technique; certainly, many issues are best examined at a very fine level of detail by using partial-equilibrium methods. The model also is inappropriate for very short-run forecasting of business and the business cycle and does not yet have the many rigidities (unions, rent controls, monopolies, transactions costs, etc.) that characterize real economies. Nonetheless, for analyzing the likely medium-run to long-run adjustments of an economy to a large policy change, the applied general-equilibrium model seems to be appropriate and to be ready for application.