I. Introduction

There is broad consensus among international and development economists that there are substantial economic costs associated with restrictive trade policy regimes. Examples of the costs most frequently cited are higher domestic prices or inferior quality of products sold, inefficient resource allocation, administrative costs of policy implementation, and as has been more recently argued, the costs of lobbying for such polices. Consequently, economists have tended to agree that import liberalization, in general, would foster productive efficiency and increase consumer welfare. Relaxing or removing trade barriers is, therefore, now a key element in the advice given to developing countries by academics and international institutions alike.

While the focus has mainly been on studying the costs of protecting final output, an important cost that has not received attention in the theoretical literature is one that emerges in trade regimes with quotas on imported inputs. Quotas on imported inputs in manufacturing industries of developing countries are often based on installed capacity. A consequence is that firms in these industries create excess capacity which have been observed to persist for prolonged periods of time. This creation of idle capacity exacerbates the problem of capital shortages in developing countries. This paper presents a simple theoretical model to explain the relationship between excess capacity in these industries and quotas on imported inputs.

Explanations of capacity underutilization that are typically given are the variability in demand conditions coupled with the observation that capital investments are irreversible decisions. Such reasons are valid in explaining variability in capacity utilization, but are inadequate in explaining the persistence of excess capacity over time. We show, in this paper, that excess capacity is a natural outcome under certain trade regimes, irrespective of demand conditions or the reversibility of capital decisions. This study, therefore, is able to directly link input quotas with excess capacity in developing economies.

Many governments in developing countries issue licenses for imported inputs on the basis of installed capacity and not actual production undertaken. ^1/ Two major empirical studies in the 1970s, the first by the OECD (Little et. al. (1970)) and subsequently by the NBER (Bhagwati, (1978)), highlight this fact for many countries. The countries studied include Argentina, Brazil, Chile, Colombia, Egypt, Ghana, India, Israel, Pakistan, Philippines, South Korea, Taiwan, and Turkey. These studies note that the justification for the above mentioned allocation rule, given by governments in these developing countries, is to introduce some notion of “fairness” by allocating input quotas in some equitable, albeit arbitrary, manner. ^2/ The consequence, as noted by Little et al. (1970, p. 226) is that firms “would invest in additional capacity, not because this was needed to produce the additional output but because it provided a basis for a more generous allocation of inputs”.

Most markets in developing countries are also imperfectly competitive. Studies by Rodrik (1987) and Kirkpatrik et al. (1984) based on four-firm concentration ratios suggest that imperfect competition is not only prevalent in manufacturing sectors of developing countries, but appears to be even more pervasive than in developed countries. In view of this evidence we examine, in addition to the perfectly competitive model, an oligopoly model. By developing such a model we are able to analyze the strategic advantages that arise in input quota regimes in oligopolistic industries when compared to perfectly competitive ones.

The policy implications of this paper are fairly straightforward. A replacement of input quotas by input tariffs leads to full capacity utilization in both perfectly competitive and imperfectly competitive markets, and eliminates strategic advantages arising in quota regimes for oligopolistic firms. This study, consequently, has a bearing on the sequencing theory of trade reforms which is still in nascent form. ^3/

This paper is organized as follows. In Section II, we describe briefly existing modeling approaches in the current literature and compare them to the approaches taken in this paper. In Section III, a theoretical model for analyzing tariffs and quotas on imported inputs is developed using a perfectly competitive framework. A comparison of input tariffs and input quotas in the perfectly competitive case reveals the existence of excess capacity under the quota regime alone. In addition to input tariffs, we show that excess capacity may also be eliminated by the introduction of secondary markets. In Section IV, input quotas under oligopoly and perfect competition are compared. Some concluding remarks close the paper.

II. The Modeling Framework

Most studies on trade of developing countries have focused on trade in final goods. A very important aspect in the problem of trade deficits is ignored if imports of intermediate inputs are not taken into consideration. The reason is that a developing country facing balance of payments deficits may be willing to reduce its imports of final goods, especially luxury consumer goods (whose demand elasticity is high) but would be reluctant to forgo the imports of intermediate inputs if the industries which use these inputs have already been established. Many industries have become so dependent on technology-embodied foreign inputs to sustain their production process that any decrease in these inputs is likely to have a direct adverse impact on GDP. Given that imported inputs are considered “essentials”, devising optimal trade policies in intermediate inputs is important for those countries facing severe balance of payments problems. ^5/

The current literature on traded inputs in developing countries has been limited to neoclassical theories of effective protection (Corden (1971)), or immiserizing foreign (Brecher and Findlay (1983)) and domestic (Johnson (1967)) investment in the presence of domestic distortions. A basic limitation of conventional neoclassical theories is their inability to capture underutilization of factors of production without imposing price rigidities.

Abel (1981) develops a dynamic model of a firm with varying capacity utilization. He explains variations in utilization rates by assuming both capital and labor as quasi-fixed factors. At any instant these factors of production are fixed and only utilization rates are varied in response to given demand conditions. In models developed below, an explicitly defined quota allocation rule linking the two factors (capital and the intermediate input on which the quota is imposed) is sufficient to generate excess capacity. In other words, excess capacity is shown to emerge even if demand is unchanged.

The possibility of excess capacity as a means of deterring entry has been well documented in the Industrial Organization literature. Spence (1977), and Bulow et al. (1985), among others, have shown that because investments in capital are irreversible decisions and represent preemptive commitments to the industry, they can be used to discourage entry. ^5/ An empirical implication would be to expect concentrated industries to have lower capacity utilization. Our model predicts a reverse relationship in countries which have inputs linked to capacity creation. Even though installed capacity in these developing countries is used as a strategic variable, it is not used for deterring entry but for optimizing input quota allocations.

The theoretical equivalence of tariffs and quotas under the assumption of perfect competition has been proven by a number of writers (e.g., Bhagwati (1969)). On the other hand, non-equivalence has been shown in the presence of existing distortions, for example, under uncertainty (Fishelson et al. (1975)), under monopoly in the domestic market (Panagariya (1980)), among others. Krishna (1983) was among the first to demonstrate the non-equivalence of tariffs and quotas in a game-theoretic framework. She shows that when oligopolistic firms took government actions as given, a quota could be used as a facilitating instrument but a tariff could not. More recently, Reitzes (1989) demonstrates the non-equivalence when R&D behavior is used as a strategic variable. In the presence of rent-seeking activities, the equivalence can still be shown (Bhagwati and Srinivasan (1980)) although the welfare loss is greater than without rent-seeking activities. This occurs because the act of lobbying for quotas or tariffs reduces the production possibility set for the economy as a whole (Krueger (1974); Bhagwati and Srinivasan (1980)).

In the models developed in this paper, we demonstrate the non-equivalence of tariffs and quotas under both perfect and imperfect competition. In addition, we show that excess capacity is less when strategic interactions between firms is taken into account. It is worth mentioning that our models demonstrate a special kind of rent-seeking activity, whereby the existence of controls on input quotas gives rise to rent-seeking behavior in the form of excess capacity creation. ^6/

III. Quotas and Excess Capacity Under Perfect Competition

This section models the existence of excess capacity in manufacturing industries of developing countries. Quantitative restrictions on imported inputs are the key to explaining this phenomenon. This model allows us to: first, examine the existence of excess capacity despite unchanged demand for the final output; and second, to illustrate the inefficiencies of quantitative versus price controls in a new perspective -- quotas lead to capacity underutilization while tariffs do not.

1. The basic model

We develop a one-period model with many industries, each producing a final output with two kinds of inputs. There is an imported intermediate input (x) and a domestically produced input, capital (k).

The principal idea is to study import-competing industries in developing countries which are protected by prohibitive tariffs on the import of final outputs, but face a quota on the imports of scarce factor inputs. This is a realistic scenario for many developing countries protecting consumable manufacturing goods and importing industrial inputs. The justification is to encourage the growth of domestic industry by protecting them from foreign competition in final output but permitting limited imports of technology-embodied inputs. Thus domestic demand-supply conditions affect the price of the final output in each industry.

The number of sellers in a typical industry, g, are fixed at a level n_g. The sellers in each industry, g, produce a standardized product, y_g. To capture the “essentiality” of imported inputs in production, we study the case in which there are no substitution possibilities for imported inputs. ^7/ In some sense, this assumption is a limiting case of a situation where domestic inputs cannot compete with foreign inputs either on price or quality grounds; or, alternatively, foreign inputs are technology-embodied with no domestic substitutes.

The production function of each firm in each industry is

y_g = min[α_gx_g,β_gk_g], g=1, 2, ........, G.

where y_g is output of a representative firm in the gth industry, x_g is the intermediate input of this firm in the gth industry, and k_g is the capital stock of this firm in the gth industry. The significance of subscripting the input coefficients α and β with g implies that we could allow the technological coefficients to be different across industries while assuming that they are same for firms within the same industry. For notational convenience we will drop the subscript g and assume that we are looking at a typical industry. Henceforth,

y = min[αx, βk].

The industry’s inverse demand function is given by

P = D(Y), where D′(Y) < 0, and Y = Σ_ny.

We assume that inputs are purchased at given prices, P_x and P_k.

Three trade regimes are analyzed in the model of perfect competition: free trade, a tariff on the intermediate input, and a quota on the same input.

(a) Free trade case

This is the case with no tariffs or quotas on the intermediate input. The firms solve the following problem: ^8/

$\begin{array}{cc}\underset{\dot{\mathrm{y}}\mathrm{,}\mathrm{x}\mathrm{,}\mathrm{k}}{\mathrm{M}\mathrm{ax}}\mathrm{\pi }\mathrm{=}\mathrm{Py}\mathrm{-}{\mathrm{P}}_{\mathrm{x}}\mathrm{x}\mathrm{-}{\mathrm{P}}_{\mathrm{k}}\mathrm{k}\mathrm{.}& \mathrm{\left(}\mathrm{1}\mathrm{\right)}\end{array}$

From cost minimization, we determine the optimum levels of x and k used in producing any arbitrary level of y. Firms minimize total costs, C, where

$\begin{array}{cc}\mathrm{C}\mathrm{=}{\mathrm{P}}_{\mathrm{x}}\mathrm{x}\mathrm{+}{\mathrm{P}}_{\mathrm{k}}\mathrm{k}\mathrm{,}& \mathrm{\left(}\mathrm{2}\mathrm{\right)}\end{array}$

subject to the production constraint

$\begin{array}{cc}\overline{\mathrm{y}}\mathrm{\ge }\min \mathrm{\left[}\mathit{\alpha }\mathrm{x}\mathrm{,}\mathit{\beta }\mathrm{x}\mathrm{\right]}\mathrm{,}& \mathrm{\left(}\mathrm{3}\mathrm{\right)}\end{array}$

where ȳ is any arbitrary level of y. The solution to this problem can be illustrated graphically. In Figure 1, the production constraint (3) is given by the shaded region, M. The appropriate cost curve, given P_x and P_k, which minimizes costs in the shaded region M is C^F. Hence, cost minimization implies the point A. Moreover, at the point A,

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$\begin{array}{cc}\mathrm{x}\mathrm{=}\overline{\mathrm{y}}/\alpha ,& \left(4\right)\end{array}$

and

$\begin{array}{cc}\mathrm{k}\mathrm{=}\overline{\mathrm{y}}/\beta \mathrm{.}& \left(5\right)\end{array}$

Using equations (4) and (5) to express ξ and k in terms of y, in equation (1), we get: ^9/

$\underset{\mathrm{y}}{\mathrm{M}\mathrm{ax}}\mathrm{\pi }\mathrm{=}\mathrm{Py}\mathrm{-}{\mathrm{P}}_{\mathrm{x}}\mathrm{y}\mathrm{/}\mathit{\alpha }\mathrm{-}{\mathrm{P}}_{\mathrm{k}}\mathrm{y}\mathrm{/}\mathit{\beta }\mathrm{.}$

Competitive equilibrium implies:

P = P_x/α + P_k/β,

or,

$\begin{array}{cc}\mathrm{D}\mathrm{\left(}\mathrm{Y}\mathrm{*}\mathrm{\right)}\mathrm{=}{\mathrm{P}}_{\mathrm{x}}\mathrm{/}\mathit{\alpha }\mathrm{+}{\mathrm{P}}_{\mathrm{k}}\mathrm{/}\mathit{\beta }\mathrm{,}& \mathrm{\left(}\mathrm{6}\mathrm{\right)}\end{array}$

where Y* is the equilibrium level of aggregate output in the industry. In other words, the price of the final output is simply a linear combination of the input prices adjusted for their respective technological coefficients. Equation (6) is the benchmark case against which subsequent comparisons of price and output levels in input tariff and input quota regimes will be made.

(b) Tariff on imported intermediate input case

Let τ be the tariff levied on input x. Therefore, if ρ_x is the tariff inclusive input price, we have,

ρ_x=(1+τ)P_x.

The firms now face the following problem:

$\begin{array}{cc}\underset{\mathrm{y}}{\mathrm{M}\mathrm{ax}}\mathrm{\pi }\mathrm{=}\mathrm{Py}\mathrm{-}{\mathit{\rho }}_{\mathrm{x}}\mathrm{x}\mathrm{-}{\mathrm{P}}_{\mathrm{k}}\mathrm{k}\mathrm{.}& \left(7\right)\end{array}$

From cost minimization we determine the optimal levels of x and k used for any arbitrary level of y. Firms minimize total cost, C, where

$\begin{array}{cc}\mathrm{C}\mathrm{=}{\mathit{\rho }}_{\mathrm{x}}\mathrm{x}\mathrm{+}{\mathrm{P}}_{\mathrm{k}}\mathrm{k}\mathrm{,}& \mathrm{\left(}\mathrm{8}\mathrm{\right)}\end{array}$

subject to the production, constraint in equation (3). In Figure 1, the appropriate cost curve, given ρ_x and P_k, which minimize costs in the shaded region M, is C^T. Equilibrium, once again, occurs at point A. Equation (2) (the free trade case), of course implies a lower cost than equation (8) (the input tariff case).

Substituting equation (4) and (5) in equation (7), the firm’s maximization problem now is:

$\underset{\mathrm{y}}{\mathrm{M}\mathrm{ax}}\mathrm{\pi }\mathrm{=}\mathrm{Py}\mathrm{-}{\rho }_{\mathrm{x}}\mathrm{y}\mathrm{/}\mathit{\alpha }\mathrm{-}{\mathrm{P}}_{\mathrm{k}}\mathrm{y}\mathrm{/}\mathit{\beta }\mathrm{.}$

In equilibrium,

P = ρ_x/α + P_k/β,

or,

$\begin{array}{cc}\mathrm{D}\mathrm{\left(}{\mathrm{Y}}_{\mathrm{\left(}\mathrm{T}\mathrm{\right)}\mathrm{*}}\mathrm{\right)}\mathrm{=}\mathrm{\left(}\mathrm{1}\mathrm{+}\mathit{\tau }\mathrm{\right)}{\mathrm{P}}_{\mathrm{x}}\mathrm{/}\mathit{\alpha }\mathrm{+}{\mathrm{P}}_{\mathrm{k}}\mathrm{/}\mathit{\beta }\mathrm{,}& \mathrm{\left(}\mathrm{9}\mathrm{\right)}\end{array}$

where Y_(T)* is the equilibrium level of aggregate output in the industry under the tariff regime.

Comparing the free trade case with the tariff case we can clearly say that price of the final output is higher under the tariff regime. That is, since τ > 0, D(Y_(T)*) > D(Y*). Also, since D′(··) < 0, we get Y* > Y_(T)*.

Moreover, regardless of input costs, we observe that cost minimization in the free trade case and the input tariff case implies point A. At A, firms utilize their capacity fully. That is, if y* is the optimal level of output for each firm, then installed capacity (y*/β) equals used capacity (y*/β), and, therefore, capacity is fully utilized. Hence there is no excess capacity under either the free trade case or the input tariff case.

(c) Quotas on imported intermediate input case

The quota on input x, is based on capacity creation. Let the quota allocation rule be,

$\begin{array}{cc}\mathrm{x}\mathrm{\le }\mathit{\theta }\mathrm{k}\mathrm{,}& \left(10\right)\end{array}$

where θ is a policy parameter, exogenously set by the government, which determines the level of imports of x based on installed capacity. We will only study the interesting case where the quota is binding. ^10/ The problem a typical firm faces is:

$\begin{array}{cc}\underset{\mathrm{y}\mathrm{,}\mathrm{x}\mathrm{,}\mathrm{k}}{\mathrm{M}\mathrm{ax}}\mathrm{\pi }\mathrm{=}\mathrm{Py}\mathrm{-}{\mathrm{P}}_{\mathrm{x}}\mathrm{x}\mathrm{-}{\mathrm{P}}_{\mathrm{k}}\mathrm{k}\mathrm{.}& \mathrm{\left(}\mathrm{11}\mathrm{\right)}\end{array}$

Once again from cost minimization we determine the optimal levels of x and k used for any arbitrary level of y. The firms now minimize total cost (equation (2)), subject to two constraints. The two constraints are the production function (equation (3)) and the quota allocation rule (equation (10)).

In Figure 2, the shaded region N represents the constraint (10) when the input quota is binding. The intersection, of. region M with region N which minimizes cost for y is given by the point B. The total cost line which goes through B is C^Q and has the same slope as in Figure 1. Also, note that the slope of OD (which goes through B) is greater than the slope of OE (which goes through A). Since the slope of OD equals 1/θ, and the slope of OE equals α/β, a binding quota implies

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Illustration of a binding quota on input x

Citation: IMF Working Papers 1989, 091; 10.5089/9781451951639.001.A001

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$\begin{array}{cc}\beta >\alpha \theta \mathrm{.}& \left(12\right)\end{array}$

At point B in Figure 2,

$\begin{array}{cc}\mathrm{x}\mathrm{=}\overline{\mathrm{y}}/\alpha ,& \left(4\prime \right)\end{array}$

which is the same as in the cases of free trade and input tariffs for arbitrary levels of y. However, the optimal k is different in the input quota case. Since we are analyzing the case where the input quota is binding, at point B,

$\begin{array}{cc}\mathrm{k}\mathrm{=}\mathrm{x}/\theta ,& \left(10\prime \right)\end{array}$

where equation (10′) is a rearrangement of equation (10) when it holds with equality, or,

$\begin{array}{cc}\mathrm{k}\mathrm{=}\overline{\mathrm{y}}/\alpha \theta \mathrm{.}& \left(13\right)\end{array}$

Substituting equation (4′) and equation (13) in equation (11), we obtain

$\underset{\mathrm{y}}{\mathrm{M}\mathrm{ax}}\mathrm{\pi }\mathrm{=}\mathrm{Py}\mathrm{-}{\mathrm{P}}_{\mathrm{x}}\mathrm{y}\mathrm{/}\mathit{\alpha }\mathrm{-}{\mathrm{P}}_{\mathrm{k}}\mathrm{y}\mathrm{/}\alpha \theta \mathrm{.}$

Thus in equilibrium,

P = P_x/α + P_k/αθ,

or,

$\begin{array}{cc}\mathrm{D}\mathrm{\left(}{\mathrm{Y}}_{\mathrm{\left(}\mathrm{Q}\mathrm{\right)}\mathrm{*}}\mathrm{\right)}\mathrm{=}{\mathrm{P}}_{\mathrm{x}}\mathrm{/}\mathit{\alpha }\mathrm{+}{\mathrm{P}}_{\mathrm{k}}\mathrm{/}\mathit{\alpha }\mathit{\theta }\mathrm{,}& \mathrm{\left(}\mathrm{14}\mathrm{\right)}\end{array}$

where Y_(Q)* is the equilibrium level of aggregate output in the industry under the quota regime.

The existence of excess capacity under the quota regime is now fairly easy to establish. From equation (13) we have installed capacity = y/αθ, and from the production function (equation (3)) we know that used capacity = y/β. Hence,

$\begin{array}{cc}\mathrm{Capacity}\mathrm{utilization}=\frac{\mathrm{Used}\mathrm{Capacity}}{\mathrm{Installed}\mathrm{Capacity}}=\frac{\alpha \theta }{\beta }& \left(15\right)\end{array}$

Since we are interested in analyzing the case where the input quota binds, we know from equation (12) that β > αθ. Given α, θ, β > 0, equation (15) shows that excess capacity is being created. Figure 2 illustrates the extent of excess capacity for any arbitrary level of y in the quota regime.

We now compare the level and price of the final output, and capacity utilization, under input quotas with the free trade and input tariff cases. Comparing equations (6) and (14) we see that since β > αθ, D(Y*) < D(Y_(Q)*), and Y* > Y_(Q)*. In addition, since K* = Y*/β and K_(Q)* = Y_(Q)*/αθ, ^11/ the relative size of the installed capacity in the industry cannot be determined. This is because Y_(Q)* < Y* but β > αθ. Nevertheless, the quota regime leads to capacity underutilization while the free trade regime does not.

In order to make a comparison between the input quota and the input tariff regimes which is meaningful in welfare terms, we can determine the tariff equivalent of the quota which implies the same level of final output and price. A comparison of equations (9) and (14) reveals that this condition is met when τ = (P_k/P_x)((β-αθ)/θβ). In this case, even though the output price is the same under the two regimes, the quota regime alone creates idle capacity which is clearly a waste in any developing economy. A replacement of input quotas by input tariffs, however, leads to full capacity utilization in equilibrium.

In summary, we can say that capacity underutilization is unique to the input quota case. As expected, the output price is the lowest (and correspondingly, level of output is the highest), under a free trade regime.

IV. A Strategic Framework for Analyzing Input Quotas ^18/

So far we have dealt only with the perfectly competitive case. It would obviously be interesting and relevant to determine if the results of the perfectly competitive case would carry over to the imperfectly competitive case. ^18/ This section shows that under similar conditions, capacity utilization under input quotas is higher in oligopolistic industries when compared to perfectly competitive ones.

All assumptions made in the first section are retained. In addition, we specify that the total amount of the input quota available for the industry is fixed at a predetermined level, $\overline{\mathrm{X}}$. (This may occur when, for example, foreign exchange shortages in the economy set the limits on the intermediate imports of each industry).

V. Conclusions

In a trade model the introduction of quotas on imported inputs clearly illustrates new distortions that are created under certain quota allocation rules. Capacity underutilization becomes the natural outcome in equilibrium when quotas are based on installed capacity. In addition to generating excess capacity, we have shown that a quota allocation rule based on installed capacity allows for strategic advantages to firms in oligopolistic competition as compared to those under perfect competition. The result is less excess capacity in equilibrium for firms under oligopoly.

This paper also throws some light on a possible sequencing of trade reforms in developing countries. It is often argued that a developing country embarking on a trade liberalization process should, at the first stage, replace import quotas by tariffs. Our analysis indicates that such a policy directed at imported inputs will have the added benefit of eliminating excess capacity in the manufacturing sector. This may be accomplished even without changing the degree of restrictions on the imported intermediate input. Furthermore, a tariff in imperfectly competitive markets eliminates strategic advantages to oligopolistic firms in input quota regimes. If the purpose of quota allocation rules based on installed capacity is to incorporate some notion of “fairness” then it is evident that governments are inadvertently favoring industries which are more oligopolistic in nature. A replacement of input quotas by input tariffs would then ensure impartiality in the trade regime.

In conclusion, we can consider some possible extensions of our modeling framework and the consequences of altering some of its basic assumptions. The assumption of fixed technological coefficients is the most noteworthy. One way of generating excess capacity within the framework of some degree of substitutability between factors of production could be to assume “lumpiness” in installing capital. ^20/ Secondly, we could change the quota allocation rule by making input quotas a function of past production instead of installed capacity. Our intuition is that by introducing these dynamics we would be able to show industrial concentration over time, since the incumbents would then receive a larger share of input quotas. And finally, we could generalize the models presented so far by introducing quotas on many intermediate inputs. This would enrich the analysis by isolating those inputs which impose the greatest restriction on capacity utilization. Such extensions, while generalizing our results, would not necessarily alter the qualitative nature of the conclusions of this paper.