Journal of Industrial Organization Education

Journal of Industrial Organization Education Volume 2, Issue 1 2007 Article 1 Simulating Tariffs vs. Quotas with Domestic Monopoly John Gilbert, Utah State University Reza Oladi, Utah State University Recommended Citation: Gilbert, John and Oladi, Reza (2007) "Simulating Tariffs vs. Quotas with Domestic Monopoly," Journal of Industrial Organization Education: Vol. 2: Iss. 1, Article 1. DOI: 10.2202/1935-5041.1010

Simulating Tariffs vs. Quotas with Domestic Monopoly John Gilbert and Reza Oladi Abstract The pro-competitive effects of international trade in the presence of monopoly, and the deleterious effects of protection, are topics commonly taught in both international trade and industrial organization classes. We present a numerical simulation model for classroom use, built in Excel, that is designed to explore the effect of international trade on a monopoly, and how the effects of protecting the monopoly may differ depending on whether a tariff or a quota is chosen. We describe the model, key results, and how to integrate the approach into the curriculum. KEYWORDS: monopoly, tariffs, quotas, simulation models Author Notes: The authors are associate and assistant professor of economics, respectively. They would like to thank the Vernon M. Buehler and Maree C. Buehler endowment for funding support. Contact: Department of Economics, Utah State University, 3530 Old Main Hill, Logan, UT 84322-3530. Ph: 435-797-8196. FAX: 435-797-2701. E-mail: oladi@econ.usu.edu.

Gilbert and Oladi: Simulating Tariffs vs. Quotas with Domestic Monopoly 1 Introduction One of many topics that appear at the interface of industrial organization and international trade is the effect that trade can have on a monopoly, and the consequences of using different policy instruments to prevent a monopoly from facing the full effect of international competition. The topic is taught in both the undergraduate trade and industrial organization curriculum. 1 It is an important topic in that it illustrates how international trade, in addition to enhancing consumption possibilities through comparative advantage, plays an antitrust role in forcing price to marginal cost. It is also an excellent example of how the choice of seemingly similar policy instruments, and the magnitudes of those instruments, can result in quite different economic outcomes. The classic reference is Bhagwati (1965). In this paper we present an aid to teaching this topic: a numerical simulation model built in Excel. Although we regard these tools as complements of traditional approaches not substitutes, numerical simulation is useful for developing intuition, exploring advanced topics, and giving students some hands on experience with models. Examples from many branches of economics can be found. Excel has proved a popular development platform because of near universal availability, ease of use, and the ability to present models both numerically and graphically. For a general overview see Cahill and Kosicki (2000). Other recent contributions include Mixon and Tohamy (2001) and Bolton (2005) in the area of microeconomics, To - hamy and Mixon (2003) and Gilbert (2004) in the area of trade and general equilibrium, and Nævdal (2003) and Strulik (2004) in the area of macroeconomics. W i g h t (1999) discusses benefits of using Excel as part of assignments. In the following section we briefly set out the problem algebraically, and derive the key solutions. The main difference between our presentation and standard textbook presentations is that we treat an import quota as an inequality constraint that does not necessarily bind, and consequently requires a piece-wise residual demand and marginal revenue curve. Section 3 discusses how we implement the model in Excel, while Section 4 contains suggestions for integrating the numerical simulation approach and this model into the curriculum. Concluding comments follow. 2 T r a d e, Protection and Monopoly Consider a simple partial equilibrium model of a monopoly that charges a single price. To implement the model numerically we need specific functional forms for demand and the costs of the monopolist. For simplicity we use a linear inverse 1 See, for example, Krugman and Obstfeld (2003), chapter 8, in the area of international trade, and Carlton and Perloff (2005), chapter 18, in the field of industrial organization. 1

Journal of Industrial Organization Education, Vol. 2 [2007], Iss. 1, Art. 1 demand function: while the cost function of the firm takes the form: P = α βq D (1) C = F +γq S +δq 2 S (2) The marginal cost function is therefore linear. The optimal level of production when the economic system is closed to trade (autarky) is: Q A S = (α γ) 2(β +δ) (3) and the price charged is: P A = α β(α γ) 2(β +δ) The familiar geometry is presented in Figure 1. In the absence of foreign competition, the monopolist faces the full market demand. Setting marginal revenue equal to marginal cost yields the profit-maximizing output, and tracing back to the demand curve the optimal price. The area between the market price and the marginal cost curve is the contribution margin. Now suppose the economy is opened to free trade, and is small relative to the rest of the world. In that case the world price can be treated as a given, P. Suppose that at P excess demand exists, so imports occur. Because any consumer can make a purchase at the world price, quantity demanded above P is zero, while the firm can sell up to the full market demand at P. 2 Hence, marginal revenue in the relevant range is simply P, which is the solution for the domestic price, and the optimal output is: Q F P S = γ (5) 2δ In Figure 2, the world price and the marginal revenue curve with free trade (MR F ) coincide. The profit maximizing output choice is where price is equal to marginal cost. That is, allowing free trade forces price to equal marginal cost, as would occur under competition. This is the pro-competitive effect of trade. The market is competitive in the sense that the firm must accept the world price. Note, however, that this does not necessarily imply zero profit for the monopolist. Now consider the implications of intervention in the form of a tariff. This drives a wedge between the price that must be paid by domestic importers and the world price. Let the ad-valorem tariff be denoted t, then the cost of importing is equal to 2 At prices below P the monopolist has the market to itself, but this range is not relevant in the case where the good is imported with trade. (4) DOI: 10.2202/1935-5041.1010 2

Gilbert and Oladi: Simulating Tariffs vs. Quotas with Domestic Monopoly Figure 1: Autarky and Free T r a d e with Domestic Monopoly P(1 + t). There are three possible outcomes. If the tariff is sufficiently small, and the cost of importing remains below the point where domestic demand intersects with marginal cost (let this be denoted ˆ P = α [β(α γ)]/(β + 2δ)), then the monopolist continues to face a horizontal demand curve over the relevant range. At the other extreme, if the world price plus the tariff is greater than or equal to the price that the monopolist would charge in the absence of trade, then the monopolist is effectively unconstrained, and the solution is the autarky solution. When the cost of importing exceeds the point where domestic demand intersects with marginal cost but is lower than the autarky price charged by the monopolist, imports will cease and the monopolist will supply the whole market, but will be constrained to 3

Journal of Industrial Organization Education, Vol. 2 [2007], Iss. 1, Art. 1 charge only the cost of importing. Formally: ( P(1 + t) γ)/(2δ) P(1 + t) P ˆ Q T S = [α P(1 + t)]/β P ˆ < P(1 + t) < P A (α γ)/[2(β +δ)] P(1 + t) P A (6) The relevant ranges of these three possible cases is shown in Figure 2, the range labeled A representing where the monopolist is constrained to by the price of imports and imports are positive, the range labeled B where imports cease but the monopolist is remains price constrained, and region C where the monopolist is unconstrained. Figure 2: T a r i f f Protection with Domestic Monopoly Finally, consider an import quota. Let the volume of the import quota be denoted q. As with a tariff, at any price below the world price, the monopolist faces the full market demand. At the world price the monopolist can sell up to the market DOI: 10.2202/1935-5041.1010 4

Gilbert and Oladi: Simulating Tariffs vs. Quotas with Domestic Monopoly demand. Above the world price the quota will be filled, and the monopolist faces the market demand less the quota volume. Hence we have piecewise residual demand function. 3 In Figure 3, the blue curve labeled RD 1 is an example, representing a binding quota of magnitude q 1. The marginal revenue curve is also discontinuous. Up until the residual quantity demanded at the world price, the marginal revenue curve is derived from the residual demand above the world price, and takes the usual form. From this point until the total demand at the world price, marginal revenue is constant and equals the world price (that is, if the quota is thought of as an inequality constraint, the monopolist can sell as much as it wishes at the world price). Prices below the world price could never be optimal given that the good in question is imported, so we have not illustrated the corresponding section of the marginal revenue curve, but it is just the corresponding section of the autarky marginal revenue curve. There are two types of outcomes. If the quota volume is relatively small, the downward sloping section of the marginal revenue curve will intersect with the marginal cost curve. The monopolist maximizes profit with respect to residual demand in the usual manner. In the limiting case of a zero quota, we have the autarky solution. On the other hand, if the quota volume is sufficiently large, the marginal cost curve will intersect the marginal revenue curve twice, on both its downward sloping and horizontal sections. In other words, the monopolist can choose between the profit associated with accepting the world price, which is always available if the quota is treated as an inequality constraint, and the profit associated with exploiting the residual market. As the quota gets larger, the former must ev e n t u a l l y outweigh the latter. A sufficiently large quota imposes no constraint on importers, and hence is equivalent to free trade. If the quota is very large, marginal cost will intersect with marginal revenue only on the horizontal segment. Let π Q be the profit available from exploiting monopoly power, and π F be the profit from accepting the free trade solution as described above. The optimal output choices under the quota regime are then: { Q Q (α γ βq)/[2(β +δ)] π S = Q > π F ( P γ)/(2δ) π Q < π F (7) The geometry of these two possibilities is presented in Figure 3, with the blue case (q 1 ) representing a solution of the first type (a binding quota), and the red case (q 2 ) a solution of the second type (a non-binding quota). In the second case, although 3 Krugman and Obstfeld (2003) and Carlton and Perloff (2005) both present the residual marginal revenue curve as linear rather than piecewise. This is consistent with an assumption that the import quota is strictly binding at all prices, e.g., that the government decides to purchase q units and put them on the market. In this paper we represent the import decision as a voluntary activity, and the quota as not filled unless it makes economic sense for the importing agent to do so. 5

Journal of Industrial Organization Education, Vol. 2 [2007], Iss. 1, Art. 1 Figure 3: Quota Protection with Domestic Monopoly exploiting residual demand remains possible, to do so would generate a contribution margin of the area shaded in red, while contribution margin under the competitive solution is the area shaded in grey. The latter is greater than the former, so accepting the competitive outcome is the profit-maximizing strategy. 3 Implementation in Excel Given the functional forms chosen, implementing this model in Excel is straightforward, and does not require the use of any add-ins. 4 A snapshot of the interface, illustrating a scenario in which the non-equivalence of tariffs/quotas under monopoly is explored, with monopoly profit highlighted in the graphics, is presented in Figure 4. T o enter the model, we start by allocating cells for the va l u e s of the parameters of 4 If required, complete details are in the file, Multimedia Guide to Creating the Excel Sheet. DOI: 10.2202/1935-5041.1010 6

Gilbert and Oladi: Simulating Tariffs vs. Quotas with Domestic Monopoly the cost (γ,δ and F ) and demand functions (α and β), and the exogenous va r i a b l e s ( P, t and q). These va l u e s are free, and can be changed by the user to any numbers that make economic sense. 180.0 Demand Marginal Cost Marginal Revenue 180.0 Marginal Cost Demand Residual Demand Residual Marginal Revenue 160.0 160.0 140.0 140.0 120.0 120.0 Price 100.0 80.0 Price 100.0 80.0 60.0 60.0 40.0 40.0 20.0 20.0 0.0 0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 Quantity 0.0 0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 Quantity Tariff Ridden Equilibrium Quota Ridden Equilibrium Tariff (%) 30.0 0.0 Quota Volume 20.0 0.0 Domestic Price 65.0 Consumer Surplus 2256.3 Domestic Price 83.3 Consumer Surplus 1469.4 Quantity Demanded 47.5 Monopoly Profit 731.3 Quantity Demanded 38.3 Monopoly Profits 983.3 Quantity Supplied 27.5 Government Revenue 300.0 Quantity Supplied 18.3 Quota Rents 666.7 Imports 20.0 Total Surplus 3287.5 Imports 20.0 Total Surplus 3119.4 Parameters of the Economy Free Trade Equilibrium Inverse Demand Marginal Cost Domestic Price 50.0 Consumer Surplus 3025.0 Intercept 160.0 Intercept 10.0 Quantity Demanded 55.0 Monopoly Profits 375.0 Slope -2.0 Slope 2.0 Quantity Supplied 20 Total Surplus 3400.0 World Price 500.0 50.0 Fixed Cost 25.0 Imports 35.0 Figure 4: Excel Interface with T a r i f f / Q u o t a Non-Equivalence Illustrated Next we allocate cells for each of the endogenous va r i a b l e s, setting up separate sections to represent a free trade equilibrium (to be used as a baseline for comparison), a tariff ridden equilibrium, and a quota ridden equilibrium. In each case we then enter the solutions for the va r i a b l e s in these cells, in terms of the va l u e s in the parameter/exogenous variable cells. For convenience we also add cells calculating the components of social welfare, so that the overall efficiency and distributive effects of policy changes can be directly observed. The model is live in the sense that changes in parameters/exogenous variables will be instantly reflected in the solution va l u e s displayed. The final two steps are to add forms so that the key policy va r i a b l e s can be easily varied without manually typing in new values, and creating graphs. The latter is accomplished using the scatter diagram from the built-in Excel charts, and calculating (in a hidden section of the sheet) the va l u e s of intercepts and key points of interest from the va l u e s in the parameter/exogenous va r i a b l e cells. W e l f a r e components can be highlighted in the graph by selecting a check box next to the desired calcu- 7

Journal of Industrial Organization Education, Vol. 2 [2007], Iss. 1, Art. 1 lation. This is useful if, for example, an instructor wants to highlight what happens to monopoly profits as parameters or policy va r i a b l e s are altered. The diagrams are an important way of integrating the simulations with a typical textbook/classroom presentation, but like the calculations, have the advantage of being live (i.e., they update instantly in response to a change in the equilibrium), and based on a clearly observable numerical example. 4 Classroom Use We have found it useful to integrate simulation into the curriculum in two ways. Most rooms are now equipped with computers and data projectors, so the simulation can be used directly in classroom demonstrations, in much the same way as a diagram or static Powerpoint slide might otherwise be used. The live nature of the diagrams has several advantages, however. In particular, the instructor is not limited to preset examples, so student participation can be facilitated by soliciting input on the magnitude and direction of the shocks to be considered. Many different cases and issues can be quickly explored. A series of suggested exercises is presented in Table 1. In principle, an exercise can be designed to illustrate most concepts covered under the topic of a single price monopoly, and the effects of international trade. The other area where we have found simulation useful, especially in lower division classes, is in directed assignments. We use this approach after ensuring that the students are familiar with both the basic theory and the mechanics of the simulation model from class. The students are directed to undertake a series of specific simulations and to observe (and in some cases record) the results. Typically assignments cover more advanced issues, and the students are not told what to expect or what to make of the results. Rather, they are expected to observe the results, spend time thinking about their meaning, and to write up an economic interpretation and explanation and/or policy implications. By discovering key results for themselves, students are able to take ownership of those results, and learning outcomes have been improved in our experience. As an example, students might be directed to set a quota and tariff such that imports are at the same level, then gradually lower the world price to represent improvements in production technology abroad (see Table 1). The students should find for themselves that the deadweight loss of the policy contracts with the tariff as the world price falls, but expands with the quota. The reason is that the domestic price falls with the world price when a tariff is used, forcing the monopolist to react. On the other hand, the monopolist protected by a quota is fully insulated from the world market. Consumers cannot take further advantage of the lower world DOI: 10.2202/1935-5041.1010 8

Gilbert and Oladi: Simulating Tariffs vs. Quotas with Domestic Monopoly T a b l e 1: Some Suggested Exercises with Learning Objectives Exercise Raise tariff to restrict level of imports then set quota volume to the restricted level Raise the tariff in constant increments and observe the changes in total surplus Raise the quota in constant increments and observe the changes in total surplus Set quota equal to zero Gradually raise the level of the quota Set tariff equal to zero Set tariff at a low level Set tariff so that price rise just above where demand crosses marginal cost Set tariff such that the price rises above the domestic price with the quota at zero Set a tariff and quota such that imports are at the same level, now lower the world price Set a tariff and quota such that imports are at the same level, now shift demand outward Learning Objective Non-equivalence of tariff and quota under monopoly Deadweight loss increases exponentially with a tariff Deadweight loss increases exponentially with a quota A zero quota leaves the full market to the monopolist A sufficiently large quota will leave the monopolist unable to exploit any market power Free trade destroys the monopoly, forcing price equal to marginal cost At low tariff levels imports remain positive, and price still equals marginal cost A high tariff will eliminate imports, but still constrain the monopolist with respect to price A very high tariff will eliminate all imports, and leave the monopolist unconstrained Deadweight loss decreases with a tariff (when ad-valorem) but increases with a quota as rest of world becomes more efficient A demand shock leaves deadweight loss unchanged with a tariff (when demand linear) but increases with quota 9

Journal of Industrial Organization Education, Vol. 2 [2007], Iss. 1, Art. 1 prices if the quota is binding, so the monopolist may continue to charge the same price, resulting in greater waste of resources relative to the alternative of importing a greater volume at the lower price. This is an important policy issue if protection of a market in which technological innovation is rapid is being considered - the choice of policy instrument is not benign. 5 Concluding Comments W e have found simulation models like this one to be useful as both a presentation device and a basis for assignments in our undergraduate international trade and industrial organization classes. Student response has been positive. It is important to note again that we do not view simulation as a substitute for other teaching methods, including plain old working through examples using the techniques of algebra and calculus, but it is a nice complement. References Bhagwati, J. On the Equivalence of T a r i f f s and Quotas in R. Caves et al. (eds.) T r a d e, Growth, and the Balance of P a y m e n t s, (Chicago: Rand-McNally). Bolton, R. Computer Simulation of the Alonso Household Location Model in the Microeconomics Course Jo u r n a l of Economic Education 36(1):59-76. Cahill, M. and G. Kosicki (2000) Exploring Economic Models Using Excel Southern Economic Jo u r n a l 66(3):770-92. Carlton, D.W. and J.M. Perloff (2005) Modern Industrial Organization (4th Edition), Addison W e s l e y. Gilbert, J. (2004) Using Nonlinear Programming in International Trade Theory: The Factor-Proportions Model Jo u r n a l of Economic Education 35(4):343-59. Krugman, P. and M. Obstfeld (2003) International Economics: Theory and Policy (6th Edition), Addison-Wesley. Mixon, J.W. and S. Tohamy (2000) Using Microsoft Excel in Principles of Economics Computers in Higher Education Review 14. Nævdal, E. (2003) Solving Continuous Time Optimal Control Problems with a Spreadsheet Jo u r n a l of Economic Education 34(2):99-122. DOI: 10.2202/1935-5041.1010 10

Gilbert and Oladi: Simulating Tariffs vs. Quotas with Domestic Monopoly Strulik, H. (2004) Solving Rational Expectations Models Using Excel Jo u r n a l of Economic Education 35(3):269-83. Tohamy, S. and J.W. Mixon (2003) Lessons from the Specific Factors Model of International T r a d e Jo u r n a l of Economic Education 34(2):139-50. Wight, J. B. (1999) Using Electronic Data Tools in Writing Assignments Jo u r n a l of Economic Education 30:21-7. 11