Export restrictions on non renewable resources used as intermediate consumption in oligopolistic industries

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1 Export restrictions on non renewable resources used as intermediate consumption in oligopolistic industries Antoine Bouët, David Laborde and Véronique Robichaud August 2, 2011 Abstract We build a dynamic world partial equilibrium model for non renewable minerals including the main consumers and one domestic supplier (monopoly) to illustrate the effects of export restrictions on these minerals on world prices and producers as well as the manufacturing sector using them as an input. We suppose that the downstream sector is a world Cournot duopoly with the presence of a domestic firm. We discuss the role of export restrictions on minerals on terms of trade improvement. We also show that export restrictions on minerals act as an input subsidies of the industry that buys rare earth for intermediate consumption. In this context, export restrictions can also be seen as strategic trade policies altering both short term and long term market equilibrium on both sectors (upstream and downstream). We derive the optimal export tax that maximizes the national surplus consisting of extraction profits, manufacturing profits and public receipts. Finally we discuss the same policies in a dynamic context where the mining sector maximise the long term domestic surplus taking into account how its current pace of extraction affects future extraction costs and profitability. Keywords: non renewable resources, export taxes, strategic trade policy JEL classification: F10, F12, F1 International Food Policy Research Institute - IFPRI, 20 K Street, NW, Washington DC, 20006, US; a.bouet@cgiar.org.- and LAREFI- Université Montesquieu Bordeaux IV. International Food Policy Research Institute - IFPRI, 20 K Street, NW, Washington DC, 20006, US; d.laborde@cgiar.org Université de Laval- Québec; vrob@videotron.ca 1

2 1 Introduction Exports restrictions are back. In particular in mineral sector. For example sector of rare earths environment (from the point of view of the Chinese governement), augmentation of world prices (improvement in terms of trade), european and US sector (input subsidies) and FDI in China. what is the rationale of all these considerations? + non renewable sector? traditional role of export restrictions strategic aspect of export restrictions Eaton and Grossman (1986) showed that an export tax is optimal under a Bertrand Duopoly. Collie and Clarke showed that the maximum-revenue export tax is always lower under Bertrand duopoly than under Cournot duopoly; that the absolute value of the maximumwelfare export tax under Bertrand duopoly is always lower than the absolute value of the maximum-welfare export subsidy under Cournot duopoly, that the maximum-revenue export tax under Bertrand duopoly always exceeds the maximum-welfare export tax under Bertrand duopoly (the reason being that the export tax always reduces domestic firm s profit, welfare being composed of domestic firm s profit and tax revenue) and that the country with the lowest cost firm imposes the largest export tax in the Nash equilibrium of export taxes under Bertrand duopoly. This paper supports the general principle that the incentive to intervene in trade is greater under Cournot duopoly than under Bertrand duopoly. increasing the world price of a mineral may cause the entry of new competitor. But dynamic relation: in mineral sector marginal cost depends on reserves. Imposing an export tax decreases current extracion and current profits but decrease future marginal cost and increase future profits by slowing down the speed of reserve depletion. review of literature objective of this article structure 2 The static model The objective of this section is to present a simple theoretical framework under which a government seeks the optimal export tax that maximizes welfare on a single period of time. We make some simplifying assumptions. In particular we suppose that China (denoted C) is the only source of extraction of rare earths. Moreover we suppose that the manufacturing sector which used rare earths as an input is a duopoly with one Chinese firm and one another firm (denoted U). Finally we study a specific export tax and not an ad valorem tax. 1 1 The reason why choosing an ad valorem tax implies difficult differentiation is that in this case the domestic price is p = W P/(1 + et) with p the domestic price, W P the world price and et the export tax while with a specific export tax the domestic price is simply p = W P et. 2

3 2.1 A static model with monopoly in the extracting sector This section describes a partial equilibrium model with a manufacturing sector and a primary sector (mineral) Hypotheses Let us suppose that the manufacturing sector is a Cournot duopoly composed of a domestic firm supplying qm d and a foreign firm supplying qm f, both on the world market. Both firms products are identical. We assume that the inverse demand function is pm = a b(qm d + qm f ) with pm the market price and by normalization, b = 1. Qm = qm d + qm f is total supply. Both firms marginal costs only consist in mineral: one unit of manufactured good requires α units of this mineral. 2. Price of mineral is W P on the world market and p in the domestic country. Since the domestic government implements a specific tax et on exports of mineral, the relation between W P and p is: p = W P et (1) It indicates that with et > 0, domestic country s local price of the mineral is less than world price. In fact with the implementation of a positive export tax, at initial prices the domestic mining sector re-orientates part of its production on the domestic market until p + et = W P. This is a traditional effect of an export tax. However we consider the case herein of a monopoly supplying this mineral which is different and requires the addition of an assumption stated later on. Concerning the duopoly using this mineral as an input there is no fixed cost. These conditions are sufficient to derive an optimum. Profits in the manufacturing sector (π md for the domestic firm and π mf ) are: π mf = (pm αw P ) qm f (2) π md = (pm α(w P et)) qm d () Extraction of mineral is a world monopoly of the domestic country: it is made by a domestic firm which selects the world price W P of this mineral which maximizes its profit π e. In fact the monopoly receives a price W P on its exports but pays an export tax worth et such that the net price it actually receives on exports is W P et. As a monopolist the mining sector could charge a higher price on domestic market to increase its profit such that equation 1 does not hold. There is no opportunity of arbitrage as the world price is higher than the domestic price. To ensure that equation 1 holds, we assume that the domestic government passes a law which enforces that the domestic price is not higher than the world price minus the export tax. This is all the more realistic if the 2 We could easily generalize by considering that there is another component of - constant - marginal cost.

4 objective of the government is to shift manufacturing profits from the rest of the world to the domestic economy and/or to attract FDI. The unique demand for the mineral comes from the manufacturing sector here considered. Let X be the inital reserves of mineral in the domestic country. Extracting an amount Y of mineral implies a variable cost V (Y ) and a fixed cost F with: V (Y ) = BY 2 X (4) F = K X (5) Thus variable and fixed costs of extraction depend negatively on level of reserves. Marginal cost of extraction is increasing. Finally the domestic government maximizes a surplus function G(.) which is simply the sum of domestic manufacturing firm s profit π md, of the profit of the domestic rare earthsextracting mine π e and of tariff revenue T R. G = π md + π e + T R (6) The timing of the game is as follows: first the domestic government selects the export tax et to be implemented; second domestic mining sector determines the world price of minerals that maximizes its profits; third in the manufacturing sector both firms set their supplies Solution of the game Let us first solve the final stage: the Cournot game in the manufacturing sector. At Cournot- Nash equilibrium, firms supplies are: qm d = am αw P + 2αet (7) qm f = am αw P αet Thus in the manufacturing sector, the domestic output is increasing in the domestic export tax on mineral (the export tax acts as an input subsidy in the sense that it decreases input price for the domestic firm) while the foreign firm s output is decreasing in the domestic export tax on mineral. In fact the domestic export tax decreases the domestic firm s marginal cost and increases the foreign firm s marginal cost. Total supply in the manufacturing sector is: (8) Qm = 2am 2αW P + αet Anyway what is important is that there is a difference in the domestic price and the world price and the former is less than the latter. We can easily imagine a different setup where the domestic mining monopoly implements price discrimination in both markets with price-elasticity conditions that ensures this condition. (9) 4

5 Therefore total supply in the manufacturing sector is decreasing in the world price of the mineral, but increasing in the export tax: the decreasing impact an export tax has on foreign manufacturer s output is more than compensated by the expanding effect its has on the domestic manufacturer s output (see equations 7 and 8). In the manufactured sector the equilibrium price is: pm = am + 2αW P αet So a positive export tax on mineral decreases market price in the manufacturing sector: Let us now solve the second stage of the game: the optimal decision of the domestic extracting monopoly. Either it sells on the domestic market to the domestic manufacturing firm at p or it exports and sells to the foreign firm at price W P. Taking into account equations 1, 4 and 5, its profits π e is: (10) π e = (W P et) αqm f + (W P et) αqm d Bα2 Qm 2 K X X The program of the domestic extracting monopoly is to select the world price W P that maximizes π e under equations 7, 8 and 9, that is to say perfectly anticipating what will be the demand for manufacturing good and therefore the demand for mineral. Consequently the price W P that maximizes profits related to extraction by domestic mine (equation 11) under these constraints is: (11) W P = 8α2 amb + 6amX + 4α Bet + 9αXet 8α B + 12αX (12) This is a maximum since d2 π e dw P < 0. Including equation 12 in equation 11 brings: 2 π e = 4X ( 6K + am 2 X ) 4αamX 2 et + α 2 ( 16BK + X 2 et 2) 8X (2α 2 B + X) (1) Therefore π e is decreasing in et. The minimg monopoly would benefit from an export subsidy. Implementing an export tax et > 0 on mineral raises the world price of this commodity but decreases volume exported with volume effect being greater. Taking into account the extracting monopoly profit-maximizing price of mineral W P the profits in the manufacturing sector are: π md = ( 2amX + 4α Bet + 5αCXet ) 2 16 (2α 2 B + X) 2 (14) π mf = ( 2amX + 4α Bet + 7αXet ) 2 16 (2α 2 B + X) 2 (15) Therefore π md and π mf are convex in the export tax et but while on et > 0, π md is monotonically increasing, π mf is decreasing, then increasing. π mf is equal to 0 and minimum for: 5

6 2amX et 0 = 4α B + 7αX Public revenues in the domestic country are expressed as: (16) RP (et) = et.α.qm f = α.et 2amX 4α Bet 7αXet 8α 2 B + 12X (17) Let us solve now the first stage of the game. The domestic government s decision is to select the export tax et that maximizies equation 6 under 14, 1 and 17. This leads to the implementation of a positive export tax defined by: et = 2.am.CX ( 4α 2 B + 5X ) 16α 5 B α BX + 5αX 2 (18) It is easy to show that 18 is positive and defines a maximum Comments The case is illustrated by figure 1 where the domestic surplus G(et) is drawn together with the evolution of the domestic manufacturing profit π md, the public revenue from export taxation RP and the extracting monopoly profit π e. describe the effect of an export tax on G. Introduction of domestic consumption of the manufactured good and of environmental concern. Comparison with production subsidy in the manufacturing sector, extraction subsidy in the mineral sector. 2.2 A static model with a duopoly in the extracting sector The dynamic model.1 A dynamic model witha monopoly in the extracting sector.2 A dynamic model with a duopoly in the extracting sector 4 Conclusion References [1] Brainard L.S. and D. Martimort, 1992, Strategic Trade Policy with Incompletely Uninformed Policymakers, NBER Working Paper Reprinted in Brainard L.S. and D. Martimort, 1997, Strategic Trade Policy for Uninformed Policy Makers, Journal of International Economics, 42, -65. [2] Brander, J. and P. Krugman, 198, A Reciprocal Dumping Model of International Trade, Journal of International Economics 15,

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