Economics 101 — Fall 2009International TradeProblem Set 2Octob er 22, 2009Due: Tue, November 3, before 12:30pmInstructor: Marc-Andreas MuendlerE-mail: [email protected] Standard Trade TheoryHome and Foreign pro duce machinery and fo od. The relative price of machineryPM/PFis 1 in the initial world-trade equilibrium.• Suppose Home exports machinery and imports food. Draw the trade line(isovalue curve) and according indifference curves for Home. Depict apoint of optimal consumption for Home.• Now suppose Home imports machinery and exports food. Draw the ac-cording indifference curves for Home and depict a point of optimal con-sumption for Home.• Return to the case of Home being a machinery exporter. The relativeworld-market price of machinery PM/PFrises to 2. How do productionand consumption change? Is an increase in the terms of trade unambigu-ously beneficial (that is, do home consumers necessarily gain in utility)?How would your answer be different if Home were a machinery importerso that its terms of trade fell?• Suppose Home is a large open economy, so that its policies affect relativeworld prices, and a machinery exporter. Machinery production is capital-intensive and Home’s capital endowment increases. Use a relative-supply-relative-demand diagram to show how Home’s terms of trade respond.• Transfer question. Suppose Home is a large open economy, so that itspolicies affect relative world prices, and a machinery exporter. Home sub-sidizes its machinery sector, paying a subsidy on every unit exported (soldabroad). How do Home’s domestic relative prices change? How are Home’sterms of trade affected? Explain why domestic and world market relativeprices change in opposite directions. How is Home’s welfare affected?• Transfer question. Suppose Home is a machinery exporter. Home now alsoimposes a tariff on its imports so that internal (domestic) relative pricesare the same as they were under undistorted trade. How are Home’sterms of trade affected? Does it matter whether Home is a small or largeeconomy? What is the effect on Home welfare?12 Intraindustry TradeMonopolistic chair makers produce with a total cost functionTC = F + c · QC,where F = 500, 000 and c = 100.• What are the average and marginal cost functions of a chair maker?Each of n chair makers faces residual demand ofQdC= S · [1/n − b · (PC−¯PC)],where S = 50 , 000, b = 1/1, 000 and¯PCis average equilibrium price.• What are marginal revenues? [Hint : You may use the formula in thetextbook. Otherwise, reformulate demand so that PM= PM(QdM) andderive total revenue; differentiate total revenue with respect to quantity.]• Graph the average-cost-variety (CC) and the price-variety (P P ) schedulesfor this industry in a diagram that shows price, average cost and thenumb er of firms (varieties).• Find the number of firms (varieties) in this industry in the absence oftrade. What is price in a symmetric autarky equilibrium?• Chairs can be traded with other countries at not cost. Using the average-cost-variety (CC) and the price-variety (P P ) schedules above, show howequilibrium price and the equilibrium number of firms change after trade.• How could you measure the gains from trade? Explain briefly.3 Monopolistic Competition and DumpingA machinery monopolist produces with a total cost functionTC = F +c2· (QM)2,where c = 1/150. You may suppose that F = 0.• What are the monopolist’s average and marginal cost functions?Demand for machines at Home isQdM= S − Sb · PM,where S = 50, 000 and b = 1/1, 000. World demand is perfectly elastic at aworld-market price of P∗M= 500.• What are the monop olist’s marginal revenues? [Hint: You may use theformula in the textbook. Otherwise, reformulate demand so that PM=PM(QdM) and derive total revenue; differentiate total revenue with respectto quantity.]2• The monopolist chooses to export at the world-market price P∗M= 500.Determine total output, domestic sales and exports in a suitable graphand show that the monopolist’s best strategy is dumping on the worldmarket.• Use the graph to show that domestic consumers suffer from high monopolyprice. [Hint: Consumer surplus is the area below the demand curve. Drawit before and after dumping.]• Free trade in machinery exposes the domestic monopolist to perfect com-petition at P∗M= 500. Show that Home consumers are better off aftertrade, while the monopolist is worse off. [Hint: Consumer surplus is thearea below the demand curve. Identify consumer rents before and afterfree trade.]• Can the monopolist remain in business if F > 0?4 Horizontal Foreign Direct InvestmentA domestic machinery monopolist faces no competition in the Home market butcan sell to the world market at some price P∗. The monopolist’s total costs areTC =c2· Q2,and domestic demand isQdM= S − Sb · PM,where c = 1/150, S = 50, 000 and b = 1/1, 000.• Calculate, and depict in a price-quantity diagram, the effective marginalrevenues of this monopolist, considering the exporting opportunity.• Calculate, and depict in a price-quantity diagram, the optimal amount ofgoods that the monopolist will choose to sell to the domestic market andthe optimal amount of goods the monopolist will export in the absence oftransportation costs.• Now suppose there are transportation costs τ =12c per unit shipped acrossborders. Calculate and depict monopoly profits from exports. [ Hint:Note that, in contrast to the case in class, these transportation costs willshift and not turn the parent company’s marginal cost curve for exportedgoods.]• Alternatively, the monopoly can open a foreign subsidiary and sell to theworld market from the new location at no transportation cost. Calculateand depict profits at the foreign subsidiary. If there are some fixed coststo open a foreign subsidiary, how large can they be at most to makehorizontal FDI worthwhile?35 Vertical Foreign Direct InvestmentA domestic machinery monopolist faces no competition in the Home marketand a domestic demand functionQdM= S − Sb · PM,where S = 50 , 000 and b = 1/1, 000.The monopolist has three choices to make or buy its product for the domesticmarket.1. To produce at the Home establishment under a cost functionTC1=c2· Q2,where c = 1/150.2. To acquire a Foreign subsidiary and to produce at the foreign locationunder a cost functionTC2=c∗2· Q2,where c∗= c/2 = 1/300.3. To enter a contract with Foreign suppliers but facing hold-up costs sothat the effective