Problem Set 7 - AnswersEcon 441 Alan DeardorffFall Term 2008 Problem Set 7 - AnswersPage 1 of 7Problem Set 7 - AnswersTopics in Trade Policy1. The figure below shows domestic demand, D, for a good in a country where there is a single domestic producer with increasing marginal cost shown as MC. Imports of the good are available from abroad at a fixed price p*, subject to a tariff of either t1 or t2, which are indicated by the points p*+t1 and p*+t2 on the vertical axis. Suppose now that domestic demand for the good expands, for each price, to 25% more than it was before, so that the demand curve shifts out to D' as shown, its vertical intercept remaining the same. Determine how profits of the firm, and tariff revenue of the government, will be affected by this change.For the case of the lower tariff, t1, shown above, the firm cannot charge a price higher than p*+t1, since consumers would otherwise buy from abroad, and it therefore cannot charge the monopoly price that would equate marginal revenue to marginal cost if there were no trade. The marginal revenue curves are drawn in above, but they are irrelevant. On the other hand, the firm can sell all it wants to at price p*+t1, since its marginal cost rises to equal p*+t1 at output Q1, which is less than demand. So it produces Q1 and sells it domestically, while demanders import the difference, M1=D1–Q1. When the demand curve shifts out to D', this does not change the firm’s marginal cost curve or the highest price that it can charge, p*+t1, so it also does not change its output. Output remains Q1, and the firm’s profit is unchanged. Meanwhile, however, imports increase from M1 to M1' = D1'–Q1, and since the size of the tariff is unchanged, the government collects more tariff revenue. D D' Q p* p*+t1 p MC MR MR' Q1 D1 D1' M1 M1'Econ 441 Alan DeardorffFall Term 2008 Problem Set 7 - AnswersPage 2 of 7For the case of the higher tariff, t2, shown below, the firm still cannot charge more than p*+t2, but now it cannot sell all it would want to produce at that price. Its only choices are to sell what it can domestically at p*+t2, or reduce price below that in order to sell more. Since its monopoly price pM, where MR=MC, is above p*+t2, however, lowering its price would only decrease its profits. Therefore it limits production to Q2, which is equal to domestic demand at that price, and it serves the entire domestic market. Now, when demand expands to D', it is able to sell more, andit does, producing and selling Q2'=D2', therefore making a larger profit. Imports are zero in both cases, so the government earns no tariff revenue in either case.2. Consider the Cournot Export Duopoly Model – two identical firms from different countries producing and selling a homogeneous product into (only) a third country and engaged in Cournot competition – and suppose that the governments of both producing countries were to consider providing subsidies for their exports of the good. Using an analysis similar to what we did in class for optimal tariffs and retaliation in competitive markets, determine what you can about the Nash equilibrium export subsidies and the well being of the two exporting countries in that Nash equilibrium compared to free trade. Also, how does welfare in the third (importing) country compare at that equilibrium to what it would have been with free trade?The reaction curves (i.e.,best-response curves) of the two firms in the Export Duopoly Model, together with their iso-profit curves, show us that for any given level of export subsidy by one firm’s government, and thus a given reaction curve for that firm, the other firm’s profit will rise to a maximum and then fall if it is able to move D D' Q p* p*+t2 p MC MR MR' Q2=D2 Q2'=D2' pM pM'Econ 441 Alan DeardorffFall Term 2008 Problem Set 7 - AnswersPage 3 of 7the equilibrium along the other’s reaction curve in the direction of larger output for itself. For example, in the diagram below, the profit of the home firm starting at the Nash equilibrium EN, rises from πxN to πxS and then falls as we move down and to the right along the foreign firm’s reaction curve, Ry from EN to ES and then on to E2 . Likewise, from the iso-profit curves for the foreign firm, we can see that this same movement reduces the profit of the foreign firm.Together with the analogous facts for movements along the home firm’s reaction curve from the perspective of the foreign firm, these results tells us what we need to know about how the two governments’ subsidies affect the profits of their national firms, not counting whatever they get in subsidy from their governments. And, since in the export duopoly model the countries do not consume the good, these profits are therefore equal to the benefits to their countries as a whole. We can then infer how national welfare in each country depends on the two levels of subsidy.That is, in the figure above, if the foreign country’s subsidy s*=0, then the home country would maximize its firm’s profit and therefore its national welfare with a positive subsidy s0. As the foreign country provides a larger subsidy to its firm, the optimal subsidy for the home firm may rise or fall, as represented by the policy reaction curve Rs. At each point along it, by definition, an iso-welfare curve for the home country is horizontal, representing the fact that home-country welfare is maximized there for the given value of the foreign subsidy, and thus for choices alonga horizontal line. Similarly, the foreign government’s optimal subsidy if s=0 is s*0, and its reaction curve Rs* shows it too perhaps varying with the level of the home country’s subsidy. Foreign welfare rises with movements to the left in the figure, and the foreign reaction curve is the collection of points where foreign iso-welfare curves are vertical. y x EN Rx ES E2 Ry πy πx πxS πyN πxNs* s s0 s*0 EN WN W0 W*N W*0 Rs* Rs Econ 441 Alan DeardorffFall Term 2008 Problem Set 7 - AnswersPage 4 of 7Together, the two policy reaction curves tell us that a Nash equilibrium in these export subsidies will have both governments subsidizing their exports. It also tells us, since the iso-welfare curves must cross at that equilibrium (one being vertical andthe other horizontal), that it would be possible to increase the welfare of both countries if they could somehow agree to both reduce their subsidies, perhaps to zero.Neither of