Homework 1, Econ 437 FA21 . Due by 11:59pm September 21 on CANVAS . Must be submitted as a single document. . Show your work. Full credit requires full explanation Krugman Consider the standard Krugman model. There are two countries, H and F. Expenditure in H is larger than in F, E" = 80 > EF = 40. The demand curve in each country is given by Q; =A(p;) ", where E A = - and o = 2 A firm must pay fixed cost f = 5 to develop its brand and then faces marginal cost c = 2. Initially, the two countries are not trading with each other (closed economy case). 1. Write down the firm's profit equation with the relevant numbers. In your equation, treat A as a constant. 2. Write down the firm's first-order condition for profit maximization. 3. Solve for the firm's optimal price and its quantity sold. 4. Solve for the total number of varieties that must appear in equilibrium in each of the two countries. Now suppose that the two countries allow for free trade between them. Initially there are no trade costs (i.e. 7 = 1). 5. If the countries start trading, what share of each firm's sales will be made in H? 6. Describe how trade has affected welfare. Melitz Consider the Melitz model as described in the Proximity-Concentration note and in the lecture notes. There are two identical countries H and F. 7. Using the equations of the model and the productivity index graph, explain which firms serve the domestic market, who exports, and why. 8. Suppose that trade costs, 7, rise. Taking into account the impact of change in tariffs on competition in each country, show using the productivity index graph what happens to the number of firms that serve the domestic market and the extensive margin (number of firms) of exporting. Use the relevant equations to explain what is causing the lines in the graph to shift. Comment on how the tariffs have affected consumer's welfare. Helpman, Melitz, and Yeaple Consider a world with the two countries H and F. Use the notation from the lecture notes to answer the questions below. 9. Use the equations of the model and the appropriate diagram to explain which H firms choose to open a foreign affiliate in F. Suppose that that the two countries had been involved in a trade war. After an international agreement, both countries choose to lower their tariffs. To answer this question, ignore the effect of changes in competition on demand levels facing firms. 10. Show in the relevant diagram how the tariff reduction affects the number of firms that export and own an affiliate (extensive margins) and the sales per firm of each type (intensive margins). Make clear why the curves are moving the way that they did