ECON 561: International Trade Problem Set 4 Professor Yang Liang Name: RED ID: Preliminaries In the past two weeksI we have learned about the Heckscher-Ohlin model of trade, which is the last comparative advantage model we study in this course. We use both graphical and mathematical tools to see the consequences of trade (the big three theorems). Good luck! Please staple your answers Questions 1. Given production function: Y = LaK, a, H 6 0,1, and determine (a) how is this production function increasing returns to scale (IRS)? decreasing returns to scale (D33) or constant returns to scale (CR3) with respect to L and K , based on the value of a and 6. (You need to give your reasonings) (b) derive marginal product of L and K. Is marginal product of labor increasing as labor increases? why? (c) holding K constant now, and suppose a = 1. now the production function becomes Y = L - K , K is fixed as a constant. Is the production function now IRS, DRS, or CRS? Why? (d) suppose the labor market is competitive; we use is to represent a single worker's wage and p to represent the nal product's price. Derive the wage equation for workers who work for under the above production technology. 2. Suppose, two sectors: Football vs. Soccer; two countries: US vs. Mexico; two factors: labor vs. capital. (standard 2> 0', suppose that Lug = Lng, HUS > Hjugx, and HUS and H ngare not too dissimilar. (a) Draw the equilibrium production possibility frontier for the U.S. and Mexico. How do we see which good the U.S. imports? How do we see that equilibrium condition #2 (consumer optimization) holds? (Graphically show this) (b) Suppose that the population of low skilled workers in Mexico doubles. Using words, gures, math or some combination thereof, show how this will affect the utility of high skilled workers, low skilled workers, and the overall welfare (i.e. the representative agent) in the United States. (c) (bonus) If the population of low skilled workers in Mexico had halved instead of doubled, would your answer just be the opposite of what you said in part (b)? \"'hy or why not