Suppose Cheese (C) and Watches (W) in Switzerland are produced using only labor and the production functions are: C = 10 /LE W = alw Le and Iw represent labor devoted to the production of cheese and watches, respectively, and o >0 is a constant. Suppose labor supply in the country is fixed at _ = 400, and the utility function of the representative Swiss consumer is U(C. W ) = VCW . Note that this utility function implies that the marginal utility of a Swiss consumer from one extra unit of watch consumption is higher if she has more cheese to consume, which is a natural assumption about Swiss preferences for Cheese and Watches. a) Suppose a = 1. That is, one unit of labor can produce one watch. Derive and draw the Swiss production possibility frontier for watch and cheese production. b) If we now make no assumption about the value of o. Suppose Switzerland didn't sell or buy any Cheese or Watches to other countries. What would be the equilibrium price ratio and equilibrium quantities of Cheese and Watches in the Swiss domestic market? [Note: Your answers will depend on a, which you should treat as an unknown for now. Of course, the solution will require finding the point of tangency between the PPF and the highest feasible indifference curve.] c) How do the equilibrium quantities change when a increases? How does the price ratio change? Notice that you can interpret a as a productivity parameter: when a rises, watchmakers get more watches with the same amount of Ly. In light of this interpretation of o, explain the intuition behind your mathematical results. d) Assume now that Switzerland can trade with other countries - specifically, France. Suppose the French price ratio is /p = 1. At the French price ratio, how much would Swiss consumers want to consume and how much would Swiss producers want to produce of each good? Find consumption bundle (C. W.) and production bundle (C. W). In your solution assume a > 1/4. Can you find the values of a whereby Switzerland will want to export Cheese to France? How about Watches