Questions 1. Suppose there is a single country (call it country 1) inhabited by L₁ iden- tical workers. Workers have one unit of time with which to produce and can choose to produce either product A or product B (or split their time between the two). A worker can make ✓ units of product A in a unit of time or units of product B in a unit of time. αβι A1 (a) Define the production possibility set and the production possibility frontier for country 1. (b) Suppose that each worker has preferences U₁(CA1, CB1), where CA1 is the quantity consumed of product A and CB₁ is the quantity con- sumed of product B. Let QA1 and QB₁ denote the quantity produced of products A and B, respectively. i. List the exogenous model parameters. ii. List the endogenous model outcomes. iii. Define the equilibrium. (c) Suppose that U₁(CA1, CB1) = ẞ₁ ln(CA1) + B2 ln(CB1), where ẞ₁ > 0 and B2 0. Find the equilibrium. 2. Now suppose that there is an additional country (call it country 2) inhab- ited by L2 identical workers. As in country 1, workers have one unit of time with which to produce and can choose to produce either product A or product B (or split their time between the two). However, the produc- tivity of workers in country 2 is different: a country 2 worker can make 1 units of product A in a unit of time or units of product B in a unit of time. aB2 (a) Suppose that workers in both countries have identical preferences U(CA, CBI), where i = {1,2} (that is, i is the name of the country). i. List the exogenous model parameters. ii. List the endogenous model outcomes. iii. Define the equilibrium. (b) Suppose that α A1 > αA2 and αB₁ > αB2 (i.e. that country 2 is more efficient at producing both goods). In equilibrium, will it be the case that CA1 > QA1, CA1 A2. In equilibrium, will it be the case that CA1 QA1, CA1 0 and ẞ2 > 0 and i = {1, 2}. i. Suppose that in equilibrium, one country completely specializes in the production of a good, while the other produces some of each good. Which country will be specializing in what good? What will the equilibrium relative price be? Find the equilibrium consumption and production of both goods in both countries. ii. Suppose that in equilibrium, both countries completely specialize in the production of a single good. How much of each good will be produced in the world? Find the equilibrium relative price and the equilibrium consumption of both goods in both countries.