Question 1: Two firms together employ 100 units of labor and 100 units of capital. Firm 1 currently employs 20 units of labor and 80 units of capital, while Finn 2 employs 80 units of labor and 20 units of capital. At this current allocation, the marginal products of the firms are as follows: for Finn 1, MPL1= 50 and MPk1 = 50; for Firm 2. MPL2 = 10 and MPk2 = 20.
a) Is the current allocation of inputs economically efficient? If not, in which direction should the firms change their allocation of labor and capital [ie. which firm should get more capital, and which one should get more labor]?
b) Now suppose that both firms have linear production functions, so that the marginal products listed above are true for all levels of labor and capital. Suppose also that the total amounts of labor and capital are fixed at 100. Draw an Edgeworth box showing both firms' isoquants relevant to the initial allocation [L1=20, K1= 80, L2 = 80, K2=20] and indicate the set of allocations that would represent a "Pareto improvement" (i.e. higher production for both firms). Finally, describe the input contract curve for this economy.
Question 2: Suppose that a small economy's production possibility frontier for chocolate (X) and raspberries (Y) is given by the equation X2 + 2Y2 = 60000.
a) Sketch this PPF m a diagram. Write down an expression for the marginal rate of transformation of chocolate for raspberries.
b) If every individual in this economy has preferences summarized by the utility function U(X,Y)=X+Y, then how much of each good will be produced in a general competitive equilibrium? What do we know about the relationship between the prices of chocolate and raspberries, px and pr, in this equilibrium? Show your answer on the diagram from part a).
c) Repeat your analysis from part b), now assuming that every individual has the utility function U(X,Y)=Min(X,2Y). Illustrate your answer in a new diagram.