Assignment, Macro & Micro economics

answer all the questions in assignment6.pdf. Try to use numbers instead of words to answer all the questions, like doing a  math problem

1. There are two goods X and Y produced with labor only. The production function of X and Y are X = 2?? and Y = ?? The total amount of labor is 100. (a) Draw the production probability frontier in a diagram. (b) Let X=25 and Y=50. Anna and Bob are sharing the goods. Their utility functions are ?? = ?? 1/2 ?? 1/2 and ?? = ?? 1/3 ?? 2/3 . Suppose the price ratio is given by ?? ?? = 5/4, find the equilibrium allocation. 2. There are only two goods, X and Y, produced in a small country. The production functions for the two goods are X = ?? 1/2?? 1/2 and Y = ?? 1/3?? 2/3 . That is, both goods are produced with labor L and capital K with constant returns to scale technology. The labor endowment in this country is L=100 and capital endowment is K=100. Assume that labor and capital are fully employed to produce these two goods. L and K are perfectly mobile between production of X or Y. (a) Draw the Edgeworth Box for X and Y with labor and capital. What’s the maximum amount of X or Y that can be produced with all the resources? Show the isoquants of the maximum X and the maximum Y. (b) Draw the isoquants of X and Y if half of L and half of K is allocated to each good. Is this allocation pareto efficient, i.e. could you relocate the resource to increase the production of one good without reducing the production of the other good? (c) Find the pareto efficient locus of production and graph it in the Edgeworth box. (d) Suppose the equilibrium price ratio of X and Y is ?? ?? = 1/2, what’s the slope of the PPF at the equilibrium? Illustrate the equilibrium output on the PPF curve and in the Edgeworth box. (e) If labor endowment increases, how will output of X and Y change comparing to the answers in (d)? 3. Find equilibria in the following matrix games. (a) PLAYER 2 L R PLAYER 1 T (1,1) (0,0) B (0,0) (2,3) (b) PLAYER 2 L R PLAYER 1 T (1,1) (2,0) B (0,2) (1,1) (c) PLAYER 2 L R PLAYER 1 T (3,3) (1,2) B (2,1) (0,0) (d) PLAYER 2 L R PLAYER 1 T (1,0) (0,2) B (0,1) (2,0)