Question

A. In an exchange economy, person A is endowed with 120 units of good x (and none of good y), and person B is endowed with 120 units of good y (and none of good x). A has utility UA(x, y) = x + y and B has utility UB = min{x, 2y}. At the competitive equilibrium, what is the value of xA?

B. In an exchange economy, two traders A and B have utility functions over two goods 1 and 2. Their utility functions are given by UA(x1, x2) = x1x2 and UB(x1, x2) = 2x1 + x2 and they are endowed with ωA = 6, 2 and ωB = 4, 8 respectively. What is the equilibrium price of good 1? (Assume p2 = 1.)

Answer 1

Person A's competitive equilibrium is achieved by allocating all their endowment to good x.

Step-by-step explanation:

In an exchange economy, for person A to have a competitive equilibrium, their utility should be maximized given their endowment and the prices of goods x and y. Since A's utility function is UA(x, y) = x + y, and they are endowed with 120 units of good x, their utility is maximized when they allocate all their endowment to good x. Therefore, xA = 120 units.