Question

Let Antonio and Kate’s preferences be represented by the utility functions, uAntonio(x1, x2) = 9((x1)^2)(x2) and uKate(x1, x2) = 17(x1)((x2)^2), where good 1 is Starbursts and good 2 is M&M’s. Antonio’s endowment is eA = (24, 0) and Kate’s endowment is eK = (0, 200). Antonio and Kate will exchange candy with each other using prices p1 and p2, where p1 is the price of one starburst and p2 is the price of one M&M.

a) Determine Antonio’s and Kate’s optimal consumption bundles xA* = (x1A*, x2A*) and xK* = (x1K*,x2K*) as a function of the exchange rate, pˆ=p1/p2. (Go back to consumer theory).

b) General equilibrium requires that xA* + xK* = eA + eK = (24, 200) (that is, total demand in
each market equals supply). Solve for the general equilibrium exchange rate pˆ = p1/p2.
  
c) In an (x1,x2) diagram, illustrate Antonio’s budget line, initial endowment, eA, and optimal consumption bundle, xA*. Draw indifference curves through each of the points eA and xA*. Has the exchange with Kate made Antonio better off? Similarly, is Kate made better off by trading with Antonio?

d) Consider the allocation xK = (24, 200) and xA = (0, 0). Is this allocation Pareto efficient?

Answer 1