Problem
Consider the following economy, with two consumers and two commodities. Consumer 1 has the endowment vector, ω1 = (1,1) and the utility function: U1(x1) = ln(x11) + A*ln(x12) where A is a positive constant. Consumer 2 has the endowment vector, ω2 = (1,1) and the utility function: U2(x2) = ln(x21) + ln(x22)
i. Define a competitive equilibrium for this economy.
ii. Calculate the competitive equilibrium price vector as a function of the parameter A.
iii. For what value of A is (x11, x12) = (1/2, 3/2) on the contract curve?