There are two consumers A and B with the following u functions and endowments U(XX) = alnx} + (1-a)nX WA (0,1)

Question

U(XX)= min(XX) WB (1.0)

Calculate the market clearing prices and the equilibrium

allocation

Answer 1

of the good.

The market clearing price is the price at which the quantity demanded by consumer A equals the quantity supplied by consumer B. This is given by the equation:

P = (a*lnX + (1-a)*X)/(1-a)

The equilibrium allocation of the good is given by the equation:

X = exp((P*(1-a)-1)/a)

Therefore, the market clearing price and the equilibrium allocation of the good are given by the equations above.