There are two consumers A and B with the following u functions and endowments U(XX) = alnx} + (1-a)nX WA (0,1)
U(XX)= min(XX) WB (1.0)
Calculate the market clearing prices and the equilibrium
allocation
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.