Question

Maurice is characterized by the utility function UMwb, wiehilip by U(bP.wP) -bPwP, where bi, i-M,P denotes the number of books that each of them has and wi the number of bottles of wine, respectively. If the bottom-left comer of the Edgeworth box reflects zero consumption for Maurice and the number of books is measured along the horizontal axis, the contract curve will contairn a) the Edgeworth box diagonal b) a straight segment with a slope of 1 including the bottom-left corner of the Edgeworth box c) a straight segment with a slope of 1 including the upper-right corner of the Edgeworth box d a curve with a slope increasing as one shifts to the right e) a curve with a slope decreasing as one shifts to the right

Answer 1

For Maurice, U_M = 6 b_M + 6 W_M For Philip, U_P = b_p W_p Where b_i and W_i denote the number of books and for i = M and P. Contract curve in the set of parts efficient allocations. H's equation is obtained by equating MRS (Marginal rate of substitution) for Maurice and MRS of Philip to obtain interior pointer of parts set. Maurice MRS_b, w = dU_M/db_M/dU_M/dW_M = 6/6 = 1 Philip MRS_b, w = dU_P/db_P/dU_P/dW_P = W_P/b_P W_P/b_P = 1 = > W_P = b_P w.r.t O_2 (origin for Philip). interior points are given by corner solution as clear from the following graph - Thus contract curve starts with a zero slope and then slope increase to 1 after a certain point as one shifts to the right. Correct Ans - D

Correct Ans - D