4. Let the endowment of the two agents A and B be L014 2 L013 2 10 and w; = w; = 10. Let good 2 be the numeraire. Derive the equation of the contract curve and the budget line and plot them in an Edgeworth box for the following combinations of utility functions of the the two agents. What is the competitive equilibrium relative price of good 2, p, and the allocation, [(9114, 23?), ($1113, 2323)] for the following combinations of utility functions of the the two agents. (Note: You don't have to derive the Cobb-Douglas demand functions. You can directly use them.) (a) (4) U (3114,3124) = (93'1\")0'5(33'2\")0'5 and U(w'1B,$)= (mf)'5(m25)'5 (b) (4) U ($14,213) = ($14)'25(m4)'75 and U03? =sz) = (w?)'25($23)'75 (C) (4) U ($14,111?) = (-'IC'1\")'5(33'2\")0'5 and U (at? #623) = (mf)'25(m23)'75