Question

Suppose there are only tuo goods (bananas and fish) and 2 consumers (Annie and Ben) in an ezchange economy. Annie has a utility function ua(b. f) = 'f where b is the amount of bananas she eats and f is the amount of fish she eats. Annie has an endoument of u=7 bananas and w= 3 kilos of fish. Ben has a utility function ug(b. f) 2f+3 log(b) and endounents of u=0 bananas and w4 kilos of fish. Assume the price of bananas is I. (a) Write doum the definition of a competitive equilibrium for this economy (b) Solve for the competitive eguilibrium fish price p; and the competitine eguilibrium allo cation of fish and bananas between Annie and Ben.

Please show all steps so I can fully understand how to solve. Thank you

Answer 1

ا ا = (ماما 47 = ملا 3 - فيها (6) = 3 +2= ( را) ولا I Case (5tos

I Case I P =0, P=0 ( Price & Price bananas f (f fish) hod (Both prices o) In such case and supply is match demand will be infinite ps both limited Demond supply will not No competitive Equilibeium in this case

Case TT same season as bepne Demand will be infinite bi bananas Case π = 1 = 0 - some reason as before Demmand infinite pr fish

Case TV ___ लिया के पुल M - 78 + 3 CAanie's Tincome) M = 4 (Ben's Income) OChandi MRS = 3 2b Demand by Annie 773 CH-4 783 b. 30 - डे

P elta for Demand - supply ba + bB = to 2 (7P13) + 3 an 3 p 6(7P+ 3) + 6 - Bed 42P 9+81 + den het sth dzh ga = e shkoi No CE

Case I MA = 10 -Mo = dim elt. 임 Im ba tbs= 2 bat be = 20 +3= no 3 2 No CE

Case π P = P <1, P 666 MA - 70+ 3 Ме - ч 21T143) 70t3 Same as Case TV No Competitive Equilibrion These is no competitive equilibrium for this