maximize utility

ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
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Suppose Tom and Jerry can buy/ sell apples at price Pa and bananas at price Pb. Both are price-takers. Given these prices, they seek to maximize utility by choosing how many apples and bananas to buy/sell.

Tom's utility Ut (At,Bt)= log At + logBt

s.t. Pa(At) + Pb (Bt) = 12 Pa + 6 Pb

Jerry utility Uj (Aj,Bj)= log Aj + logBj

s.t. Pa(Aj) + Pb (Bj) = 9 Pa + 15 Pb

How many apples and bananas should Tom and Jerry consume?

Answer in terms of Pa and Pb

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