Assume Jerry and Tom can buy or sell the apples at price Pa and the bananas at price Pb. Both are price-takers. Given these prices, they seek to maximize utility by choosing determine how many apples and bananas to buy or sell.
Jerry utility Uj (Aj,Bj)= log Aj + logBj
s.t. Pa(Aj) + Pb (Bj) = 9 Pa + 15 Pb
Tom's utility Ut (At,Bt)= log At + logBt
s.t. Pa(At) + Pb (Bt) = 12 Pa + 6 Pb
Calculate how many apples and bananas should Tom and Jerry consume?