Question

c). x 100x 20,000 7. If a cocoa shipping firm sells Q tons of cocoa in the UK, the price received is given by PE-al-1Q 0n the other hand, if it buys Q tons from its only source in Ghana, the price it has to pay is given by Pc -a Q. In addition, it costs y per ton to ship cocoa from its supplier in Ghana to its customers in the UK (its only market). The numbers ar, a2, and y are all positive. a. Express the cocoa shipper's profit as a function of Q, the number of tons shipped. b. Assuming that a - a2 y 0, find the profit-maximizing shipment of cocoa.

Answer 1

a) The profit of shipping firm is pi = P_E Q - P_G Q - y Q = a_1 Q - 1/3 Q^2 - a_2 Q - 1/6 Q^2 - y Q Therefore pi = (a_1 - a_2 - y) Q - 1/2 Q^2 b) The profit maximizing FOC yield d phi/d Q = a_1 - a_2 - y - Q = 0 Therefore Q^* = a_1 - a_2 - y