Question

Hans Gruber is a purveyor of fine chocolates. He sells a regular dark chocolate gift pack and an organic dark chocolate gift pack. The inverse demand function for the regular gift pack is P_R = 150 – 6Q_R and the inverse demand for the organic gift pack is P_O = 130 – 2Q_O. Assume that the marginal costs are given by MC_R = 20 and MC_O = 40.

A. Based on this information, what is the optimal price of the organic gift pack that will maximize the profit

B. What is the optimal quantity of the regular gift packs?

Answer 1

a) From inverse demand function we found marginal revenue function, with same intercept and twice the slope, as MO = 130 - 4QO. Using MR = MC we have 130 - 4QO = 40 or QO = (130 - 40)/4 = 22.5 units. The optimal price of the organic gift is thus, PO = 130 - 2*Q = $85.

b) From inverse demand function we found marginal revenue function, with same intercept and twice the slope, as MR = 150 - 12QR. Using MR = MC we have 150 - 12QR = 20 or QR = (150 - 20)/12 = 10.83 units. The optimal price of the regular gift is PR = 150 - 6*Q = $85