Hans Gruber is a purveyor of fine chocolates. He sells a regular dark chocolate
ID: 1214035 • Letter: H
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 PR = 150 – 6QR and the inverse demand for the organic gift pack is PO = 130 – 2QO. Assume that the marginal costs are given by MCR = 20 and MCO = 40. Based on this information, what are the optimal prices and quantities of each gift pack that will maximize the profit for Hans so he isn’t forced to rob Nakatomi Plaza. (Perfect Compeition)
Explanation / Answer
Given,
PR= 150-6QR
PO= 130-2QO
Hence optimal price is where PR=PQ
150-6Q=130-2Q
20=4Q
Q=5
PR= 150-6x5=120
PQ= 130 -10=120 Hence optimal price= 120 and optimal quantity= 5
We have equilibrium where
MCR = MRR
therefore, 20=150-6Q
130 = 6Q
Q for R= 21.6
Also, for Q,
40=130-2Q
90=2Q
Hence Q=45
Price for R=21x120=2520
Price for O= 45 x 120=5400
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