The Hawaiian Sea Salt Company sells salt to retail grocery chains in Hawaii and

Question

The Hawaiian Sea Salt Company sells salt to retail grocery chains in Hawaii and on the mainland. The demand function in each of these markets is: Hawaii grocery chains: P1 = 180 – 8Q1 Mainland grocery chains: P2 = 100 – 4Q2 Where P1 and P2 are the prices charged and Q1 and Q2 are the quantities sold in the respective markets. Hawaiian Sea Salt Company’s total cost function for salt is: TC = 50 + 20 (Q1 + Q2) Assuming that the Hawaiian Sea Salt Company is able to charge different prices in the two markets, what are the profit maximizing prices and output levels for sea salt in the two markets? Please explain your answer a. Q1 = 8.75 & P1 = $110 and Q2 = 7.5 & P2 = $70 b. Q1 = 20 & P1 = $100 and Q2 = 20 & P2 = $60 c. Q1 = 10 & P1 = $100 and Q2 = 10 & P2 = $60 d. Q1 = 20 & P1 = $20 and Q2 = 20 & P2 = $20

Explanation / Answer

TR = P1Q1 +P2Q2

TC = 50 + 20 (Q1+Q2)

Totalprofit function = TR-TC

= P1Q1+P2Q2-50-20(Q1+Q2)

= 180Q1 -8Q1^2 + 100Q2-4Q2^2 -50-20Q1-20Q2

=160Q1 -8Q1^2 + 80Q2 -4Q2^2 -50

for hawai grocery chains

profit maximizing quantity is

d(P)//dQ1 =0

160-16Q1=0

Q1 =10 units

P1= 180-80 = 100

for mainland grocery chains

profit maximizing quantty

d(P)/dQ2 =0

80-8Q2 =0

Q2 =10

P2 = 100 - 40 = 60

hense the answer is (c)

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