During the war, the same arms merchant often sells weapons to both sides of the
ID: 1108638 • Letter: D
Question
During the war, the same arms merchant often sells weapons to both sides of the conflict. In this situation, a different price could be offered to each side because there is no danger of resale. Suppose a US arms merchant has a monopoly of a special air-to-sea missiles and is willing to sell them to both India and China. India's demand for missiles is P = 820 - 1.5x and China's is P = 1010 - 2.5y, where P is in millions of dollars. The marginal cost of missiles is MC = 2Q, where Q = x + y. How many missiles will be sold to each country and what price will be charged to each country? Show your work in details. (2+2+2+2+6 = 14 points)
Explanation / Answer
India's demand for missiles is as follows -
P = 820 - 1.5x
Total revenue from India is as follows -
TR = P * x = (820 - 1.5x) * x = 820x - 1.5x2
MR = dTR/dx = d(820x - 1.5x2)/dx = 820 - 3x
MC = 2Q = 2x + 2y
Equating MR and MC to ascertain profit-maximizing quantity sold to India,
MR = MC
820 - 3x = 2x + 2y
5x + 2y = 820
2y = 820 - 5x
y = 410 - 2.5x
China's demand for missiles is as follows -
P = 1010 - 2.5y
Total revenue from China is as follows -
TR = P * y = (1010 - 2.5y)y = 1010y - 2.5y2
MR = dTR/dy = d(1010y - 2.5y2)/dy = 1010 - 5y
MC = 2Q = 2x + 2y
Equating MR and MC to ascertain profit-maximizing quantity sold to China,
MR = MC
1010 - 5y = 2x + 2y
7y + 2x = 1010
7(410 - 2.5x) + 2x = 1010 ....y = 410 - 2.5x
2870 - 17.5x + 2x = 1010
-15.5x = -1860
x = 1860/15.5 = 120
y = 410 - 2.5x = 410 - (2.5 * 120) = 410 - 300 = 110
So,
Merchant will sell 120 missiles to India.
P = 820 - 1.5x = 820 - (1.5 * 120) = 640
Merchant will charge $640 million per missile from India.
Merchant will sell 110 missiles to China.
P = 1010 - 2.5y = 1010 - (2.5 * 110) = 735
Merchant will charge $735 million per missile from China.
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