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zysi [14]
2 years ago
5

In a purely monopolistic market with a demand curve P = -Q / 10 + 2000, to maximize profit the firm provides the application at

the output level:
Mathematics
1 answer:
Rudiy272 years ago
7 0

Answer: hello your question lacks some data hence I will be making an assumption to help resolve the problem within the scope of the question

answer:

≈ 95 units ( output level )

Step-by-step explanation:

Given data :

P = 2000 - Q/10

TC = 2Q^2 + 10Q + 200 ( assumed value )

<u>The output level where a purely monopolistic market will maximize profit</u>

<u>at MR = MC </u>

P = 2000 - Q/10 ------ ( 1 )

PQ = 2000Q - Q^2 / 10 ( aka TR )

MR = d (TR ) / dQ = 2000 - 2Q/10 = 2000 - Q/5

TC = 2Q^2 + 10Q + 200 ---- ( 2 )

MC = d (TC) / dQ = 4Q + 10

equating MR = MC

2000 - Q/5 = 4Q + 10

2000 - 10 = 4Q + Q/5

1990 = 20Q + Q

∴ Q = 1990 / 21 = 94.76 ≈ 95 units ( output level )

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