Question

( I am posting this for the third time. The first time I posted, whoever did it, he did not read the instruction and did not mention the letters with the answer, such as which one is A, B, C, D, E, F, while he was answering. The 2nd time I posted, whoever did it, he had handwritten it. So, I faced difficulty to understand the handwriting. The handwriting was horrible. Please mention the letters with the answers this time and do not handwrite it, PLEASE. Thank you very much for helping me.)

Managerial Economics Question

1. The Poster Bed Company believes that its industry can best be classified as monopolistically competitive. An analysis of the demand for its canopy bed has resulted in the following estimated demand function for the bed:

P= 1760 - 12Q

The cost analysis department has estimated the total cost function for the poster bed as

TC = (1/3)Q^3 - 15Q^2 + 5Q + 24,000

A) Calculate the level of output that should be produced to maximize short-run profits.

B) What price should be charged?

C) Compute total profits at his price-output level.

D) Compute the point price elasticity of demand at the profit-maximizing level of output.

E) What level of fixed costs is the firm experiencing on its bed production?

F) What is the impact of a $5,000 increase in the level of fixed costs on the price charged, output produced, and profit generated?

Answer 1

Part (A)

A monopolistically competitive firm maximizes profit at MR = MC
P = 1760 -12Q

=> TR = PQ

=> TR = (1760 - 12Q)*Q

=> TR = 1760Q - 12Q²

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MR = ΔTR / ΔQ

=> MR = 1760 - 24Q

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TC = (1/3)Q³ - 15Q² + 5Q + 24000

=> MC = ΔTC/ΔQ

=> MC = 3*(1/3)Q^3-1 - 15(2) Q^2-1 + 5

=> MC = Q² - 30Q + 5

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Set MR = MC

=> 1760 -24Q + 5 = Q² -30Q

=> Q² -30Q = 1760 -24Q + 5

=> Q² - 30Q - 1760 + 24Q -5 =0

=> Q² - 6Q -1755 =0

After solving the above quadratic equation, we got two values of Q.

i.e., Q = 45 or Q = -39.

Quantity can't be negative, so profit maximizing quantity is 45 units.

Answer: Profit maximizing quantity is 45 units.

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Part (B)

P = 1760 - 12Q

Put Q =45

=> P = 1760 - 12(45)

=> P = 1760 - 540

=> P = 1220.

Answer: Profit maximizing price level is 1220.

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Part (C)

TR = PQ
=> TR = 1220 * 45

=> TR = 54900

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TC = (1/3)Q³ - 15Q² + 5Q + 24000

=> TC = (1/3)(45)³ - 15(45)² + 5(45) + 24000

=> TC = 30375 - 30375 + 225 + 24000

=> TC = 24225

----

Profit = TR - TC

=> Profit = 54900 - 24225

=> Profit = 30675

Answer: Maximum profit is 30675

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Part (D)

Point Price elasticity of demand (ed) = (ΔQ/ΔP) * (P/Q)

We have, P = 1760 - 12Q

=> ΔP / ΔQ = - 12

=> ΔQ /ΔP = -(1/12)

and

At P = 1220, Q is 45 (i.e., profit maximizing combination of price and quantity)

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ed = (ΔQ/ΔP) * (P/Q)

=> ed = (-1/12) * (1220 /45)

=> ed = -2.26

Answer: Point price elasticity of demand at profit maximizing level of output is -2.26

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Part (E)

TC = (1/3)Q³ - 15Q² + 5Q + 24000

Fixed cost is that part of TC which does not depends on quantity (Q) (or fixed cost is that part of TC which is constant)

So, fixed cost is 24000

Answer: Fixed cost is 24000

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Part (F)

The increase in fixed cost by $5000 will make no change in price charged and output produced. But it will decrease the profit by $5000.

Answer: Price (No change)

Quantity produced (No change)

Profit (Decrease by $5000)