Economics math question

2008-08-02 10:49 am

Total Revenue (TR) = 25Q- 0.05Q^2

Total Cost (TC) = 80+ 5Q+ Q^0.4

Marginal Cost (MR) = 5+ 0.4Q

Demand Function is Q = 500- 20P

What is the Marginal Revenue(MR) function?
What are the profit-maximizing price and output?
Depict answer in a relevent diagram.
Also, calculate the total profit under the profit-maximizing output.

回答 (1)

garlic2010

2008-08-03 2:06 am

✔ 最佳答案

MR falls twice as fast as demand, the slope of MR is twice that of demand.

D function Q = 500 - 20P or P = 25 - 0.05Q
MR function therefore is P = 25 - 0.1Q
because the slope of MR is twice that of demand.

Profit maximizing output is where MC = MR
MC is C = 5 + 0.4Q
MR is P = 25 - 0.1Q
MC = MR --> 5 + 0.4Q = 25 - 0.1Q
Profit maximizing output Q = 40
Put Q in the demand function to get the profit maximizing price
40 = 500 - 20P
Profit maximizing price P = 23

TR = 25(40) - 0.05(40) ^ 2 = 996
TC = 80 + 5(40) + (40)^0.4 = 284.37
Total Profit = 996 - 284.37 = 711.63

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