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Profit max, average cost, long-run equilibrium

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Please help with the following problem. Provide step by step calculations for each problem.

1. The Alpha Company is a member of the lamp industry, which is perfectly competitive. The price of a lamp is $50. The firm's total cost function is:

TC = 1,000 + 20Q +5Q²

Where TC is the total cost (in dollars) and Q is hourly output.

a. What output maximizes profit?
b. What is the firm's economic profit at this output?
c. What is the firm's average cost at this output?
d. If the other firms in the lamp industry have the same cost function as this firm, is the industry in long-run equilibrium? Why or why not?

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Solution Summary

The following problem helps with a macroeconomics problem. It helps calculate output, economic profit and average cost. It also helps with a problem about long-run equilibrium. Step by step calculations are given.

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a) Profit will be maximized when MC=P
To calculate MC, differentiate the TC function by Q, we get MC=20+10Q
So we have 20+10Q=50
Solving we get Q=3

b) Economic Profit = ...

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