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Economics - Average Cost, Total Cost and Profit Maximization

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1.
A company that manufactures T-shirts produces and sells its products in a perfectly competitive T-shirts market. The manager forecasts the wholesale price of T-shirts next year to be $7.00. The firm's estimated marginal cost is
SMC=12-0.005Q+0.0000008Q^2

where Q is the number of T-shirts produced and sold each month. The Company will have a fixed cost of $2,000 per month.
a. What is:
(i). The total cost function for the company?

(ii). The average total cost function for the company?

(iii). The average variable cost function for the company?

b. At what output level does average variable cost reach its minimum value? What is the value (in dollars) of the average variable cost at its minimum point?

c. How many T-shirts should the company produced and sell each month?

d. What is its monthly profit (loss)?

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Solution Preview

A company that manufactures T-shirts produces and sells its products in a perfectly competitive T-shirts market. The manager forecasts the wholesale price of T-shirts next year to be $7.00. The firm's estimated marginal cost is
SMC=12-0.005Q+0.0000008Q^2

where Q is the number of T-shirts produced and sold each month. The Company will have a fixed cost of $2,000 per month.
a. What is:
(i). The total cost function ...

$2.19