The firm \"Talbots & Co.\" faces the following cost function c(x) = 11.5x 2 + 70

Question

The firm "Talbots & Co." faces the following cost function

c(x) = 11.5x2 + 70

where c is the total production cost and x is the quantity produced.

The quantity they can sell depends on the price they charge: the lower the price, the more they will sell. Equivalently, the price they can charge depends on the quantity they want to sell, giving rise to the following relation between price and quantity

p(x) = 1,000 - x

where p is the price that "Talbots and co." charges for its product.

Answer the following questions about this firm.

What is the profit-maximizing level of output for this firm?

What is the maximum profit that this firm can make?

Explanation / Answer

C = 11.5X2 + 70

MC = 23X

P = 1,000 - X

TR = P * X = 1,000X - X2

MR = 1,000 - 2X

The profit maximizing condition is

MR = MC

1,000 - 2X = 23X

25X = 1,000

X = 1,000 / 25 = 40 (This is profit-maximizing level of output)

P = 1,000 - X = 1,000 - 40 = $960

Profit = TR - TC

         = ($960 * 40) - (11.5(40)2 + 70)

        = 38,400 - 18,470

        = $19,930

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