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.

(a) What is the revenue function for the firm "Talbots and co."?

(b) the marginal cost is equal to?

(c) the marginal revenue is equal to?

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

(e) What is the maximum profit that this firm can make?

Explanation / Answer

a) Revenue is the product of price and quantity.
r = 100x - x2

b) MC = 23x

c) mr = 100 - 2x

d) mr = mc
100 - 2x = 23x
x = 4

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