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."?

Select one:

a. r(x) = 1,000x - x2

b. r(x) = 11.5x3 + 70 x

c. r(x) = 23x

d. r(x) = 1,000 - x - (11.5x2 + 70)

e. r(x) = 1,000x - x2 - (11.5x2 + 70)

f. r(x) = 1,000 - 2x - 23x

(b) the marginal cost is equal to...

Select one:

a. MC = 11.5

b. MC = 1,000 - 2x

c. MC = 23x

d. MC = 31

e. MC = 1,000x

f. minus infinite

g. MC = 23

(c) the marginal revenue is equal to...

Select one:

a. MR = 2x

b. MR = 1,000 - 2x

c. MR = 1,000

d. MR = 1,000 + 2x

e. MR = 1,000x - 25

(d) What does the principle of profit maximization imply?

Select one:

a. Profits are maximized when marginal revenue equals marginal cost.

b. It implies that the firm should maximize profits.

c. The firm faces a trade-off between maximizing profits and minimizing costs.

d. The firm will always want to produce some positive level of output (although in some cases it could be very small).

e. It implies that profits are equal to revenue minus production costs.

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

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

Explanation / Answer

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

TR = P*X, where X is output

P = 1000-X

R = 1000X-X^2

the marginal cost is equal to...

c(x) = 11.5x2 + 70

dTC/dX = 2*11.5X = 23X

the marginal revenue is equal to...

dR/dX = 1000-2X

What does the principle of profit maximization imply?

Profits are maximized when marginal revenue equals marginal cost MR=MC

for this firms profit max position

23X = 1000-2X

25X = 1000

X = 40

P = 1000-40 = 960

c(x) = 11.5x2 + 70 at X = 40

C = 18470

R = 40*960 = 38400

Profits = R-C = 19930

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