Show the steps or formula to solve the questions.

1. A goatherd has the cost function c(y) = 4y2, where y is the number of

tubs of goat cheese she makes per month. She faces a competitive market

for goat cheese, with a price of $40 a tub. How many tubs should she

produce per month? (hint; you need to figure out the marginal cost

first)

a. The square root of 40

b. 16

c. 5

d. The square root of 10

e. 2.50

2. A competitive firm has the short-run cost function c(y) = 2y3 16y2 +

128y + 10. The firm will produce a positive amount in the short run if and

only if the price is greater than

a. $192.

b. $48.

c. $99.

d. $96.

e. $95.

Hint: figure out the AVC first, then........

3. A competitive firm has the short-run cost function c(y) = 2y3 16y2 +

128y + 10. The firm will produce a positive amount in the short run if and

only if the price is greater than

a. $192.

b. $48.

c. $99.

d. $96.

e. $95.

Hint MC= 6y2-32y + 128

4. The labor supply curve faced by a large firm in a small city is given by w =

60 + 0.05L, where L is the number of units of labor per week hired by the large

firm and w is the weekly wage rate that it pays. If the firm is currently hiring 1,000

units of labor per week, then the marginal cost of a unit of labor to the firm

a. equals the wage rate.

b. is twice the wage rate.

c. equals the wage rate plus $100.

d. equals the wage rate plus $50.

e. equals the wage rate plus $150.

5. A profit-maximizing monopolist faces a downward-sloping demand curve that

has a constant elasticity of 3. The firm finds it optimal to charge a price of $12 for

its output. What is its marginal cost at this level of output? Hint: first set MR=

MC, the substitute MR = P ( 1+ 1/{e}).

a. $5

b. $25

c. $24

d. $8

e. $12

6. An industry has two firms, a leader and a follower.

The demand curve for the industry's output is given by p = 456 6q,

where q is total industry output. Each firm has zero marginal cost. The

leader chooses his quantity first, knowing that the follower will observe

the leader's choice and choose his quantity to maximize profits, given the

quantity produced by the leader. The leader will choose an output of

a. 25.33.

b. 38.

c. 19.

d. 76.

e. None of the above.

Hint MR= 456-12q

7. A monopolist faces a constant marginal cost of $1 per unit and has no

fixed costs. If the price elasticity of demand for this product is constant and equal

to 4, then

a. to maximize profits, he should charge a price of $4.

b. he is not maximizing profits.

c. to maximize profits, he should charge a price of $1.33.

d. to maximize profits, he should charge a price of $1.25.

e. None of the above.

8. A monopolist has discovered that the inverse demand function of a person

with income M for the monopolist's product is p = .002M q. The monopolist is

able to observe the incomes of its consumers and to practice price discrimination

according to income (second-degree price discrimination). The monopolist has a

total cost function, c(q) = 100q. The price it will charge a consumer depends on the

consumer's income, M, according to the formula

a. p = .001M + 50.

b. p = .002M 100.

c. p = M 2 .

d. p = .01M 2 + 100.

e. None of the above.

Hint : MC=100 , MR= 0.002 M-2q.

9. A monopolist sells in two markets. The demand curve for her product is

given by p 1 = 122 2x 1 in the first market and p 2 = 306 5x 2 in the second market,

where x i is the quantity sold in market i and p i is the price charged in market i. She

has a constant marginal cost of production, c = 6, and no fixed costs. She can

charge different prices in the two markets. What is the profit-maximizing

combination of quantities for this monopolist?

a. x 1 = 58 and x 2 = 32.

b. x 1 = 29 and x 2 = 30.

c. x 1 = 59 and x 2 = 29.

d. x 1 = 39 and x 2 = 28.

e. x 1 = 49 and x 2 = 40

10. A competitive firm has to sell its product at its marginal cost ( greater

than the ATC). If the product is sold at $ 40, and the marginal cost of its product is

MC= y 2+ 15- 110, where y is the unit of output. What is the level of output which

will maximize its profit?

a. 10

b. 15

c . 110

d.150

e 40.

11. A price-discriminating monopolist sells in two separate markets such

that goods sold in one market are never resold in the other. It charges p 1 = $5 in

one market and p 2 = $10 in the other market. At these prices, the price elasticity in

the first market is 1.40 and the price elasticity in the second market is 0.10.

Which of the following actions is sure to raise the monopolist's profits?

a. Lower p 2 .

b. Raise p 2 .

c. Raise p 1 and lower p 2 .

d. Raise both p 1 and p 2 .

e. Raise p 2 and lower p 1 .

12. A price-discriminating monopolist sells in two separate markets such

that goods sold in one market are never resold in the other. It charges p 1 = $2 in

one market and p 2 = $8 in the other market. At these prices, the price elasticity in

the first market is 2.20 and the price elasticity in the second market is 0.10.

Which of the following actions is sure to raise the monopolist's profits?

a. Lower p 2 .

b. Raise p 2 .

c. Raise both p 1 and p 2 .

d. Raise p 1 and lower p 2 .

e. Raise p 2 and lower p 1 .

13. A monopolist faces a constant marginal cost of $1 per unit and has no

fixed costs. If the price elasticity of demand for this product is constant and equal

to 3, then

a. to maximize profits, he should charge a price of $1.50.

b. to maximize profits, he should charge a price of $3.

c. to maximize profits, he should charge a price of $1.33.

d. he is not maximizing profits.

e. None of the above.

14. A profit-maximizing dairy farm is currently producing 10,000 gallons of

milk per day. The government is considering two alternative policies. One is to

give the farm a lump sum subsidy of $500 per month. The other policy is to give

the farm a subsidy of $.05 per gallon of output.

a. Both kinds of subsidy will increase production at this farm.

b. Neither subsidy will affect production at this farm, since output is

determined by profit maximization.

c. Production at this farm will be increased if the per-unit subsidy is

adopted but not if the lump sum subsidy is adopted.

d. Which subsidy has the greater effect on production at this farm

depends on whether fixed costs are greater than variable costs.

e. Production will be increased by either kind of subsidy if and only if

there are not decreasing returns to scale

15. The marginal cost curve of a firm is MC = 8y. Total variable costs to

produce 11 units of output are

a. $484

b. $484.

c. $176.

d. $88.

e. $30.

( hint: can you write TC from MC ?)

16. If output is produced according to Q = 4LK, the price of K is $10, and

the price of L is $40, then the cost minimizing cost minimizing combination of K

and L capable of producing 64 units of output is

a. L = 16 and K = 1.

b. L = 2 and K = 8.

c. L = 2 and K = 2.

d. L = 32 and K = 32.

e. L = 1 and K = 16.

17. A firm uses a single input to produce its output, which is sold in a

competitive market. It gets quantity discounts on purchases of its input. If it buys x

units of the input, the price it must pay per unit of input is $3. If it buys no inputs,

it doesn't have to pay anything. The firm's production function is f(x) = 45x x 2 . If

the price of the firm's output is 1, the profit-maximizing amount of input to buy is

a. 21.

b. 0.

c. 42.

d. 31.50.

e. None of the above.

hint: MP= 45-2x

18. A firm uses a single input to produce its output, which is sold in a

competitive market. It gets quantity discounts on purchases of its input. If it buys x

units of the input, the price it must pay per unit of input is 400/x + 4. If it buys no

inputs, it doesn't have to pay anything. The firm's production function is f(x) = 40x

x 2 . If the price of the firm's output is 1, the profit-maximizing amount of input to

buy is

a. 0.

b. 36.

c. 18.

d. 27.

e. None of the above.

Hint: MP = 40-2x.

19. The cheese business in Lake Fon-du-lac, Wisconsin, is a competitive

industry. All cheese manufacturers have the cost function C = Q 2 + 4, while

demand for cheese in the town is given by Q d = 120 P. The optimal level of

output for the firm is

a. 30.

b. 58.

c. 56.

d. 120.

e. 59.

Hint MC= 2Q, First, use inverse demand curve P=120-Q, then derive

MR=120-2Q. Why ??

20. A monopolist faces the inverse demand function described by p = 50

4q, where q is output. The monopolist has no fixed cost, and his marginal cost is

$10 at all levels of output. The optimal level of output for this monopolist is

a. 5

b. 50

c. 4

d. 3

e. None of the above

hint: try to derive MR then set MR=MC.