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  1. (15 points) Maximizing Profits

See Lecture 13

 

For the following profit functions, calculate the marginal profit functions and find the Q* that maximizes profits (i.e., the Q* so that marginal profits are equal to 0).

 

Remember that quantities must be greater than or equal to 0 (no negative quantities!)

 

a. (3 points)  Π(Q)=17,136Q-7Q^2

 

 

b.(3 points) Π(Q)=1215Q-0.05Q^3

 

 

 

c. (3 points) Π(Q)=1,984Log(Q)-16Q

 

Note: Log (Q) denotes the natural log of Q (Ln on calculator)

d. (3 points) Π(Q)=15475Q-0.001e^0.25Q

 

e. (3 points) Π(Q)= 166,410Log(Q)-5Q^2

 

 

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Related questions

(Please show as much work as possible)

 

1. You are bidding in a second-price auction for a painting that you value at $800. You estimate that other bidders are most likely to value the painting at between $200 and $600. Which of these is likely to be your best bid?

a. $1,000

b. $800

c. $600

d. $400

 

2. Which of the following is true about different ways of conducting a private-value auction?

a. A first-price auction is strategically equivalent to a second-price auction.

b. A first-price auction is strategically equivalent to an English auction.

c. A second-price auction is strategically equivalent to an English auction.

d. None of the above

 

3. Suppose that five bidders with values of $500, $400, $300, $200, and $100 attend an oral auction. Which of these is closest to the winning price?

a. $500

b. $400

c. $300

d. $200

 

4. In the above auction, if the bidders with the first- and third-highest values ($500 and

$300) collude, which of these is closest to the winning price?

a. $500

b. $400

c. $300

d. $200

 

5. If a seller is concerned about collusion among bidders, which of the following changes to the auction, should the seller make?

a. Hold frequent, small auctions instead of infrequent large auctions.

b. Conceal the amount of winning bids.

c. Publically announce the name of each auction's winner.

d. Hold a second-price instead of a first-price auction.

 

6. You're holding an auction to license a new technology that your company has developed. One of your assistants raises a concern that bidders' fear of the winner's curse may encourage them to shade their bids. How might you address this concern?

a. Release your analyst's positive scenario for the technology's future profitability.

b. Release your analyst's negative scenario for the technology's future profitability.

c. Use an oral auction.

d. All of the above

 

7. In a first-price auction, you bid ________ your value, and in a second-price auction you bid _________ your value.

a. at; above

b. below; above

c. below; at

d. below; below

8. You hold an auction among three bidders. You estimate that each bidder has a value of either $16 or $20 for the item, and you attach probabilities to each value of 50%. What is the expected price? If two of the three bidders collude, what is the price?

9. In Sweden, firms that fail to meet their debt obligations are immediately auctioned off to the highest bidder. (There is no reorganization through Chapter 11 bankruptcy.) The current managers are often high bidders for the company. Why?

10. When a famous painting becomes available for sale, it is often known which museum or collector will be the likely winner. Yet, representatives of other museums that have no chance of winning are actively wooed by the auctioneer to attend anyway. Why?

 

11. The deities Mars and Venus often do battle to create the weather conditions on Earth. Venus prefers extreme temperatures (especially heat), while Mars prefers temperate conditions. The payoffs (expressed in Points of Wrath) are given below.

 

 

Venus

 

 

Warm

Chill

Mars

Warm

20 , 0

0 , 10

Chill

0 , 90

20 , 0

What is the unique mixed-strategy equilibrium of the above game?

(Let p be the probability of "Warm" for Mars, and q the probability of "Warm" for Venus.)

a) p=9/10, q=1/2

b) p=1/2, q=1/10

c) p=1/2, q=1/2

d) p=1/10, q=1/10

Player 2

 

 

H

D

Player 1

H

0 , 0

4 , 1

D

1 , 4

2 , 2

 

12. The above game is the title of the hawk-dove game and used by evolutionary biologists to describe evolutionary processes. It is also used to model how a business should grow. In the above game, what is the Nash equilibrium in pure strategies and mixed strategies.?

Assume the cost of producing the goods is zero and that each consumer will purchase each good as long as the price is less than or equal to value. Consumer values are the entries in the table.

 

Good 1

Good 2

Consumer A

$2,300

$1,700

Consumer B

$2,800

$1,200

 

13. Suppose the monopolist only sold the goods separately. What price will the monopolist charge for good 1 to maximize revenues for good 1?

a. $2,300

b. $2,800

c. $1,200

d. $1,700

14. What is the total profit to the monopolist from selling the goods separately?

a. $4,500

b. $6,300

c. $7,000

d. $6,000

15. What is a better pricing strategy for the monopolist? At this price, what are the total profits to the monopolist?

a. Bundle the goods at $2,800; Profits = $5,600

b. Bundle the goods at $4,000; Profits = $8,000

c. Charge $2,800 for good 1 and charge $1,700 for good 2; Profits = $4,500

 

d. Charging the lowest price for each good individually is the best pricing strategy; Profits = $7,000

 

16. The prisoners' dilemma is an example of

a. a sequential game.

b. a simultaneous game.

c.a shirking game.

d. a dating game

 

17. Nash equilibrium

a. is where one player maximizes his payoff, and the other doesn't.

b. is where each player maximizes his own payoff given the action of the other player.

c.is where both players are maximizing their total payoff.

d. is a unique prediction of the likely outcome of a game.

 

MULTIPLE CHOICE.

1) Which of the following is true of the typical relationship between marginal product (MP) and average product (AP)?

A) The AP curve intersects the MP curve at minimum MP.

B) If MP is less than AP, then AP is increasing.

C) If MP is greater than AP, then AP is falling.

D) The MP curve intersects the AP curve at maximum AP.

TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false.

2) If, for a particular short-run production, we observe that marginal product is decreasing we can conclude that average product is decreasing as well.

MULTIPLE CHOICE.

3) An implicit cost is defined as:

A) the amount by which the money spent on an input to production exceeds its opportunity cost.

B) the difference between an input's explicit cost and its actual cost.

C) the opportunity cost of using a resource that is not explicitly paid out by the firm.

D) the amount by which economic profit exceeds accounting profit.

MULTIPLE CHOICE.

4) The amount of output a firm can produce with a given quantity of fixed and variable inputs is called:

A) total fixed product.

B) average variable product.

C) marginal product.

D) total product.

5) Which of the following statements is true of the relationship among the average cost functions?

A) AFC = ATC + AVC

B) ATC = AFC - AVC
C) AVC = AFC + ATC

D) AFC = ATC - AVC

 

TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false.

6) A firm's production function is the relationship between the factors of production and the resulting outputs of the production process.

MULTIPLE CHOICE.

Scenario 2:
Output (Q): 0 1 2 3 4 5 6

Total Cost (TC): $24 $33 $41 $48 $54 $61 $69

7) Refer to Scenario 2. Diminishing marginal returns starts to occur between units:

A) 2 and 3.

B) 3 and 4.

C) 4 and 5.

D) 5 and 6.

8) Which of the following would be classified as a short-run decision?

A) trucking firm's decision to move to a smaller facility.

B) A firm's decision to decrease the amount of electricity used in day-to-day operations by encouraging employees to adopt conservation strategies, e.g., shut off lights when leaving a room.

C) A university's decision to add a new residence hall.

D) A restaurant's decision to increase the number of patrons it can accommodate by adding on a new dining room.

9) Economic profit is equal to the difference between: 9)

1.

2.

3.

4.

TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false.

10) At the point where a firm incurs diminishing marginal returns, total product will begin to decline.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

11) In the context of a production function, the remote order takers in the fast food industry would be classified as:

A) a fixed input.

B) a marginal input.

C) an inframarginal input.

D) a variable input.

Scenario 3:
Total Product (Q): 0 1 2 3 4 5 6

Total Cost (TC): $50 $80 $105 $125 $155 $195 $250

12.

13.

increase; lower

decrease; lower

increase; higher

decrease; higher

 

TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false.

14.

15.

 

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

16) A labor-intensive method of production is one that:
A) combines a small but sophisticated labor force with a large amount of capital.

B) requires employees to work harder than they would in other occupations.
C) relies on large quantities of labor and smaller quantities of capital equipment. D) relies exclusively on labor.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

17) Assume a firm produces 500 units of a good by using two inputs, capital and labor, whose per unit prices are $10 and $4. Assume also that the marginal physical product of the last unit of capital is 30 and the marginal physical product of the last unit of labor is 10. To minimize costs this firm should employ:

A) more labor and less capital. B) more capital and less labor.
C) the existing combination of resources. D) both more labor and more capital.

TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false.

18) All else constant, a decrease in the per unit price of labor would create an incentive for a firm manager to substitute labor for capital in the firm's production process.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

19) All else constant, as the price of petroleum increases relative to the prices of other inputs to the production process, in their effort to minimize their total costs of production, we can expect to see firms employ:

A) the same amount of petroleum since there are no substitutes for petroleum. B) less petroleum and more of the other inputs to production.
C) less of each of the inputs of production.

D) more petroleum and less of the other inputs to production.

1.

A consultant has advised Consolidated Fish, Inc., a perfectly competitive firm, that it should cut back its production in order to increase its profits. We can conclude from this that

CF's total costs must be greater than its total revenues.

CF's marginal cost must be greater than the price of its product.

CF's costs are increasing at a rate less than its revenues.

fixed costs are not being covered and CF should shut down.

2.

If marginal cost is equal to marginal revenue

the firm should hold output constant.

the firm should expand output.

there is no way to determine if the firm should expand output, contract output, or hold output constant.

the firm should contract output.

3.

Which statement is true?

The minimum point on the firm's marginal cost curve is the shutdown point.

The minimum point on the firm's average variable cost curve is the shutdown point.

The minimum point on the firm's average total cost curve is the shutdown point.

The minimum point on the firm's marginal cost curve is the break-even point.

4.

As output expands beyond the break-even point, the vertical distance between the AVC and ATC will

remain constant.

get smaller.

get larger.

5.

Total revenue divided by output equals

average variable cost.

marginal cost.

price.

average total cost.

6.

A monopoly firm selling mustache wax to vain men in a small town is currently maximizing profits by charging a price of $5. It follows that the marginal cost of mustache wax

is equal to $5.

is greater than $5.

is less than $5.

None of these choices are true.

7.

A firm can sell 14 units at $18, but to sell 15 units, the firm must cut the price to $17. The marginal revenue derived from selling the 15th unit is

-$18

$3

$17

0

8.

If total revenue is increasing as output is rising, then

marginal revenue must be greater than zero.

marginal revenue must be less than zero.

marginal revenue must be equal to zero.

price must be increasing.

9.

Firms that had virtual monopolies, that is control over at least 80 percent of industry production, because of control over an essential resource include all of the following except

the DeBeers Diamond Company.

the Standard Oil Company.

the Ford Motor Company.

the International Nickel Company.

10.

Which statement is true?

None of these statements are true.

Most natural monopolies are government regulated or government owned.

All monopolies are bad.

All monopolies are good.

11.

Which is the most accurate statement?

There are virtually no oligopolies in the U.S.

The most important aspect of oligopoly is product differentiation.

There are a whole range of oligopolistic models, from a cartel to cutthroat competition.

An oligopolistic industry cannot have more than five firms

12.

Oligopolists have more control over prices than monopolistic competitors because

their prices are always set by the government.

since an oligopolist is the only competitor in the market, setting prices is no problem.

they can legally collude whereas monopolistic competitors may not.

with fewer competitors, they are able to monitor and determine their own prices much easier.

13.

The definition of monopolistic competition differs from that of perfect competition

in neither the number of firms nor the type of product.

in both the number of firms and the type of product.

with respect to the type of product.

with respect to the number of firms in the industry.

14.

The typical monopolistic competitor

may compete on the basis of physical differences, convenience, service, and ambience.

always competes on the basis of producing a product that is physically different from those of its competitors.

never uses price discrimination.

is a large firm.

15.

Which statement is true?

The monopolistic competitor may make a profit in the long run.

The monopolistic competitor has a perfectly elastic demand curve.

None of these statements are true.

The monopolistic competitor operates at the minimum point of her ATC curve.

16.

Which statement is true about the monopolistic competitor in the long run?

It will be breaking even.

It will be making a profit.

It may be making a profit or taking a loss.

It will be taking a loss.

17.

Which statement is true?

Most monopolistic competitors are large firms.

Monopolistic competitors produce goods or services for which there are no close substitutes.

None of these statements are true.

Monopolistic competitors usually operate at the minimum point of their average total cost curves.

18.

Which statement is false?

As the price of a good rises the consumer surplus decreases.

A person would maximize her total utility when she had no consumer surplus.

We will consume a service when its marginal utility is equal to its price.

A product's utility to a buyer is measured by how much the buyer is willing to pay for it.

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