Matthew is considering selling a painting in an English auction. There are n bidders whose valuations are distributed independently and uniformly on [vL,vU].
a. What is his expected payoff from the auction?
b. A private buyer is willing to pay (vL+vU)/2. What is the minimum number of bidders required for Matthew to choose the auction rather than sell to the private buyer? (Assume Matthew is risk-neutral.)
Matthew is considering selling a painting in an English auction. There are n bidders whose valuations are distributed independently and uniformly on [vL,vU].
a. What is his expected payoff from the auction?
b. A private buyer is willing to pay (vL+vU)/2. What is the minimum number of bidders required for Matthew to choose the auction rather than sell to the private buyer? (Assume Matthew is risk-neutral.)
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Related questions
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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.
1).
A consumer spends more time searching for a good when her reservation price is:
increased.
reduced.
fixed.
None of the statements is correct.
2).
In the game shown below, firms 1 and 2 must independently decide whether to charge high or low prices.
Which of the following are Nash equilibrium payoffs in the one-shot game?
(0, 0)
(5, -5)
(-5, 5)
(10, 10)
3).
A risk-neutral individual would:
prefer $5 with certainty to a risky prospect with the expected value of $5.
prefer a risky prospect with an expected value of $5 to a certain amount of $5.
be indifferent between a risky prospect with an expect value of $5 to a certain amount of $5.
prefer a risky prospect with the expected value of $0.50 to $5 with certainty.
4).
Snowpeak Ski Resort offers a price for a lift ticket that is barely over its marginal cost, but the high equipment rental fee keeps generating big profits. Which pricing strategy is the management using?
Price discrimination
Two-part pricing
Commodity bundling
Cross-subsidization
5).
The short run is defined as the time frame:
in which there are no fixed factors of production.
in which there are fixed factors of production.
less than one year.
less than three years.
6).
Fixed costs exist only in:
the long run.
capital-intensive markets.
the short run.
labor-intensive markets.
7).
Top of Form
Non-fed ground beef is an inferior good. In economic booms, grocery managers should:
increase their orders of non-fed ground beef.
reduce their orders of non-fed ground beef.
not change their orders of non-fed ground beef.
neither increase, reduce, nor maintain their current orders for non-fed ground beef.
Bottom of Form
8).
Which of the following pricing strategies is NOT used in markets with special cost and demand structures?
Peak-load pricing
Cross-subsidization
Transfer pricing
Low-price guarantees
9).
A perfectly competitive firm faces a:
perfectly elastic demand function.
perfectly inelastic demand function.
demand function with unitary elasticity.
None of the answers is correct.
10).
The special demand structure that induces a firm to use a cross-subsidization strategy is:
perfect substitution among products.
imperfect substitution among products.
independent demand for products.
interdependent demand for products.
11).
Which of the following factors reduces the need for government involvement in the marketplace?
The presence of externalities
The incentive to rent-seek
The need for public goods
Incomplete information
12).
Which of the following statements is true?
A mineral rights auction is not the same as a common-value auction.
An auctioneer is always indifferent between different kinds of auctions.
The Dutch and first-price, sealed-bid auctions are strategically equivalent.
An English auction always yields lower expected revenues than a second-price, sealed-bid auction.
13).
Which of the following is true concerning negative externalities?
Firms tend to produce more than the efficient level of output.
Society gains because firms do not pay the external costs of production.
Perfect competition is better than monopoly from the viewpoint of society even in the presence of negative externalities.
With negative externalities, a monopoly will always produce an output level less than is socially efficient.
14).
Which of the following is true under monopoly?
P > ATC
P > MC
P = MR
P = ATC
15).
Differentiated goods are NOT a feature of a:
perfectly competitive market.
monopolistically competitive market.
monopolistic market.
perfectly competitive market and monopolistic market.
16).
Producer surplus is measured as the area
below the demand curve and above the market price.
above the demand curve and below the market price.
above the supply curve and below the market price.
below the supply curve and above the market price.
17).
Jaynet spends $25,000 per year on painting supplies and storage space. She recently received two job offers from a famous marketing firm â one offer was for $105,000 per year, and the other was for $85,000. However, she turned both jobs down to continue a painting career. If Jaynet sells 30 paintings per year at a price of $9,000 each:
a. What are her accounting profits?
$
b. What are her economic profits?
$
18).
You are the manager of a monopoly that sells a product to two groups of consumers in different parts of the country. Group 1âs elasticity of demand is -2, while group 2âs is -4. Your marginal cost of producing the product is $40.
a. Determine your optimal markups and prices under third-degree price discrimination.
Instruction: Round your answers to two decimal places.
Markup for group 1:
Price for group 1: $
Markup for group 2:
Price for group 2: $
b. Which of the following are necessary conditions for third-degree price discrimination to enhance profits.
Instructions: You may select more than one answer. Click the box with a check mark for the correct answers and click twice to empty the box for the wrong answers. You must click to select or deselect each option in order to receive full credit.
| At least one group has elasticity of demand less than one in absolute value. | |
| There are two different groups with different (and identifiable) elasticities of demand. | |
| We are able to prevent resale between the groups. | |
| At least one group has elasticity of demand greater than 1 in absolute value. |
19).
You are the manager of a firm that receives revenues of $60,000 per year from product X and $80,000 per year from product Y. The own price elasticity of demand for product X is -1.5, and the cross-price elasticity of demand between productY and X is -1.4.
How much will your firm's total revenues (revenues from both products) change if you increase the price of good X by 2 percent?
Instructions: Round your answer to the nearest dollar. Include a minus (-) sign if applicable.
$
