ECON2209 Lecture 5: 1February_EconStats_Karagodsky

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12 May 2017

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P(f c) = the probability of f union c = f, or c, or both . 51. 9 + 80. 5 46. 7 (right circle + left circle - overlap) or. 100 14. 3 ( all probability - outside probability ) There are many other ways to compute the union. 3 terminology: null space/ null event: , when the probability is 0, complement: prime, f", union: , intersection: , mutually exclusive: don"t intersect, collectively exhaustive: add up whole space, add up probability of getting. 1, 2, 3, 4, 5, or 6 on a 6 sided dice. P(a b) = p(a) + p(b) - p(a b) P (a b) = p (a | b) p (a) P(d) = . 02, probability that an athlete is actually doping. P (t p | d ) = . 05 ,the probability that there is a false positive. P (t p | d) = 1 ,the probability that they will test positive given they are doping.

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.

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Part I. Multiple Choice Questions. Please circle the right answer (one mark each)

1. Which of the following are economic goods?

a. Atlantic Ocean sea water.

b. Iowa farm land.

c. California coast line.

d. All of the above.

e. All of the above, except a.

2. The three fundamental questions of economic organization are:

a. closely related to the concept of scarcity.

b. not nearly as important today as they were at the dawn of civilization.

c. what, how, and why.

d. land, labor, and capital.

e. all of the above.

3. Which of the following statements applies to a mixed economy?

a. There is confusion and a lack of organization.

b. The allocation of resources changes from production period to production period.

c. There are no real examples of truly mixed economies.

d. Mixed economies include aspects of both market and command economies.

e. None of the above statements apply.

4. Capital is:

a. the same as money.

b. the headquarters of economic planning.

c. both an input and an output.

d. all of the above.

e. none of the above.

5. Land, labor, and capital are:

a. available only in finite amounts.

b. used to produce outputs.

c. the primary factors of production.

d. combined with technology in the production process.

e. all of the above.

6. Which of the statements below does not apply to the production-possibility frontier, or PPF?

a. The PPF is closely related to the concept of scarcity.

b. Quantities of inputs are measured along the axes of the PPF.

c. The PPF may shift over time.

d. Movements along the PPF may occur as the allocation of resources changes.

e. Technology may change the shape of the PPF.

7. Which of the statements below is a reason why an economy might produce a level of output that is beneath its production-possibility frontier?

a. The available resources are not equally suited to the production of both outputs.

b. The available body of technological knowledge is not being fully utilized.

c. Society prefers one product over the other.

d. In reality, economies produce thousands of goods not just two.

e. There are no frontiers left anymore.

8. In order to shift the PPF out (above and to the right), an economy would have to:

a. somehow increase its stock of inputs.

b. remove some incompetent bureaucrats from their jobs.

c. eliminate the sources of significant abuse of monopoly power.

d. all of the above.

e. none of the above.

9. Sana notices that no matter how many paper cups she buys, she always pays the same price per cup. This means that the supply curve which confronts her is:

a. perfectly inelastic.

b. perfectly elastic.

c. unit-elastic.

d. elastic, but not necessarily perfectly elastic.

e. none of these things, necessarily

10. A perfectly inelastic supply curve would be shown in the ordinary supply-and-demand graph as a:

a. vertical line.

b. horizontal line.

c. straight line, but neither horizontal nor vertical.

d. curved line.

e. any of the above.

1. Using supply-and-demand diagrams, show the effect of the following events on the market for sweatshirts.

(a) A hurricane in South Carolina damages the cotton crop.

(b) The price of leather jackets falls.

(d) New knitting machines are invented.

2. (a) What is the definition of quantity demanded?

(b) What is the definition of quantity supplied?

(d) Choose one of the factors from part (b) and consider the market for bananas. On a well-labeled diagram, demonstrate what will occur in this market if there is a change in this factor.

(e) List the 4 factors that cause the supply curve to shift to the left or the right.

(f) Choose one of the factors from part (e) and consider the market for scooters. On a well-labeled diagram, demonstrate what will occur in this market if there is a change in this factor.

(g) Choose one factor from part (b) and another from part (e) and consider the market for minivans. On a well-labeled diagram, demonstrate what will occur in this market given the change in both factors. (Hint: Draw separate diagrams for parts (d), (f), & (g))

3. Suppose that the price of basketball tickets at your college is determined by market forces. Currently, the demand and supply schedules are as follows:

page1image3877024

(a) Draw the demand and the supply curves. What is unusual about this supply curve? Why might this be true?

(b) What are the equilibrium price and quantity of tickets?

(c) Your college plans to increase total enrollment next year by 5,000 students. The additional students will have the following demand schedule:

page1image3870304

Now add the old demand schedule and the demand schedule for the new students to calculate the new demand schedule for the entire college. What will be the new equilibrium price and quantity?

4. Market research has revealed the following information about the market for chocolate bars: The demand schedule can be represented by the equation QD = 1600 − 300P, where QD is the quantity demanded and P is the price. The supply schedule can be represented by the equation QS = 1400 + 700P, where QS is the quantity supplied.

(a) Sketch a graph representing the market for chocolate bars. Identify the equilibrium point on your graph.

(b) Calculate the equilibrium price and quantity in the market for chocolate bars.

5. For each of the following pairs of goods, which good would you expect to have more elastic demand and why?

(a) Required textbooks or mystery novels

(b) Beethoven recordings or classical music recordings in general

(d) Root beer or water

(e) Insulin or Tylenol

(f) Food or bananas

6.Consider the following information from the market for lemonade:

Price	Quantity Demanded	Quantity Supplied
$1	500 cups	150 cups
$2	200 cups	310 cups

(a) As the price changes from $1 to $2, what is the value of price elasticity of demand?

(b) As the price changes from $1 to $2, what is the value of price elasticity of supply?

(c) Sketch a diagram demonstrating the market for lemonade. Are the supply and demand curves relatively inelastic or elastic? Explain.

(d) Suppose that when the price of lemonade increases from $1 to $2, the quantity demanded of orange juice increases from 150 cups to 190 cups. Calculate cross-price elasticity of demand for orange juice.

(e) Are orange juice and lemonade substitute or complementary goods? Explain.

7. Suppose that business travelers and vacationers have the following demand for airline tickets from New York to Boston:

page2image1834528

(a) As the price of tickets rises from $200 to $250, what is the price elasticity of demand for (i) business travelers and (ii) vacationers? (Use the midpoint method in your calculations)

(b) Why might vacationers have a different elasticity from business travelers?

8. Suppose the price elasticity of demand for heating oil is 0.2 in the short run and 0.7 in the long run.

(a) If the price of heating oil rises from $1.80 to $2.20 per gallon, what happens to the quantity of heating oil demand in the short run? In the long run? (Use the midpoint method in your calculations)

(b) Why might this elasticity depend on the time horizon?

9. The Government has decided that the free-market price of cheese is too low.

(a) Suppose the government imposes a binding price floor in the cheese market. Draw a supply-and-demand diagram to show the effect of this policy on the price of cheese and the quantity of cheese sold. Is there a shortage or surplus of cheese?

(b) Farmers complain that the price foor has reduced their total revenue. Is this possible? Explain

(c) In response to farmer's complaints, the government agrees to purchase all the surplus cheese at the price floor. Compared to the basic price floor, who benefits from this new policy? Who loses?

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ECON2209 Lecture 5: 1February_EconStats_Karagodsky

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