# Nash Equilibrium and Microeconomics

1. Consider the following information for a simultaneous move game. If you advertise and your rival advertises, you each earn $5 million in profits. If neither of you advertise, you will each earn $10 million in profits. However, if one of you advertises and the other does not, the firm that advertises will earn $15 million and non-advertising firm will earn $1 million. If you and your rival plan to be in business for 10 years, then the Nash equilibrium is :

A. For each firm to advertise each year.

B. For neither firm to advertise every year

C. For each firm to not advertise in any year.

D. For each firm to advertise in early years, but not advertise in later years.

2. If this one-shot game is repeated 3 times, the Nash equilibrium payoffs for Firm A and B will be ______________ each period. (low, low (10,9); low high (15,8); high, low (-10,7); high, high (11,11).

A. (10,9) B. (11,11) C. (-10,7) D. (15,8)

3. Which of the following conditions are necessary for the existence of a Nash equilibrium?

A. The existence of dominant strategies for both players.

B. The existence of a dominant strategy for 1 player and the existence of a secure strategy for another players.

C. The existence of secure strategies for both players.

D. None of the above.

4. Management and a labor union are bargaining over how much of a $50 surplus to give to the union. The $50 is divisible up to one cent. The players have one-shot to reach an agreement. Management has the ability to announce what it wants first, and then the labor union can accept or reject the offer. Both players get zero if the total amounts asked for exceed $50. Which of the following is true?

A.There are multiple Nash equilibria. B. $25/$25 is a Nash equilibria.

C. A Nash equilibrium is also a perfect equilibrium. D. A and B

5. Normal form game low,low (0,0); low, high (50,-10); high, low (-10,50); high, high ((20,20)

Suppose the game is infinitely repeated, and the interest rate is 10%. Both firms agree to charge a high price, provided no player has charged a low price in the past. If both firms stick to this agreement, then the present value of firm A's payoff are:

A. 220 B. 110 C. 330 D. 550

6. If you advertise and your rival advertises, you each earn $4 million in profits. If neither of you advertise, you will each earn $10 million in profits. However, if one of you advertises and the other does not, the firm that advertises will earn $1 million and non-advertising firm will earn $5 million. Which of the following is true?

A. A dominant strategy for Firm A is to advertise.

B. A dominant strategy for Firm B is to advertise.

C. A Nash equilibrium is for both firms to advertise.

D. None of the above is true.

7. Consider the following innovation game. Firm A must decide whether or not to introduce a new product. Firm B must decide whether or not to clone firm A's product. If firm A introduces and B clones, Firm A earns $1 and B earns $10. If A introduces and B does not clone, then A earns $10 and B earns $2. If firm A does not introduce, both firms earn profits of 0. Which of the following is true?

A. The subgame perfect Nash equilibrium profits are ($10, $2)

B. It is not in A's interest to introduce.

C. Firm A does not care if B clones.

D. None of the above are true.

8. Consider the following innovation game. Firm A must decide whether or not to introduce a new product. Firm B must decide whether or not to clone firm A's product. If firm A introduces and B clones, then firm A earns $1 and B earns $10. If A introduces and B does not clone, then A earns $10 and B earns $2. If firm A does not introduce, both firms earn profits of 0. How many Nash equilibria are there for this game?

A. 0 B. 1 C. 2 D. 0, but there are secure strategies

9. You are the manager of a gas station and your goal is to maximize profits. Based on your past experience, the elasticity of demand by Missourians for a car wash is 4, while the elasticity of demand by non-Missourians is 6. If you charge Missourians $20 for a car wash, how much should you charge a person with an Ohio license plate for a car wash?

A. $1.50 B. $15.00 C. $18.00 D. $20.00

10. Suppose P=20-2Q is the market demand for a local monopoly. The marginal cost is 2Q. The firm currently uses a standard pricing strategy. Which of the following will allow the firm to enhance the profits?

A. Engage in two-tier pricing. B. Engage in bundling. C. Engage in randomized pricing. D. Both A and B.

11. Which of the following statements is true?

A. The more elastic the demand, the higher is the profit-maximizing markup.

B. The more elastic the demand, the lower is the profit-maximizing markup.

C. The higher the marginal cost, the lower the profit-maximizing price.

D. The higher the average cost, the lower the profit-maximizing price.

12. Which of the following strategies will most likely NOT enhance profits in a Bertrand oligopoly?

A. Two-tier pricing B. Price matching C. Randomized pricing D. Brand loyalty

13. If a monopolist claims his profit-maximizing markup factor is 3, what is the corresponding price elasticity of demand?

A. -1.5 B. -2 C. -2.5 D. -3

14. Which of the following pricing policies enhances profits by creating brand-loyal consumers?

A. Frequent flyer programs B. Beat-or-pay strategies C. Trigger strategies

D. A and B.

15. If the profit-maximizing markup factor in a 10-firm Cournot oligopoly is -2, what is the corresponding market elasticity of demand?

A. -1 B. -1.2 C. -2 D. None of the above

16. First degree price discrimination:

A. Occurs when a firm charges each consumer the maximum price he or she would be willing to pay for each unit of the good purchased.

B. Results in the firm extracting all surplus from consumers

C. Both A and B

D. None of the above

17. Suppose a risk-neutral competitive firm must produce output before the market price is known. If the uncertain price is given by P=P* + e, where e is a random term with an expected value of 0, a competitive firm should shut down in the short-run if:

A. P*<AVC B. P*+e<AFC C. P*<AFC D. P*<MC

18. A fair coin is flipped. You will be paid $1 when it is heads and penalized $1 otherwise. What is the variance of the payoffs?

A. 0 B. 1 C. .50 E. .25

19. Which of the following is a possible critique of the decision theory under uncertainty presented in the text?

A. People do not always know the true probability of complicated events.

B. Decision theory assumes that people are good at math.

C. Decision theory assumes that people fact the same situation (uncertainty repeatedly.

D. People are not risk averse.

20. People having a bad driving record find it difficult to buy automobile insurance because insurance companies fear that _____________ may happen if they raise the premiums.

A. Adverse selection B. Moral hazard C. Risk aversion D. None of the above

21. John is a seller in an affiliated values auction environment where bidders are risk-neutral. Which auction yields John the greatest expected revenue?

A. English B. First Price C. Second price D. All of the above are revenue equivalent

22. Holding the mean constant, the larger the standard deviation, the -- the gamble will be. A. More risky B. Less risky C. Higher utility D. None of the above

23. A risk neutral monopoly must set output before it knows for sure the market price. There is a 50% chance the firm's demand will be P=20-Q and a 50% chance it will be P=40-Q. The marginal cost of the firm is MC=Q. What is the expression for the expected marginal revenue function?

A. E(MR)=20-2Q B. E(MR)=30-2Q C. E(MR)=40-2Q D. E(MR)=50-2Q

24. Consider an antique auction where bidders have independent private values. There are 2 bidders, each of which perceives that valuations are uniformly distributed between $100 and $1,000. One of the bidders is Sue, who knows her own valuation is $200. What is Sue's optimal bidding strategy in a Dutch auction?

A. Submit a bid of $150

B. Submit a bid of $200

C. Submit a bid that is less than $150

D. Yell "mine" when the bid reaches $150

E. None of the above

25. A risk neutral monopoly must set output before it knows for sure the market price. There is a 50% chance the firm's demand curve will be P=20-Q and there is a 50% chance it will be P=40-Q. The marginal cost of the firm is MC=Q. The expected profit-maximizing quantity is:

A. 5 B. 10 C. 15 D. 20

26. The external marginal cost of producing coal is Mcexternal = 6Q while the

Internal marginal cost is Mcinternal = 4Q. The inverse demand for coal is given by P=120 - 2Q. What is the socially efficient level of output?

A. 10 B. 20 C. 15 D. 8

27. The external marginal cost of producing coal is Mcexternal = 6Q while the internal

marginal cost is Mcinternal = 4Q. The inverse demand for coal is given by P=120-2Q. If the government taxed output at $2 per unit, what would a competitive industry produce?

A. 10 B. 20 C. 15 D. 8

28.If a price ceiling on a monopolist results in NO shortage:

A. the full economic price is lower than in the absence of the ceiling.

B. Rent-seeking must be effective

C. The firm is on the verge of leaving the market

D. The firm must be making zero economic profits

29.When the government imposes an excise tax on foreign imports:

A. domestic consumers are harmed

B. domestic firms benefit

C. domestic firms are harmed

D. a and b

30.The marginal cost of producing a good to society is:

A. the horizontal sum of the supply curve and marginal cost of polluting

B. the vertical sum of the demand curve and marginal cost of polluting

C. the horizontal sum of the demand curve and marginal cost of polluting

D. the vertical sum of the supply curve and the marginal cost of polluting

31. Which cost measures the pollution cost to society?

A. internal cost B. external cost C. social cost D. b and c

32. The domestic demand and supply for sugar are Qd=40,000-200P, and

Qsd=10,000+300P. The foreign supply is Qsf=20,000+100P. What is the total supply of sugar in the domestic market?

A. Q=50,000 + 100P B. Q=30,000+400P C. Q=15,000+200P D. Q=10,000+300P

33. Producing the efficient amount of a public good, government should account for:

A. only the demand for high-demand consumers

B. only the demand for low-demand consumers

C. the vertical sum of all individual inverse demand curves

D. the horizontal sum of all individual inverse demand curves

34.Rent-seeking:

A. results in less market share for the rent seekers

B. involves lobbyists influencing government policies to benefit their interests

C. results in more negative externalities

D. none of the above

35.An un-regulated monopolist will likely:

A. charge a price below MR

B. charge a price above MC

C. charge a price equal to MR

D. a and b

36. If you advertise and your rival advertises, you each will earn $5 million in profits. If neither of you advertise, you will each earn $10 million in profits. However if one of you advertises and the other does not, the firm that advertises will earn $15 million and the non-advertising firm will earn $1 million. Which of the following is true?

A. A secure strategy for Firm A is to not advertise.

B. A secure strategy for Firm B is to not advertise.

C. Firm A does not have a secure strategy.

D. None of the above is true

37. A firm with market power has an individual consumer demand of Q =20-4P and costs of C=4Q. What is the optimal price to charge for a block of 20 units?

A. $15 B. $30 C. $50 D. $100

38. The average consumer at a firm with market power has an inverse demand function of P=10-Q. The firms' cost function is C=2Q. If the firm engages in optimal two-part pricing, it will earn profits of?

A. $2 B. $32 C. $64 D. None of the above

39. Which of the following statement is NOT true?

A. The Dutch and first price sealed bid auctions are strategically equivalent.

B. A mineral rights auction is a common value auction.

C. An auctioneer is always indifferent between kinds of auctions.

D. An English auction yields higher expected revenues than a second-price sealed bid auction when bidders are risk averse.

40. A risk neutral monopoly must set output before it knows for sure the market price. There is a 50% chance the firm's demand curve will be P=20-Q, and a 50% chance it will be P=40-Q. The marginal cost of the firms is MC=Q. The expected price-maximizing price is:

A. $5 B. $10 C. $15 D. $20

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#### Solution Preview

1. Consider the following information for a simultaneous move game. If you advertise and your rival advertises, you each earn $5 million in profits. If neither of you advertise, you will each earn $10 million in profits. However, if one of you advertises and the other does not, the firm that advertises will earn $15 million and non-advertising firm will earn $1 million. If you and your rival plan to be in business for 10 years, then the Nash equilibrium is :

A. For each firm to advertise each year.

B. For neither firm to advertise every year

C. For each firm to not advertise in any year.

D. For each firm to advertise in early years, but not advertise in later years.

Answer 1: (A)

In game theory, the Nash equilibrium (named after John Nash) is a kind of optimal strategy for games involving two or more players, where no player has anything to gain by changing only one's own strategy. If there is a set of strategies for a game with the property that no player can benefit by changing his strategy while the other players keep their strategies unchanged, then that set of strategies and the corresponding payoffs constitute a Nash equilibrium. In this case, if any of the companies is advertising, it does not make sense for the other company to not advertise. Thus each company will advertise each year.

2. If this one-shot game is repeated 3 times, the Nash equilibrium payoffs for Firm A and B will be ______________ each period. (low, low (10,9); low high (15,8); high, low (-10,7); high, high (11,11).

A. (10,9) B. (11,11) C. (-10,7) D. (15,8)

Answer 2: (A)

Follow the same logic as the logic for Answer 1. If Firm B knows that Firm A is playing low, then it has no incentive to change its strategy from low to high. Conversely, if Form A knows that Firm B is playing low, then it also has no incentive to change its strategy from low to high. Please keep in mind that the number of times the game is repeated does not matter as long as it is a finite game. For infinitely repeated games, we will follow some other strategy.

3. Which of the following conditions are necessary for the existence of a Nash equilibrium?

A. The existence of dominant strategies for both players.

B. The existence of a dominant strategy for 1 player and the existence of a secure strategy for another players.

C. The existence of secure strategies for both players.

D. None of the above.

Answer 3: (D)

None of the conditions mentioned above are necessary. Question 2 is a violation of (A) and a Nash equilibrium still exists for question 2 (there is a dominant strategy for Firm A but not for Firm B). B and C also need not be true for a Nash equilibrium to exist. Existence of a dominant strategy is a sufficient condition but not a necessary condition for a Nash equilibrium to exist.

4. Management and a labor union are bargaining over how much of a $50 surplus to give to the union. The $50 is divisible up to one cent. The players have one-shot to reach an agreement. Management has the ability to announce what it wants first, and then the labor union can accept or reject the offer. Both players get zero if the total amounts asked for exceed $50. Which of the following is true?

A.There are multiple Nash equilibria. B. $25/$25 is a Nash equilibria.

C. A Nash equilibrium is also a perfect equilibrium. D. A and B

Answer 4: (D)

There are multiple Nash equilibrium for this case. This is because the labor union has to accept whatever the management offers. For example $49/$1 is one NE and so is $25/$25. In sequential bargaining games, there are always multiple Nash equilibriums and the person going second is usually at a disadvantage. In this particular case management can have the deal structured so that it gets $49.99 and labor union gets $0.01. Since $0.01 is better than nothing, labor union will have to agree.

5. Normal form game low,low (0,0); low, high (50,-10); high, low (-10,50); high, high ((20,20)

Suppose the game is infinitely repeated, and the interest rate is 10%. Both firms agree to charge a high price, provided no player has charged a low price in the past. If both firms stick to this agreement, then the present value of firm A's payoff are:

A. 220 B. 110 C. 330 D. 550

Answer 5: (A)

The formula is:

PV = 20 + 20/.1 = 220

6. If you advertise and your rival advertises, you each earn $4 million in profits. If neither of you advertise, you will each earn $10 million in profits. However, if one of you advertises and the other does not, the firm that advertises will earn $1 million and non-advertising firm will earn $5 million. Which of the following is true?

A. A dominant strategy for Firm A is to advertise.

B. A dominant strategy for Firm B is to advertise.

C. A Nash equilibrium is for both firms to advertise.

D. None of the above is true.

Answer 6: (A)

If the other firm selects to advertise, then the second firm should also advertise. If the other firm selects to not advertise, then also the second firm should chose to advertise. Thus the dominant strategy for both is to advertise.

7. Consider the following innovation game. Firm A must decide whether or not to introduce a new product. Firm B must decide whether or not to clone firm A's product. If firm A introduces and B clones, Firm A earns $1 and B earns $10. If A introduces and B does not clone, then A earns $10 and B earns $2. If firm A does not introduce, both firms earn profits of 0. Which of the following is true?

A. The subgame perfect Nash ...

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