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microeconomics

Questions and Answers of Microeconomics

e. How would your answer change if the large rather than the small firm had this credit constraint?
d. How does your answer change when firm S has the credit constraint described in A(h), that is, when the small firm has no access to credit markets?
c. Derive the evolution of output price as the industry declines.
B. Suppose c 5 10, k L 5 20, k S 5 10, and pt 1x2 5 50.5 2 2t 2 x until price is zero.a. How does this example represent a declining industry?b. Calculate t S, t L, and t as defined in part A of the
i. How does price now evolve differently in the declining industry (when the small firm cannot access credit markets)?
h. Suppose that the small firm has no access to credit markets and therefore is unable to take on any debt. If the large firm knows this, how will this change the subgame perfect equilibrium?True or
g. Let t denote the last period in which 1pt 1k S 1 k L2 2 c2 $ 0. Describe what happens in a subgame perfect equilibrium, beginning in period t 5 1, as time goes by, that is, as t, t L, and t
f. Suppose both firms are still in business at the beginning of period (t L 2 1) (before exit decisions are made). Under what condition will both firms stay? What has to be true for one of them to
e. Suppose both firms are still in business at the beginning of period t Lbefore firms make their decision of whether to exit. Could both of them producing in this period be part of a subgame perfect
d. What are the two firms’ subgame perfect strategies in periods (t L 1 1) to t S?
c. What are the two firms’ subgame perfect strategies beginning in period (t S 1 1)?
denote the last period in which demand is sufficiently high for firm i to be profitable(that is to make profit greater than or equal to zero) if it were the only firm in the market. Assuming they
where subscripts indicate the time periods t 5 1,2,3,…. If firm i is the only firm remaining in period t, what is its profit p it? What if both firms are still producing in period t?b. Let t i
a. Since demand is falling over time, the price that can be charged when the two firms together produce some output quantity x declines with time; that is, p1 1x2 . p2 1x2 . p3 1x2 . …
. The output that is, produced is produced at constant marginal cost MC 5c. (Assume throughout that once a firm has exited the industry, it can never produce in this industry again.)
A. Since our focus is on the decision of whether or not to exit, we will assume that each firm i has fixed capacity k iat which it produces output in any period in which it is still in business; that
25.5 Business Application: Quitting Time: When to Exit a Declining Industry:13 We illustrated in the text the strategic issues that arise for a monopolist who is threatened by a potential entrant
j. ** Are there any scenarios in your table that would result in the same level of overall production if the marginal costs for each of the two firms were the same and equal to the average we have
i. Which of the oligopoly/monopoly scenarios in your table is most efficient? Which is best for consumers?
h. What would be the efficient outcome? Add a row to your table illustrating what would happen under the efficient outcome.
g. ** Add a column to your table in which you calculate profit in each case. What market conditions are most favorable in this example for the good manager to leverage his or her skills?
f. ** Suppose A 5 1000, a 5 10, c1 5 20, and c2 5 40. Use your results from parts (a) through (e) to calculate the equilibrium outcome in each of those cases. Illustrate your answer in a table with
e. How would each firm behave if it were a monopolist?
d. What if the two firms are engaged in Stackelberg competition, with firm 1 as the first mover?What if firm 2 is the first mover?
c. How does your answer change if the two firms are Cournot competitors (assuming that both produce in equilibrium)?
b. Does your answer to (a) change if the Bertrand competition is sequential, with firm 1 moving first? What if firm 2 moves first? (Assume subgame perfection.)
a. In a simultaneous move Bertrand model, what price will emerge, and how much will each firm produce?
B. The two oligopoly firms operate in a market with demand x 5 A 2 ap. Neither firm faces any recurring fixed costs, and both face a constant marginal cost. But firm 1’s marginal cost c1 is lower
g. * In (b) you were asked to find the subgame perfect equilibrium in a sequential Bertrand pricing market where firm 1 moves first. How would your answer change if firm 2 moved first?Is there a
f. If firms set quantity sequentially, do you think it matters whether firm 1 or firm 2 moves first?
e. Could it be that firm 2 does not produce in the Cournot equilibrium? If so, how much does firm 1 produce?
d. Next, suppose that instead firms have to choose capacity and they therefore are engaged in quantity competition. What happens in equilibrium compared to the situation where both firms face the
c. When firms face the same costs, we concluded that the Bertrand equilibrium is efficient. Does the same still hold when firms face different marginal costs?
b. Does your answer change if the firms post prices sequentially, with firm 1 posting first?
a. Suppose first that the market conditions are such that firms compete on price and can easily produce any quantity that is demanded at their posted prices. If the firms simultaneously choose
25.4 Business Application: Entrepreneurial Skill and Market Conditions: We often treat all firms as if they must inherently face the same costs, but managerial or entrepreneurial skill in firms can
h. Characterize the equilibrium in this case for the range of FC from 0 to 20,000.
g. What is the lowest FC at which neither firm will produce?
f. What is the lowest FC at which firm 1 does not have to engage in strategic entry deterrence to keep firm 2 out of the market?
e. Now suppose there is a recurring fixed cost FC . 0. Given that firm 1 has an incentive to keep firm 2 out of the market, what is the highest FC that will keep firm 2 producing a positive output
d. What is the equilibrium Stackelberg price?
c. What output level does that imply firm 2 will choose?
b. What output level will firm 1 choose?
B. * Consider again the demand function x1p2 5 100 2 0.1p and the cost function c1x2 5 FC 1 5x 2(as you did in exercise 25.1 and implicitly in the latter portion of exercise 25.2).a. Suppose first
f. Will firm 1 be able to engage in entry deterrence to keep firm 2 from producing?
e. Suppose instead (that is suppose again FC 5 0) that the firms have linear, upward-sloping MC curves, with MC for the first output unit equal to what the constant MC was in the text. Can you guess
d. Could FC be so high that no one produces?
c. At what FC does firm 1 not have to worry about firm 2?
b. Is there a range of FC under which firm 1 can strategically produce in a way that keeps firm 2 from producing?
a. Suppose that both firms have a recurring FC (that does not have to be paid if the firm chooses not to produce). Will the Stackelberg equilibrium derived in the text change for low levels of FC?
A. Suppose that firm 1 decides its quantity first and firm 2 follows after observing x1. Assume initially that there are no recurring fixed costs and that marginal cost is constant as in the text.
25.3 In exercise 25.2, we considered quantity competition in the simultaneous Cournot setting. We now turn to the sequential Stackelberg version of the same problem.
h. What happens if FC lies above the range you calculated in (g)?
g. For what range of FC is there no pure strategy equilibrium in which both firms produce but two equilibria in which only one firm produces?
f. How high can FC go without altering the fact that this is at least one of the Nash equilibria?
e. How high can FC go with this remaining as the unique equilibrium?
d. Suppose that A 5 100, c 5 10, and a 5 0.1. What is the equilibrium output and price in this industry, assuming FC 5 0?
c. What is the equilibrium price?
b. Assuming that both firms producing is a pure strategy Nash equilibrium, derive the Cournot equilibrium output levels.
B. Suppose that both firms in the oligopoly have the cost function c1x2 5 FC 1 1cx2/22, with demand given by x1p2 5 A 2 ap (as in the text).a. Derive the best response function x1 1x2 2 (of firm
g. Suppose that, instead of a recurring fixed cost, the marginal cost for each firm was linear and upward sloping, with the marginal cost of the first unit the same as the constant marginal cost
f. True or False: With sufficiently high recurring fixed costs, the Cournot model suggests that only a single firm will produce and act as a monopoly.
e. Can you illustrate a case where FC is sufficiently high such that both firms producing x Cis no longer a Nash equilibrium? What are the two Nash equilibria in this case?
should convince yourself that the best response functions are the same as before for low quantities of the opponent’s production but then, at some output level for the opponent, jump to 0 output
a. First, suppose both firms paid a fixed cost to get into the market. Does this change the predictions of the Cournot model?b. Let x Cdenote the Cournot equilibrium quantities produced by each of
25.2 In exercise 25.1, we checked how the Bertrand conclusions (that flow from viewing price as the strategic variable) hold up when we change some of our assumptions about fixed and marginal costs.
b. What is the highest recurring fixed cost FC that would sustain at least one firm producing in this industry? (Hint: When you get to a point where you have to apply the quadratic formula, you can
B. Suppose that demand is given by x1p2 5 100 2 0.1p and firm costs are given by c1x2 5 FC 1 5x 2.a. Assume that FC 5 11,985. Derive the equilibrium output x Band price p Bin this industry under
g. Suppose next that, in addition to a recurring fixed cost, the marginal cost curve for each firm is upward sloping. Assume that the recurring fixed cost is sufficiently high to cause AC to cross MC
f. You should have concluded that the recurring fixed cost version of the Bertrand model leads to a single firm in the oligopoly producing. Given how this firm prices the output, is this outcome
e. True or False: The introduction of a recurring fixed cost into the Bertrand model results in p 5 AC instead of p 5 MC.
d. What is the simultaneous move Nash equilibrium? (There are actually two.)
c. Consider the same costs as in (b). Can both firms produce in equilibrium when they move simultaneously?
25.1 In the text, we demonstrated the equilibrium that emerges when two oligopolists compete on price when there are no fixed costs and marginal costs are constant. In this exercise, continue to
Suppose again the two firms engage in price (Bertrand) rather than quantity competition, and suppose c L , c , c H . This case is easier to analyze if we assume sequential Bertrand competition, with
Suppose the two firms engage in price (Bertrand) competition, and suppose c . c H. What price do you expect will emerge?
Can you tell whether the Cournot price will be higher or lower under this type of asymmetric information than it would be under complete information? (Hint: For both the case of a high cost and a low
Verify x M and p M in equation (25.2).
In circumstances where firms are not certain about demand conditions in any given period, why might a more forgiving trigger strategy (like tit-for-tat) that allows for the reemergence of cooperation
Why would oligopolists who cannot voluntarily sustain cartel agreements want to have such agreements enforced?
The Prisoner’s Dilemma you and I face as we try to maintain a cartel agreement but it works toward making us worse off. How does it look from the perspective of society at large?
Can you verify the last sentence by just looking at the best response functions we derived earlier in Graph 25.2?
How might the cartel agreement have to differ if we were currently engaged in Stackelberg competition? (Hint: Think about how the cartel profit compares to the Stackelberg profits for both firms,
Is the smallest fixed cost of entering that will prevent firm 2 from coming into the market greater in panel (a) or in panel (b)?
True or False: Once the entrant has paid the fixed entry cost, this cost becomes a sunk cost and is therefore irrelevant to the choice of how much to produce.
Where is the predicted Stackelberg outcome in Graph 25.3c?
Determine the Stackelberg price in terms of p M—the price a monopolist would charge—and MC
True or False: Under Bertrand competition, x 1 B 5 x B2 5 x M.
Which type of behavior under simultaneous decision making within an oligopoly results in greater social surplus: quantity or price competition?
What is the slope of the best response function in panel (a) of Graph 25.2? (Hint: Use your answer to exercise 25a.5 to arrive at your answer here.)
Can you identify in panel (b) of Graph 25.2 the quantity that corresponds to the horizontal intercept of firm 2’s best response function in panel (a)?
Suppose our two firms know that we will encounter each other n times and never again thereafter. Can p . MC still be part of a subgame perfect equilibrium in this case assuming we engage in pure
How would you think about subgame perfect equilibria under sequential Bertrand competition with three firms (where firm 1 moves first, firm 2 moves second, and firm 3 moves third)?
Is there a single Nash equilibrium if more than two firms engage in Bertrand competition within an oligopoly?
Can you see how this is the only possible Nash equilibrium? Is it a dominant strategy Nash equilibrium?
c. Everyone in your neighborhood would love to see some really great neighborhood fireworks on the next national independence day, but somehow no fireworks ever happen in your neighborhood.d. People
b. People get in their cars without thinking about the impact they have on other drivers by getting on the road, and at certain predictable times, this results in congestion problems on roads.
a. When I teach the topic of Prisoner’s Dilemmas in large classes that also meet in smaller sections once a week, I sometimes offer the following extra credit exercise: Every student is given 10
24.17 Policy Application: Some Prisoner’s Dilemmas: We mentioned in this chapter that the incentives of the Prisoner’s Dilemma appear frequently in real-world situations.A. In each of the
h. How is the probability of a crime being reported (in this equilibrium) affected by c and b?Does this make sense?

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