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microeconomics

Questions and Answers of Microeconomics

True or False: Under perfect competition (and assuming that insurance companies incur no costs other than the benefits they pay out), risk-averse individuals with state-independent tastes will fully
Can you show mathematically (by evaluating utilities) that this equilibrium is inefficient relative to the equilibrium identified in Graph 22.3c?
Why is it possible for a signaling equilibrium to result in a pooling equilibrium in which no information is revealed, but it is not possible to have such a pooling equilibrium emerge when firms
Suppose 1p* 2 MC2 2 , d 5 g , 1MC1 2 p*2. Will there be a separating equilibrium?
Is it possible under these conditions for there to also be a pooling equilibrium in which no one sends any signals? (Hint: What would insurance companies have to believe in such an equilibrium if
Would your analysis be any different if the insurance companies did the screening themselves rather than hiring firms in a separate industry to do it for them?
Could there be a screening-induced separating equilibrium in which p 2is higher than p*?
. Can you illustrate a case where the introduction of asymmetric information causes type 2 consumers to no longer purchase any car insurance? What price would type 1 consumers then pay?
Suppose that type 1 consumers valued car insurance more highly, implying D 1lies above D 2
, the greater the deadweight loss from the introduction of asymmetric information.
True or False: The greater the difference between MC1 and MC2
Suppose the current market price for car insurance were less than p*. What would happen under perfect competition with free entry and exit? What if instead the market price for car insurance were
Conditional on only B-insurance being allowed, is this equilibrium efficient?
What would be the equilibrium price pA F for an F student if that student will earn an F with 75% probability and a D with 25% probability?
Would I be able to sell A-insurance if students were always willing to pay 2c for every increase in their letter grade? Would the resulting equilibrium be efficient?
Verify that my break-even insurance premium for A-insurance would have to be approximately 2.69c if only the 65 C, D, and F students bought the insurance.
If all types of insurance policies were available—A-insurance, B-insurance, etc.—who would have what type of insurance under efficiency? (Hint: Compare the marginal cost of raising each student
would yield for each student type.)
In an efficient allocation of grade insurance (when only A-insurance is offered), who would have A-insurance? (Hint: Compare the total cost of raising each student type’s grade to the total
What would be the equilibrium insurance premium if, in a system that forced all students to buy insurance, the only insurance policy offered were one that guarantees a B? What if the only policy
j. Compare your prediction for xm when the subsidy is $7,500 to the evolution of xm in your table from part (e). Once we have converged to the new equilibrium, what would you predict will happen to
i. Explain now why the $2,500 and $5,000 subsidies would be expected to cause no change in behavior by “meanies” while a $7,500 subsidy would cause a dramatic change.
h. Relate this to the notion of “stable” and “unstable” equilibria introduced in exercise 21.8B(e).Given that you can calculate x for different prices, what are the stable equilibria when p 5
g. * Now consider the same problem from a slightly different angle. Suppose that the number of green cars driven by “greenies” is x. Then the total number of green cars on the road is N 5 x 1 xm.
f. Explain what you see in your table in the context of network externalities and changing social norms.
e. ** Suppose that a subsidy of $7,500 per green car is implemented, and suppose that the market adjusts to this in stages as follows: First, “greenies” adjust their behavior in period 0. Then,
d. Would your answer change if the subsidy were raised to $5,000 per green car? What if it were raised to $7,500 per green car?
c. Suppose that the purchase of a green car entails a positive externality worth $2,500. For the case described in (a), what is the impact of a Pigouvian subsidy that internalizes this externality?
b. Explain how it is possible that no green cars are bought by “meanies”?
a. Let the car industry be perfectly competitive, with price for cars set to marginal cost. Suppose the marginal cost of a green car x is $25,000. How many cars are bought by “greenies”?
B. Suppose you live in a city of 1.5 million potential car owners. The demand curves for green cars x for “greenies” and “meanies” in the city are given by xg 1p2 5 1D 2 p2/d and xm 1p2 5 1A
h. How could sin taxes like this be justified as a means of maintaining social taboos and norms through network externalities?
g. Sometimes people advocate for so-called “sin taxes,” taxes on such goods as cigarettes or pornography. Explain what you would have to assume for such taxes to be justified on efficiency
f. Explain how the imposition of a larger initial subsidy has changed the “social norm,” which can then replace the subsidy as the primary force that leads people to drive green cars.
e. How can raising the subsidy above the Pigouvian level have an impact far larger than one might initially think from the imposition of the original Pigouvian tax? If the network externalities are
d. Does the subsidy in (b) have any impact on the behavior of the “meanies”? In the absence of the network externality, is this efficient?
c. The second externality emerges in this case from the formation of social norms, a form of network externality. Suppose that the more green cars the “meanies” see on the road, the more of them
b. There are two types of externalities in this problem. The first arises from the positive impact that green cars have on the environment. Suppose that the social marginal benefit associated with
a. Draw a graph with the aggregate demand curve D0 for the “greenies.” Assume that green cars are competitively supplied at a market price p*, and draw in a perfectly elastic supply curve for
21.12 Policy Application: Social Norms and Private Actions: When asked to explain our actions, we sometimes simply respond by saying “it was the right thing to do.” The concept of “the right
g. What is the optimal level of vouchers for the government to sell, and what will be the rental rate of the vouchers if the government does this?
f. Suppose next that the government instead creates a tradable pollution permit, or voucher, system in which one voucher allows a firm to produce the amount of pollution that gets emitted from the
e. What is the total surplus before and after the tax, and how much deadweight loss does this imply in the absence of the tax?
d. Determine tax revenue from the Pigouvian tax.
c. Determine the total cost of pollution before and after the tax is imposed.
b. ** Calculate (for our numerical example) consumer surplus with and without the Pigouvian tax.(Skip this if you are not comfortable with integral calculus.) Why is (long-run) producer surplus, or
a. If you have not already done so in part B(f) of exercise 21.9, determine the Pigouvian tax that would cause producers to behave the way the social planner would wish for them to behave. What price
B. Continue with the functional forms for costs and demand as given in exercises 21.9 and 21.10. Suppose, as you did in parts of the previous exercises, that b 5 1, d 5 0.1, and A 5 10,580
k. What would the government have to know to set the optimal cap on the number of pollution permits?
j. Suppose the government instead wanted to impose a cap-and-trade system on this lake, with pollution permits that allow a producer to produce the amount of pollution necessary to produce one unit
i. Is there a deadweight loss from not using the tax?
h. Is there additional pollution damage under the market outcome (in the absence of the tax)?
g. True or False: The pollution cost under the Pigouvian tax is, in this example, equal to the tax revenue that is raised under the tax.
f. Keeping in mind what you concluded in exercise 21.9, has (long-run) producer surplus, or long-run industry profit, changed as a result of the tax?
e. Where in your graph does consumer surplus before and after the tax lie?
d. Suppose N* is the number of firms in the industry in the market outcome, N opt is the optimal number of firms and d continues to be as defined throughout. What does the government have to know in
c. Illustrate the Pigouvian tax that would be necessary to get the market to move to equilibrium B.
b. Next, without drawing any additional curves, indicate the point B in your graph where the market would be producing if firms were taking the full cost of the pollution they emit into account.
a. Begin by illustrating the market demand and long-run industry supply curves, labeling the market equilibrium as A.
21.11 Policy Application: Pollution that Increases Firm Costs—Policy Solutions: This exercise continues to build on exercises 21.9 and 21.10. Assume the same basic set-up of firms located around a
g. Verify that your Pigouvian tax in fact results in prices for consumers and the industry that lead them to demand and supply the output level you calculated in part (d). (Note: You will need to
f. What is the Pigouvian tax that is required in order for competitive firms to implement the equilibrium you just calculated in (d)? What price does this imply consumers would pay and what price
e. Compare these to your answers in exercise 21.9. Can you give an intuitive explanation for why these answers differ despite the fact that pollution only affects the firms in the industry?
d. Suppose, as in part (j) of exercise 21.9, that b 5 1, d 5 0.1, and A 5 10,580. What are X*, p*, and N*? How much does each individual firm produce?
c. Compare your answers to those from exercise 21.9. How do they differ?
b. Repeat parts (c) through (i) from exercise 21.9 using the cost functions Barney would use for each firm to arrive at N*, p*, and X*.
a. Now consider the cost function that benevolent Barney would use for each firm: From the social planner’s perspective, the firm’s variable costs (captured by bx 2) would still matter, as would
B. * Consider the same set-up as in part B of exercise 21.9. In the previous case where we derived the market equilibrium, we said that in a model with many firms it was reasonable to model each
g. If a single corporation acquired all the firms around the lake, would that corporation take the costs of pollution into account more like Barney or more like the individual competitive firms?(In
f. True or False: Under the efficient outcome, the industry would produce less at a higher price.
e. True or False: If firms used Barney’s suggested cost curves, the long-run industry supply curve would be upward sloping, as you should have concluded in exercise 21.9 it is in the absence of
d. What does your answer imply about the relationship between the firm’s AC curve and Barney’s suggestion for what the firm’s AC curve should be?
c. Suppose that our benevolent social planner Barney can tell firms what to count as costs. Illustrate how Barney’s suggestion for each firm’s marginal cost curve is related to the marginal cost
b. How much of this pollution-related cost does firm i not take into account? If firm i is one of a large number of firms, is it a good approximation to say that firm i does not take any of the
a. Suppose there are N firms in the equilibrium you described in exercise 21.9. What is the pollution-related cost of firm i producing one more unit of x?
21.10 Policy Application: Pollution that Increases Firm Costs—Barney’s Solution: Consider the same situation as the one described in exercise 21.9.A. Assume again that the only impact of
j. Suppose that b 5 1, d 5 0.01, and A 5 10,580. What are X*, p* and N*? How much does each individual firm produce? (Do exercise 21.10 to compare these to what is optimal.)
i. Use your answer to (g) to determine the equilibrium number of firms N* (as a function of A, d, and b).
h. Use your answer to (g) to determine the equilibrium price level p* (as a function of A,d, and b).
g. Suppose the aggregate demand for X is given by the demand curve pD 1X2 5 A/1X 0.5 2. Set the industry supply curve equal to the demand curve to get the equilibrium market output X* (as a function
f. Substitute N1X2 into p1N2 to get a function p1X2. Can you explain why this is the long-run industry supply curve with free entry and exit?
e. Since each firm produces x1N2, multiply this by N to get the aggregate output level X1N2, then invert it to get the number of firms N1X2 as a function ofb, d, and X.
d. Since all firms are identical, in equilibrium the single firm we are analyzing will produce the same as each of the other firms; that is, x 5 x. Use this to derive a single firm’s output level
c. Assuming the firm is in long-run equilibrium, all firms will make zero profit. Use your answer to (b) to derive the output level produced by each firm as a function ofd, b, N, and x.
b. Derive the marginal and average cost functions for a single firm (using the final version of our approximate cost function). (Be careful to realize that the second part of the cost function is,
a. How is our treatment of a producer’s contribution to her own costs similar to our “price-taking” assumption for competitive firms?
f. In Chapter 14, we briefly mentioned the term decreasing cost industries, industries in which the long-run industry supply curve is downward sloping despite the fact that all firms might have
e. Usually we can identify producer surplus, or firm profit, as an area in the demand and supply picture. What is producer surplus here? Why is your answer different from the usual?
d. In side-by-side graphs of a firm’s cost curves and the (long-run) industry supply and demand curves, illustrate the firm and industry in long-run equilibrium.
c. Now consider this example here. Why is the long-run industry supply curve now upward sloping despite the fact that all firms are identical?
b. In our discussion of long-run competitive equilibria, we concluded in Chapter 14 that the long-run industry supply curve is horizontal when all firms have identical cost curves. Can you recall the
a. Suppose all firms have identical decreasing returns to scale production processes, with the only fixed cost created by the pollution. For a given amount of industry production, what is the shape
21.9 Business Application: Pollution that Increases Firm Costs—The Market Outcome: In the text, we assumed for convenience that the ill effects of pollution are felt by people other than producers
g. Suppose that we begin in the equilibrium in which no one owns a computer and the marginal cost of producing computers is $2,000. Why might firms launch an aggressive campaign in which they give
f. Suppose the supply curve is horizontal at p 5 2,000. Our model implies there are three equilibria: two that are stable and one that is not stable. What network sizes are associated with each of
e. In models like this, we say that an equilibrium is stable if it does not lie on an upward-sloping portion of the demand curve. Can you guess why? (Hint: Suppose that x* is the equilibrium quantity
d. Check your answer to (c) by graphing the demand function when A 5 100 and a 5 1. Continue with these parameter values for the rest of the exercise.
c. Suppose A . 2a. What is the shape of this demand curve? Explain.
b. The consumer side of the market is in equilibrium if the network size N is equal to the number of computers sold. Use this to derive the actual demand curve P1x2 that takes the network
a. Does this demand function give rise to the parallel demand curves (for different levels of network size) you analyzed in part A?

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