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Question 6 (20 points) Consider an economy with 2-period lived overlapping generations of agents. Popu- lation is constant and normalized to one. When young, agents have a unit endowment of labor, which they supply inclastically on the labor market at the wage w. They consume cut and save w - Ct,. For the moment, assume all their savings go into phys- ical capital ke+1, which fully depreciates after use. When old, they rent capital at the rate n+1 and consume cat+1 = reiki+1. Their preferences are u(Ct,t) + Bu(ct,+1) where u(c) = log c. The production function is Cobb-Douglas yo = kall-a a) Find the optimal savings decision of the consumer born at time t, taking as given the prices wt and rt+1. b) Solve the problem of the representative firm and use market clearing in the labor market to derive expressions for w, and r, as functions of ki. c) Obtain a law of motion for equilibrium ke+1- d) Find a steady state with constant capital stock ke = kiss. Show that if a 1+8 1 - Q B , and hence a planner would be able to make all agents better off by reducing the capital stock in all periods. f) Suppose now that the agents are allowed to trade a useless, non-reproducible asset in fixed unit supply, which trades at the price p. We call this asset a "bubble". Argue that if p. > 0 and ke+1 > 0 the agent must be indifferent between holding capital and the bubble asset, and derive the associated arbitrage condition. g) Show that if (14) holds, there exists a steady state equilibrium with p = pss > 0.Exercises Question 1 (Monopolistically Competitive Market) 1. Which of the following statements is false in a monopolistically competitive market? a. In the long run, each firm will earn zero economic profit. b. The cost of variety arises from each firm not producing at the lowest average total cost in the long run. c. Since each firm is earning zero economic profit in the long run, there is no deadweight loss. d. Product differentiation is one of the features of this market. 2. In the long run, the demand for a particular firm in a monopolistically competitive industry as the positive profits attracts entry. In other words, the demand for this particular firm is [ more / less ] elastic. 3. Suppose the restaurants industry is initially in the long-run equilibrium and there are many varieties of restaurants. The economy recovers from recession in the city of Madison, causing a rise in demands for eating out. Explain what would happen to the restaurants industry in both short run and long run. Question 2 (Monopolistically Competitive Market) Price, cost. marginal 1. This firm in a monopolistically competitive industry revenue is in the [ short-run / long-run ] equilibrium and earning a profit/ loss of The profit-maximizing level of output for this firm is setting the price at If this picture does not represent long-run equilibrium, this industry is expected to witness [ entry / exit ] of firms in the long-run. This firm will receive a profit of by producing [ more / less ] and selling at MR [ lower / higher ] price in the long run. This arises due to Highlight the 4,800 6,008 7-100 quantity area that represents deadweight loss. 2. For a monopolistically competitive firm that is experiencing AC > P > MC = MR. This firm is in the [ short-run / long-run ] equilibrium, it is expected that firms [ enter / exit ].Business Learning Center - Econ 101 (Hansen) - Handout 18 (December 7, 2015) Tutor: Kanit Kuevibulvanich Question 3 (Monopolistically Competitive Market 16 This firm in a monopolistically competitive industry is in [ short-run / long-run ] equilibrium. The profit-maximizing level of output is and it sells the output at the price of The profits this firm earn is The consumer surplus is Explain how one would find the deadweight loss, highlight the said area. MR D 16 Question 4 (Externalities) The production of fluorescent lamp involves hazardous Mercury (Hg), which is dumped into the river after the production process. Firms have marginal (private) cost of producing fluorescent lamp given by MPC = 30 + Q. For each lamp produced, the mercury cleanup in the river costs $30. The firms face the demand for fluorescent lamp given by P = 480 - 2Q, which is marginal private benefit. There are no externalities from consuming the lamps. 1. Is the externality negative or positive on production or consumption? Give the equations for marginal social cost and marginal social benefit. 2. Without consideration of societal consequence, what is the market equilibrium quantity that firms produce? At what price? 3. If firms think about the societal consequence, what is the socially optimal quantity that firms produce? At what price? 4. Observing the devastating result from firms neglecting the social cost, the government wishes to step in and imposes the regulation so that firms produce at the socially optimal quantity. Design a regulation to dis-incentivize producers from the market outcome. 5. From the regulation designed in 4., which is a taxation, who bears the burden of this taxation? Calculate the tax burden on each party. Which side of the market is relatively more elastic? Question 5 (Externalities) You are hosting a post-game party at Camp Randall. The marginal cost to you in hosting the party is given by MPC = 20 + Q. The marginal private benefit of partying is MPB = 100 - Q. The party makes everyone happy, so the positive externality caused by the party is given by 20. 1. Write down the marginal social cost and marginal social benefit. 2. Is the party under-supplied or over-supplied compared to socially optimal outcome? 3. Find both market outcome by market arrangements and socially optimal outcome, compare the answers. 4. How can the government incentivize you to achieve the socially optimal outcome?Exercises Question 1 (Externalities) Demand for cigarettes in a casino is given by P= 400-Q. The consumption of cigarettes in general causes the negative externalities of MDC = 20. Suppose the supply curve of cigarettes is P = Q. 1. Give the equations for marginal social cost and marginal social benefit. 2. Without consideration of societal consequence, what is the market equilibrium quantity of cigarettes consumed? At what price? If consumers and producers think about the societal consequence, what is the socially optimal quantity of cigarettes consumed? At what price? 4. Observing the devastating result from firms neglecting the social cost, the government wishes to step in and imposes the regulation so that smokers consume the socially optimal quantity. Design a regulation to dis-incentivize smokers from the market outcome. 5. If the law says the non-smokers have the rights to clean air, what would the smokers do? 6. If the casino owner and the smoking law say the smokers have the rights to smoke in casinos, what would the non-smokers do? Question 2 (Public Good) In the town of Prince William Sound, there are only three people - Alice, Bob and Charlie. Their valuations for a public park are provided in the table above. Suppose a public park would cost $6. The town holds a vote to determine whether or not to build the park. If most vote yes, each person must contribute $2 towards the park. Otherwise, the park is not built and no money is spent. The valuation of each person to a public park is summarized in the table. Assume every citizen votes according to their own self-interest. Citizen of Prince William Sound | Valuation to a Public Park Vote (Yes/No) Alice $4 Bob $1.5 Charlie $1 Can you tell who will vote yes or no for a public park to be built? 2. What is the total valuation to a public park? Should the park be built? 3. Does voting result in the socially efficient outcome? 4. Repeat this question when Alice, Bob, and Charlie value a public park at $3, $2.5 and $0, respectively. Business Learning Center - Econ 101 (Hansen) - Handout 19 (December 9, 2015) Tutor: Kanit Kuevibulvanich Question 3 (Public Good) Consider the problem of dorm room toilet used by two roommates: Alice and Bob. Alice has the valuation towards the cleanliness of toilet as P = 10 -Q, where Q is the cleanliness score and P is the per-unit price of cleanliness, i.e. time-value in cleaning. Bob has the valuation of P = 14 - Q. The marginal cost of cleaning the toilet is MC = 8. 1. If Alice decides to free-ride Bob in cleaning, what would be the market outcome? 2. Clearly the bathroom cleanliness is a public good, find the total demand for toilet cleanliness. What is the socially optimal cleanliness? At what price? 3. Compare the answers from 1., 2., and 3., is there the problem of under-provision of cleanliness? To implement the socially optimal outcome, what should be the scheme of time-value contributed by Alice and Bob? 5. What would happen if the MC = 16 and Alice decides to free-ride Bob in cleaning? Question 4 (Tax Incidence) Suppose there is no externalities from consumption or production of this good. The market demand is given by P = 120 - Q. The market supply is P = 20. The initial market equilibrium is P* = 80 and Q* = 40. Suppose the government imposes a unit tax of $30 to this good. 1. Write down the new supply curve after the tax is imposed. Sketch the demand, the supply curve before and after taxation. Find the new equilibrium price and quantity. What is the price that producers receive? What is the price that consumers pay? 3. Calculate the deadweight loss, the incidence borne by consumers, and the incidence borne by producers. Who bears the higher incidence and why