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# A consumer lives three periods, called the learning period, the working period, and the retirement period. Her income is 200 during the learning period, 800 during the working period, and 200 again during the retirement period.

Intermediate Macroeconomics, 302

Problem Set 2

N4.9.  A consumer lives three periods, called the learning period, the working period, and the retirement period. Her income is 200 during the learning period, 800 during the working period, and 200 again during the retirement period. The consumer’s initial assets are 300. The real interest rate is zero. The consumer desires perfectly smooth consumption over her lifetime.

a. What are consumption and saving in each period, assuming no borrowing constraints? What happens if the consumer faces a borrowing constraint that prevents her from borrowing?

b.     Assume that the consumer’s initial wealth is zero instead of 300. Repeat part (a). Does being borrowing-constrained mean that consumption is lower in all three periods of the consumer’s life than it would be if no borrowing constraints applied?

A4.2. A country loses much of its capital stock to a war.

a. What effects should this event have on the country’s current employment, output, and real wage?

b.     What effect will the loss of capital have on desired investment?

c. Assume that the desired saving function doesn’t change. What effect does the loss of capital have on the country’s real interest rate and the quantity of investment?

A4.3.              a. Analyze the effects of a temporary increase in the price of oil (a temporary adverse supply shock) on current output, employment, the real wage, national saving, investment, and the real interest rate. Because the supply shock is temporary, you should assume that the expected future MPK and households’ expected future incomes are unchanged. Assume throughout that output and employment remain at full‐employment levels

(which may change).

b. Analyze the effects of a permanent increase in the price of oil (a permanent adverse supply shock) on current output, employment, the real wage, national saving, investment, and the real interest rate. Show that in this case, unlike the case of a temporary supply shock, the real interest rate need not change. (Hint: A permanent adverse supply shock lowers the current productivity of capital and labor, just as a temporary supply shock does. In addition, a permanent supply shock lowers both the expected future MPK and households’ expected future incomes.)

A4.4.  Economists often argue that a temporary increase in government purchases— say, for military purposes—will crowd out private investment. Use the saving– investment diagram to illustrate this point, explaining why the curve(s) shift. Does it matter whether the temporary increase in military spending is funded by taxes or by borrowing?

Alternatively, suppose that the temporary increase in government purchases is for infrastructure (roads, sewers, bridges) rather than for military purposes. The government spending on infrastructure makes private investment more productive, increasing the expected future MPK at each level of the capital stock. Use the saving–investment diagram to analyze the effects of government infrastructure spending on current consumption, national saving, investment, and the real interest rate. Does investment by private firms get crowded out by this kind of government investment? If not, what kind of spending, if any, does get crowded out? Assume that there is no change in current productivity or current output and assume (for simplicity) that households do not expect a change in their future incomes.

# Problem Set #2

EC 360: Private Enterprise and Public Policy

Paul HS Kim

Michigan State University

Assigned Date: September 20, 2023

Due Date: October 2, 2023 at 12:40pm

Note: Your score will be based on your overall performance in answering all questions in this problem set. Show all logical steps in your arguments. Answers without any explanation will get at most half credit. You are strongly encouraged to form study groups of two-three students (at most three) and submit one homework per group. Make sure you write all group members’ names and student IDs on your submitted work.

This problem set covers the material discussed in lectures 4-7. Problem 4 is a bonus question and you will not get penalized even if you do not submit answers to it. However, if you do decide to answer it you will get bonus points of upto 2 points that will be added to your score in this problem set.

Problem 1. Suppose the market demand for pizza in East Lansing is given by:

Qd = 1110 − 5P

Currently, there are 120 pizza stores in the East Lansing area that produce identical pizzas and as such the market is perfectly competitive. Suppose each pizza store has identical cost function given by:

C(q) =       100      +q + q2,

|{z}

fixed-cost

MC(q) = 1 + 2q

where C(q) is the total cost, and MC(q) is the marginal cost function. As shown in the total cost function, each pizza store incurs a \$100 fixed cost which is a sunk-cost in the short-run but avoidable in the long-run.

Recall that the market supply is the sum of individual firm’s supply functions, and that individual’s (inverse) supply curve is given by its marginal cost function i.e.

individual firm’s inverse-supply : P = mc(q) = 1 + 2q individual firm’s supply : qs = 0.5P − 0.5 market supply : Qs = 120 ∗ qs = 60P − 60

(a) What is the short-run equilibrium market price/quantity of pizza in East Lansing?

(b)   What is the firm’s average cost function? [Hint: you know what the firms’ total cost function is, so how do you compute Average cost from total cost?]

(c)    In the SR, what is each firm’s total profit or loss? [Hint: you know the market price, and know the cost functions]

(d)   Given your answer to the above, would you expect more firms to enter the pizza market or existing firms to exit the market? Why?

(e)    Suppose there’s free entry/exit of firms in the long-run. What is the long-run market equilibrium price/quantity? [Hint: what happens to a perfectly competitive market in the long-run with free entry/exit? Something about each firm producing at efficient scale?]

(f)     How many pizza stores will there be in this LR equilibrium?

Problem 2. DTE energy is a local monopolist of retail electricity and provides electricity to homes in Ann Arbor. Suppose the electricity demand in Ann Arbor is given by:

Qd = 160,000,000 − 200,000,000P = 160M − 200M P

where P is the price (in \$ per kWh), and Q is the total electricity consumption demand in kilowatthours (kWh) and M is one million. DTE’s marginal cost of generating each kWh of electricity is \$0.20. That is its marginal cost of generating electricity is constant regardless of how much it produces.

(a) What is DTE energy’s profit-maximizing quantity and price of electricity?

(b)   What is DTE energy’s mark-up and price-cost margin? [Note: compute the mark-up and margin using monopoly’s variable cost i.e. ignore any fixed-cost it may have]

(c) What is the consumer surplus and producer surplus in the monopoly market?

(d) If this market was perfectly competitive, what would be the equilibrium quantity and price of electricity? [Hint: take monopoly’s marginal cost curve as the market inverse-supply curve] (e) What is the consumer surplus and producer surplus in the perfectly competitive market?

(f)    What would be the deadwight loss associated with DTE energey’s market power? Show the deadweight loss on the supply & demand graph.

(g)   Now suppose that DTE energy generates most of its electricity via fossil fuels. As a result, byproduct of electricity generation is CO2 emissions which imposes negative externality on the society. Assume that DTE energy doesn’t internalize this negative extrnality when thinking about its production cost. Qualitatively, how does your answer to previous question change? That is what happens to the deadweight loss associated with DTE energy’s market power in the presence of negative externality?

Problem 3. Consider the electricity market in Ann Arbor in problem 2, where DTE energy is a monopoly producer. Suppose that it cost DTE energy \$12 million to build a generator (i.e. DTE energy’s fixed cost). [Note: Assume that the electricity is generated via green energy so there is no pollution being emitted]

a)    What is DTE energy’s overall profit (taking into account how much it took DTE energy to build the generator) assuming it faces the same market demand and charges its profit-maximizing monopoly price?

b)   Suppose now that the local government wants to regulate DTE energy due to it being a monopoly. It wants to do so by enforcing a price ceiling in the electricity market (i.e. putting a maximum possible market price for electricity sale). If the government puts a price ceiling of \$0.3, what will be the profit-maximizing price/quantity that DTE energy charges?

c)    What happens to DTE energy’s profit (taking its fixed-cost into account) when there’s a price ceiling of \$0.3/kWh? If DTE energy knew that the local government would regulate the electricity price (i.e. put the price ceiling), would it have chosen to enter the market at all?

d) Suppose Clean Energy Inc., a new energy company is thinking of entering the Ann Arbor electricity market. If it chooses to enter the market, it will also have to incur a fixed cost of \$12M to build a generator. If it chooses to enter the market, it will have the same technology as DTE energy i.e. it can generate electricity at constant marginal cost of \$0.2/kWh. And if it does enter the market, it will split the electricity market demand by half with DTE energy i.e. both companies will be an effective monopoly for half of Ann Arbor’s electricity market and will face market demand of

If Clean Energy Inc. enters the market, what would be its profit-maximizing price/quantity?

e)    If Clean Energy Inc. enters, how much profit will it generate? (including its fixed-cost) Given your answer, do you think Clean Energy Inc. should enter the Ann Arbor electricity market?

Problem 4. [Bonus Question: while you are not required to complete this question, you are highly encouraged to at least read the associated articles!] For this problem, please read the WSJ articles, “Google’s Antitrust Trial to Set ‘Future of the Internet,’ DOJ Says” and U.S. v. Google: What to Know About the Biggest Antitrust Trial in 20 Years.[1] Please answer the below questions based on the information provided in the articles.

a) Why is DOJ bringing an antitrust lawsuit against Google? What is DOJ’s allegations?

b) What is Google’s response (defense) to the lawsuit?

c) In terms of search engine platforms in the US, what are Google’s competitors if any?

d) Find out how much market share Google (and its competitors) has for its search engine business

i.e. what percentage of people use Google as their search engine?

•   Try using Google to search this information.

• Try using Bing to search this information.