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(solution) Intermediate Microeconomics (ECON 2020) Problem Set # 2 Markus P.

Just for Q 2 - Q7, PLZ help me !!!! the questions are attached below.

Intermediate Microeconomics (ECON 2020)

Problem Set # 2

Markus P. A. Schneider

September 28, 2015 Answer each question completely (all parts) and indicate your final answer clearly. It is important that you show all

the steps in your reasoning to receive full credit for your answer. 1. Answer the following questions about the model of the firm.

(a) What is the firm?s primary motivation? Under what constraint does the firm try operate?

(b) What is the secondary (or dual) problem that the firm is also solving?

(c) Define decreasing-, constant-, and increasing returns to scale in terms of how average cost changes

as the scale of production is increased.

2. Assume that there are 6 firms producing a good and all have the cost function C[y] = 0.5y 2 + 8

(M C[y] = y), where y is the quantity of the good a single produces. Use this information to answer

the following questions.

(a) Sketch the marginal cost curve and average cost curve. Be sure to clearly label your axes and

which curve is which.

(b) If demand is given by X[p] = ?10p + 80, at what price will the market clear in the short-run?

How many units will be sold in the short-run?

(c) Sketch the short run-supply curve for this market and add the demand curve to your sketch to

indicate the competitive market equilibrium.

(d) Calculate the total profit / loss each firm is making / incurring by selling the good at this price

you found in (c).

3. Assume that the cost function for each firm and market demand are the same as given in problem 2,

and answer the following questions.

(a) Based on your answer to 2 (d), will some of the 6 firms stop producing this good or will more

firms enter this industry in the long-run?

(b) Add the long-run supply curve to the sketch you made for 2 (c) and indicate the long-run market

equilibrium.

(c) How many firms will there be in the long-run and how much of the good will be produced? What

will the long-run price of the good be?

(d) Based on the shape of the long-run supply curve, do you think production in this sector uses a

scarce natural resource? What shape should the long-run supply curve have if there was ?congestion?? 1 4. Imagine that one of the firms described in problem 2 (C[y] = 0.5y 2 + 8 and M C[y] = y) is able to take

over the market and act as a monopolist. Use this information to answer the following questions.

(a) Given that the demand of the good remains unchanged (X[p] = ?10p + 80), sketch the marginal

revenue curve for the monopolist on the same graph as the demand curve and the single firm?s

supply curve (M R[y] = ?0.2y + 8).

(b) How much of the good will the monopolist produce? At what price will the monopolist sell the

good?

(c) Calculate the monopolists profit. How does it compare to each firm?s profit when there are 6

firms, i.e. the answer to 2 (d)?

(d) At this level of production, is technology exhibiting increasing, constant, or decreasing returns to

scale?

5. Answer the following questions assuming there are two firms with the same cost function given in

problem 2.

(a) Describe the three strategies the two firms might choose for how to determine how much to

produce and at what price to sell the good. What are the benefits and costs of each strategy from

the perspective of the individual firm.

(b) If the two firms take each other as given, we can derive a response function for each of them:

yi = ? 20

1

hyj i +

12

3 where hyj i refers to the output that the ith firm expects the j th firm to produce (if i = 1, then

j = 2 and vice versa). Solve for the Nash equilibrium level of output that each firm will produce.

At what price will the firms sell the good if they take each other as given?

(c) Calculate how much profit each firm will make if both play their Nash equilibrium strategy.

(d) Calculate the amount of profit each firm would make if both engaged in cutthroat price competition.

(e) Why might these firms act competitively? Construct a game in which each firm can choose to

either take the other as given as in part (b) or try to undercut the other?s price. Assume that

if a firm successfully wins a price-war, it becomes the sole monopolist (problem 4). The firm

that looses has debt equivalent to the fixed costs implied by the cost function. Identify the Nash

Equilibrium of this game and discuss the implications.

6. Compare the market outcomes across problems 2 - 5 by doing the following:

(a) Sketch the market demand curve (X[p] = ?10p+80) and the long-run supply curve that you found

in problem 3. Indicate the different market outcomes when there are 6 firms, 2 firms engaged

in cutthroat price competition, 2 firms acting as Cournot duopolists, and when only one firm

supplies the good (as in 4).

(b) Calculate the consumer surplus associated with each situation and compare it to the individual

firm?s level of profit in each outcome. 2 7. If a group of firms can exercise some price-setting by taking each others? output as given, they can

charge a ?mark-up? above the marginal cost of producing the good. This mark-up will proportional

to the elasticity of demand, ?, and the number of firms, k. The following equation gives the exact

relationship between marginal cost and the price charged by each producer:

p= 1

MC

1 + k1 ?1 The elasticity of demand is ? = ?3 and each producer has a marginal cost of producing the good that

depends on the level of output, M C[y]. Use this information to answer the following questions.

(a) What is the relationship between price and marginal cost in a competitive market? Does this

imply that firms make zero profit? Explain your answer.

(b) How much is the markup above marginal cost that a single firm acting as a monopolist could

charge?

(c) What would the markup be if there were two firms that took each other as given (acted as Cournot

duopolists)? What if there were four such firms?

(d) What happens if there are many producers that take each other as given so that k is a very large

number? (Hint: calculate the markup for k = 100 and k = 1, 000 and compare them if you are

not sure.)

(e) If the k firms formed a cartel, what markup would they charge? How would each firm?s individual

profit compare to the profit of one firm acting as a monopolist?

Extra Credit (2 pt) Expand the game that you constructed in problem 5 (e) to incorporate the possibility

that the two firms might collude and effectively form a Cartel. Be sure to calculate the amount of profit

that each firm receives in this case. 3

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