Help with Microeconomics

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Economics 105 DePaul University Burhan Biner Winter 2014

Problem Set III Due Thursday March 13, 5PM. Before you begin writing your answers make sure that you read and fully understand the assignment rules. As long as your handwriting is legible you can write your homework rather than type. Assignment rules:

1. Homework assignments must be submitted at the end of the lecture, in class, on the due date.

2. Late homework assignments will not be accepted under any circumstances. 3. Submitted assignments must be stapled. Non-stapled assignments will receive a

maximum grade of 80%. A non-stapled homework will be graded as normal and then the grade will be multiplied by 80%.

4. Your answers must be numbered and must be presented in a neat and orderly fashion. This means that the answers must be ordered in the same order as the questions and within each question, the sections must appear in the alphabetical order. You are required to place the entire answer for a question or a section within that section. For example, if the answer to section d of question 3 contains some verbal answer as well as a graph, then both the verbal answer and the graph must appear together in your answer to section d of question 3. You cannot provide the verbal answer and write, “see the attached graph”. I instructed the Grader to give a maximum of 80% to an assignment in which the answers are in the wrong order. In an extreme case, if the submitted assignment is not comprehensible and the graders cannot figure out which answer corresponds to which question, the assignment will receive the grade of 0%.

5. Assignments must be typed, except graphs and formulas or they will receive a maximum grade of 80%. Otherwise, the homework will be graded as normal and then the grade will be multiplied by 80%.

6. In all of the questions you are required to show the way you got to the solution. Presenting only the final answer, without showing your work will result in zero points for that question, even if the answer is correct.

7. Only those graphs that I ask to plot with Excel need to be plotted with Excel. Other graphs can be drawn either with pencil or using Excel.

8. You are encouraged to collaborate on the homework assignments, but submitted work must be your own. This means that you should write your answers independently. On each assignment you are required to note the names of your collaborators. NOTE: Turning in identical homework assignments will result in a zero for both parties.

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1. (25 Points) Consider the market for bikes. Suppose it is a perfectly competitive market. The market demand for bikes is given by the equation QQPD 5110)( −= and the market supply for bikes is given by the equation .25)( QQPS += A firm faces costs given by the total cost function 1305.2)( 2 += QQTC . Its marginal cost curve is given by QQMC 5)( = .

(a) What is the profit-maximizing quantity for this firm? (b) What profit/loss does the firm earn (specify if it is a profit or loss)? (c) What are the fixed costs for this firm? (d) What should this firm do in the short-run? Explain. (e) Suppose the fixed costs of the firm decreased, what would happen to the profit-

maximizing quantity? Clearly explain your reasoning. 2. (25 Points) Consider the market for scooters. Suppose it is a (single-price) monopolistic market. The market demand for scooters is given by the equation QQPD 8100)( −= . The firm faces costs given by the total cost function

10343)( 2 ++= QQQTC and marginal cost function 346)( += QQMC . (a) Draw the firm’s problem. Your graph should include (ATC, MC, MR, D). (b) Calculate the profit maximizing quantity of this firm. Show it on your graph. (c) What profit does the firm earn? (d) Calculate the deadweight loss generated by this monopoly.

3. (25 Points) Suppose that a monopoly faces a demand curve QP 230 −= and its marginal cost curve is QMC = .

(a) Plot the average revenue, marginal revenue and marginal cost curves for this monopoly.

(b) Find the profit maximizing price and output for this monopoly. (c) Find the consumer surplus, the producer surplus, the total surplus and the

deadweight loss in the (monopolized) market. (d) Find the competitive price and quantity (as if the above marginal cost

curve represents the market supply curve). (e) Find the consumer surplus, the producer surplus and total surplus in the

competitive market. (f) Plot a graph on which you illustrate the monopoly equilibrium, the

competitive equilibrium and the deadweight loss due to the monopoly.

4. (10 Points) Suppose that Kerasotes Crown Village Theaters Cinema is a local monopoly. It estimated the following demand curves for different groups of customers:

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Adults QP 212 −= Children QP 38 −= Students QP 410 −=

The marginal cost of the cinema is $2 per customer. (a) What is the marginal revenue in each submarket? (b) What price should the cinema charge in each of the submarkets if its goal is to maximize profits?

5. (15 Points) The following table shows the profits of two producers of pancakes for various combinations of prices that each firm might charge.

Aunt Jemima

$1 $2 $3 $4

$1 20, 40 25, 50 30, 40 35, 30

$2 25, 50 30, 60 35, 50 40, 40

$3 30, 60 35, 70 30, 60 45, 50 Hungry Jack

$4 25, 70 30, 80 40, 75 35, 70

a. (3) Does “Hungry Jack” have a dominant strategy? If he does, find it. b. (3) Does “Aunt Jemima” have a dominant strategy? If she does, find it. c. (3) In this game there is a unique Nash equilibrium (in pure strategies).

Find it and prove that it is indeed Nash equilibrium. d. (3) Choose one outcome other than the Nash equilibrium and show why it

is not Nash equilibrium. e. (3) Is the Nash equilibrium in this game Pareto optimal? Prove your

answer.