ECON 601 Final: ECON 601 Iowa State Econ601FinalF14

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turquoisegnu128

15 Feb 2019

School

Iowa State University

Department

Economics

Course

ECON 601

Professor

All

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Harvey lapan: consider a monopoly firm with cost curve: q= , where costs are measured in terms of the numeraire good. The firm has two types of customers, with quasi-linear preferences as follows: There are an equal number of each type of customer. In the above, ( consumption vector of customer of type h, where m is the numeraire whose price is one and x is the monopolist"s product. Assume each consumer"s income is high enough so that solutions are interior. ,h: consider the case of pure monopoly, in which the firm charges the same price to all customers, and customers choose how much to buy at that price. Find the profit maximizing solution for the monopolist, and calculate the inefficiency (deadweight loss) due to pure monopoly. (11 points: second degree price discrimination. Suppose the monopolist can offer two different packages.

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PROBLEM 1 (This one is designed to give you lots of math practice!)

Consider the following individual utility functions:

Adam Smith: U(x,y) = xy

Jeremy Bentham: U(x,y) = x^ay^b (Cobb-Douglas utility function)

Alfred Marshall: U(x,y) = ln x + ln y

John M. Keynes: U(x,y) = x + y^b (Quasi-linear utility function)

Joan Robinson: U(x,y) = aX + bY (linear; perfect substitutes)

a. Solve for the MRS(XY) for each of the gentlemen (i.e., all but Joan Robinson). Show that Mr. Smith, Mr. Bentham, and Mr. Marshall all have diminishing MRS(XY), but that if a=b=2, their preferences exhibit constant, increasing, and decreasing marginal utility respectively. (Fortunately, diminishing MRS is the condition that guarantees convex indifference curves, so we can solve for their optimal consumption!)

b. What is the general formula for Mrs. Robinsons (constant) MRS?

c. Find demand functions for x and y for Smith, Bentham, Marshall, and Keynes. Assume that each man has income I and that the prices of x and y are p_x and p_y respectively.

d. Now assume that a=1/2, b = 1/4, I = 600, p_x = 10 and p_y = 20. Use these values to find the utility-maximizing quantities of x and y consumed by each man.

e. Find an expression for the share of income Mr. Bentham and Mr. Marshall each devote to the consumption of good x, where this share, s_x, is defined as

(p_x x)/I.

f. Find expressions for the income elasticity of demand for good x for Mr. Bentham and Mr. Marshall. Find expressions for the (own) price elasticity of demand for good y for these two men.

aquamarinescorpion997

This question explores the quasi-linear utility function. Consider Thomas who has preferences over food, QF, and clothing, QC. His preferences are represented by

U (QF,QC) = [alpha]QF^(1/3) + QC

where [alpha] > 0. Let pF, pC, and I represent the prices of food, clothing, and Thomas's budget for food and clothing.

i. Using the Lagrangian method, solve mathematically for the demand function for each good. Make sure to show each step of your work.

ii. Determine whether food and clothing are normal or inferior goods for Thomas. Prove your answer mathematically.

iii. Are food and clothing substitutes or complements for Thomas? Prove your answer mathematically.

iv. Now assume that [alpha] = 3, and I = $1,224.

1. If pf = $3, and pc = $12 what is Thomas's demand for food and clothing?

2. If the price of food goes down to pf = $4/3, what happens to Thomas's demand for food and clothing?

3. If Thomasâ income falls to $996, what happens to quantity consumed of each good?

4. Graph Thomas's inverse demand curve (i.e price on y-axis, quantity on x-axis) for food when his income is I = $996 and the price of clothing is pc = $12. Be as precise as possible, labeling the exact value of any important points on the graph.

mauvefox570

Essay questions are due at the end of the course. It is strongly recommended that you accumulate your answers as you complete each unit and don't leave them all until the last minute. Please type your responses to the following short answer/discussion questions and short problems. Although your answers need not be lengthy (generally, 1-2 short paragraphs is fine), you should be careful to respond to all parts of the question asked. It is very important that your answers demonstrate that you have made the effort to read the chapter that relates to the question and thoroughly studied the relevant topic. Answers should be submitted in complete sentence and paragraph form, and writing presentation is important. Please remember that late essay questions are NOT accepted. 1. How is a "market" defined? Distinguish between an industry and a market. (1 point) 2. Suppose a market becomes more competitive over time. What happens to the elasticity of demand for a particular firm's good as its market becomes more competitive? (1 point) 3. Why are the monopolist's and the monopolistically competitive firm's demand curves downward sloping while the competitive firm's demand curve is horizontal? (1 point) 4. Why is a perfectly competitive firm's long-run supply curve the same as its marginal cost curve above the average total cost curve? (1 point) 5. Explain why monopolists do not achieve efficiency. (1 point) 6. Another student advocates the forced break-up of large firms, such as Microsoft and AT&T, on the grounds that they have a lot of monopoly power, which they use to charge inefficiently high prices. According to Schumpeter, would breaking apart these gigantic firms guarantee consumers lower prices? Explain. (1 point) 7. Explain why firms should not shut down in the short run until price falls below average variable cost. (2 points) 8. Suppose your economics professor publicly states that she grades on a curve (i.e., the top 10% of the students get an A, the next 20% get a B, the next 40% get a C, the next 20% get a D, and the lowest 10% fail). The whole class could save itself a lot of work by agreeing privately not to study at all for the final exam and just letting the rankings thus far determine the final grades. Why might such an agreement be difficult to maintain and enforce? Which market structure, if any, is this situation most analogous to? (1 point) 9. Why do firms practice price discrimination? Is efficiency affected by price discrimination? If so, how? (1 point)

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ECON 601 Final: ECON 601 Iowa State Econ601FinalF14

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