QUESTIONS:

;Solve all the problems.

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Problems (Soluband to problems mariged * appear at the burck al this book. Problems adapted to one calculon is availabin grains it 1. Which assumption about consumer preferences does by three different consumers (Auon, Barbara, and each of the following individuals violate? Camina), holding everything else constant: a. Adam likes basketball more than football; Auon Football more than baseball; and baseball more Barbara Camina than basketball. b. Christina prefers prune juice to orange juice but 02 cannot decide how she feels about grapefruit juice. Blake likes superhero comic books but prefers 5 comic books to 10 comic books. 54 2. By assumption, individual preferences must be tran- sitive so that if A is preferred to B, and B is preferred to C. then A is preferred to C. Suppose that Marsha, 175 24 Jan, and Cindy individually have transitive prefer- ences over three goods: oranges, apples, and pears. Compute the marginal utility of X for each of the If Marsha, Jan, and Cindy were to vote on whether three consumers at each level of X. to name oranges, apples, or pears the "fruit of the b. Based on the data in the table, can you tell month," show that it is possible the preferences for whether any of these consumers are violating any the group might not be transitive. of the standard assumptions about preferences? 3. Draw two indifference curves for each of the follow- c. Is it possible that any of these three consumers ing pairs of goods. Put the quantity of the first good have the same preferences, and that columns for the on the horizontal axis and the quantity of the second three consumers differ only because of the arbitrary good on the vertical axis. units that are used to measure utility? Explain Paul likes pencils and pens, but does not care $6. A consumer's utility function is given by U= XY. which he writes with. where MU, = F and MU, = X. Rhonda likes carrots and dislikes broccoli. a. What is the utility derived from 1 unit of X and Emily likes hip-hop ITunes downloads and 2 units of Y? What is the utility derived from doesn't care about heavy metal downloads. 2 units of X and I unit of 1? What is the utility d. Michael only likes dress shirts and cufflinks in 1 derived from 5 units of X and 2 units of Y? to 2 proportions. b. How does the consumer rank the following E. Carlene likes pizza and shoes. bundles? *4. Suppose that John is indifferent between consuming Bundle Quantity of I Quantity of F bundle A, which consists of 4 apples and 1 peach, and bundle B, which consists of 4 peaches and A 2 2 1 apple. If John were given the choice between bun- dle A and bundle C, which contained 3 peaches and 2 apples, which should be pick? (Hint: Draw an 1 5 indifference curve or two.) 3 2 5. The following table displays the total utility ((X ) that 3 comesponds to the number of units of X consumedGraph an indifference curve that shows the bun- e. Connect the dots to create Jose's budget con- dles of X and Y for which U = 6 and U = 8. Is straint. What is the slope of the budget constraint? the "more is better" assumption satisfied for X f. Divide the price of fireworks by the price of and Y? music. Have you seen this number before while 7. Kelly's utility function is given by U= 5X + 2F, working on this problem, and if so, where? where MUx - 5 and MU, = 2. R. Suppose that a holiday bonus raises Jose's in- a What is MRS,.? come temporarily to $360. Draw Jose's new b. What is MRS. when X = | and Y - 57 When budget constraint. X = 2 and Y = 257 h. Indicate the new bundles of music and fireworks c. Draw a sample indifference curve. that are feasible, given Jose's new income. 8. Andrea loves to cat burritos with hot sauce. In fact, 1 1. Suppose that only one person in the world sells ice she cannot enjoy a burrito (8) unless it has three cream. She employs a strange pricing policy: You can servings of hot sauce (H ). She gets no additional en- buy I ice cream cone for $1, but if you buy 2 cones, joyment from more than three servings per burrito. you have to pay $2 each. If you buy 3, you have to Thus, her utility function is U= min [ R,-H ]. Graph pay $3 each, etc., so that if you buy 10, you have Andrea's indifference curves for U= 1 and U= 2. to pay $10 cach. You have $100 dollars to spend on ice 9. Suppose John's utility function is 4XY, where X is cream comes and chocolate milk, and chocolate milk consumption of beer and Y is consumption of pizza. costs $1 per unit Draw your budget constraint. This For this utility function, the marginal utility of X' is strange ice cream pricing, where buying more costs given by MU, = 41, the marginal utility of F is given you more, is called a quantity surchingc. by MU, = 4X. 12. John enjoys ordering out for pizza and renting move I Suppose Y= 3. Calculate John's utility for * = 2. ies online. He makes $30 each week at a part-time 3, 10, and 11. For a given level of Y, does good X job. If movies cost $2 per rental and pizza costs display diminishing marginal utility? $7.50 per slice. graph John's budget constraint. Then illustrate the effects of each of the following b. Suppose X - 3. Calculate John's utility for Y - 2. 3, 10, and 1.1. For a given level of X, does good Y display diminishing marginal utility? a. John's mother finds a coupon good for one free pizza and gives it to John. Find three different bundles containing X and Y' that give John 48 utils of satisfaction. Plot the The company John rents movies from sponsor a thece bundles and connect them with an indiffer. holiday wock promotion: Rent the first five mov- ance curve. What happens to the marginal rate tea at their regular price, and all movies after the of substitution between X and Y as consumption of fifth are half off X increases? C. John's favorite pizza place increases the price of 4. Does the principle of diminishing MAS depend pizza from $7 50 to $10. on the diminishing marginal utility of X and IT 13. Good X sells for $4, and good F sells for $2. At your 10. Jood gets satisfaction from bach music and fireworks. current level of consumption, the marginal rate of Joad's income is $340 per week. Music costs $12 per substitution between X and Fis4. CD, and fireworks cost $8 per bag. Draw an indifference curve and budget constraint it Graph the budget comuralet Jose faces, with that reflects the facts given above. (Mar: You music on the vertical axis and fireworks on the will have to choose an inhial income level and horizontal suit an initial bundle of X and F.) b. IT Just spends all his income on music, how b. Are you maximizing your utility? much music can be afford? Plot s point that c. If you are not maximizing your utility, are you illustrates thin scenario, buying too much X or too much IT Explain. c.If hand spends all his incoat on fireworks, hue Id. Andre gets utility from playing lower tag and read many bags of fireworks can be afford? Plot a ing books. Each week, Andre spends his entire $100 point that Whoirates this scenario paycheck on both pooda. One hour of lover bop coun If Joad spends half his income on fingworks anal 130: a book costs $10. bull his income un mails, how much of each a. Graph Andre's budget constraint. Pat books on can be allland? Plot a point that illustrates this the honvontal anis and hours of laser tag on theQuestion 1 (40 pts) Consider the following model of a vertical market. In a market for a good, there exists a monop- olist manufacturer with a marginal cost of 5 who charges a wholesale price of Pm to a monopolist retailer. The retailer's only marginal cost if the manufacturer price; however, the retailer must pay a fixed cost F in order to sell the manufacturer's goods. (For example, he must remodel parts of his store.) The retailer charges a price to consumers of pr. Demand is linear with p, = 15 - Q. a. Write down the retailer's profit function. b. What is the price the retailer charges as a function of P.? c. Write down the manufacturer's profit function as a function of p.. What is the optimal pm set by the wholesaler? d. Given p.,, what is the retailer's profit? At what level of F will the retailer no longer be willing to purchase from the manufacturer? e. Consider the vertically integrated monopolist. At what level of F will the vertically inte- grated monopolist no longer be willing to stock the good in his retail division? At what values of F will the manufacturer carry the good if and only if it is vertically integrated with the retailer? Question 2 (35 pts) Suppose that two types of people exist, high (H) and low (L) productivity. Education is worthless other than to potential employers. Those workers that receive an education are identified as H- type and get a wage of wy = $9,000 while those that do not are identified as L-type and receive WL = $7,500. H-types can obtain an education at a cost of CH = $1,000, and L-types receive an education at a cost of GL = $3,000. Denote A as the probability that an individual is high productivity, A = P(H). a. Show a separating equilibrium exists. b. Does a pooling equilibrium exist at A = !?146 Part 2 Consumption and Production probably look like? Explain your reasoning by ence curve that reflects Cheryl's situation. What drawing a graph that includes her indifference curves must her indifference curves look like? and a hypothetical budget constraint. C. Suppose Cheryl receives a gift of one ugly 21. Economist Joel Waldfogel may be America's biggest sweater from a coworker. Show the effect of the Grinch, He bemoans what he calls the "deadweight gift on Cheryl's budget constraint. Where on the loss of Christmas" created when people give gifts constraint is Cheryl likely to maximize her utility? (such as ugly sweaters) the recipients would rarely. d. Waldfogel suggests that the world might be a if ever, buy for themselves. happier place if instead of giving ugly sweat- a. Draw a graph with a budget constraint showing ers, people simply gave an equivalent amount of affordable bundles of a composite good costing cash. Draw the budget constraint Cheryl would $1 and ugly sweaters. (You may assume some face were this the case. Add an indifference curve level of income and a price for ugly sweaters.) or two to show what happens when Cheryl maxi- h. Cheryl might get some utility from an ugly mizes her utility. Does the cash gift make her sweater, but is currently spending all of her in- happier than the sweater? come on the composite good. Add an indiffer