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SP10.1 Price discrimination Valair is an airline flying a particular route that has seasonal demand. The firm's total demand is given by: Q = 600 - 4P (10.5) where Q is the number of passengers per year, in thousands, and P is the fare (in f). In the peak season the demand is given by: QH = 320 - 1.5PH (10.6) and in the off-season the demand is given by: Q1 = 280 - 2.5P1 (10.7) assume that fixed costs are $6 million per year and that marginal costs are constant at $60 per passenger. Thus the cost function is given by: C = 6000 + 60Q (10.8) where C is total costs (in E'000). a. Calculate the profit-maximizing price and output without price discrimination, and the size of the profit. b. Calculate the profit-maximizing price and output with price discrimination, and the size of the profit. c. Calculate the demand elasticities of the two segments at their profit-maximizing prices.Multiple-Choice 1 . Picture a graph with chicken on the vertical axis and pork on the horizontal axis. Larry's indifference curves are vertical. This implies that he 3. receives no satisfaction from pork. b. receives no satisfaction from chicken. c. dislikes pork. d. dislikes chicken. 2. Wrestling tickets sell for $10 and stock car race tickets sell for $20. Suppose that Billy Bob, whose preferences satisfy all the usual assumptions, buys five wrestling tickets and two stock car race tickets each month. With this consumption bundle, his marginal rate of substitution of wrestling matches for stock car races is 3. Which of the following is correct? 3. Billy Bob could increase his utility by buying more wrestling tickets and fewer stock car race tickets. b. Billy Bob could increase his utility by buying more stock car race tickets and fewer wrestling tickets. c. Billy Bob is at an interior solution and is maximizing his utility. d. Billy Bob is at a corner solution and is maximizing his utility. 3. Ginny must spend her entire income on sunscreen and Silly Putty and chooses to spend it all on sunscreen. buying ten bottles. Which of the following statements musrbe true'il a. she considers SillyI Putty to be a bad. b. the first unit of Silly Putty must have zero marginal utitity. c. the first unit of Silly Putty must generate less utility than the tenth bottle of sunscreen. d. the first unit of Silly Putty must generate less utility per dollar than the tenth bottle of sunscreen. Fill-in 4. Il' Gaston's marginal rate of substitution for two goods is the same, no matter how much of each good he buys, then the two goods must be 5. Indifference curves are convex to the origin because of marginal rates of substitution. Tme-False-Ambiguous and Explain Why 6. People's Indifference curves for oatmeal and caviar are parallel to one another. 3". If you know the slope of the budget constraint for two goods, then you know the prices of the two goods. 3. Derek likes one scoop of chocolate ice cream better than one scoop of vanilla ice cream and one scoop of vanilla ice cream better than one scoop of strawberry ice cream. Therefore, he will like one scoop of chocolate ice cream betterthan one scoop of strawberry ice cream. 9. Both Tums and Rolaids will cure David's heartburn, and he regards them as perfect substitutes. Therefo re. his indifference curves will be linear with a slope of H1. Short-Answer 10. Rose loves to eat eggs, but they make her bteak out in a rash. Luckily, two capsules of Rash- B-Gone per egg are a perfect antidote. Rose has budgeted $5 for eggs and RashaEl-Gone this month. The cost of an egg is 1 I} cents and the cost per Ras h-B-Bone tablet is 20 cents. Rose will, therefore, buy how many eggs and how many capsutes of RashBGcne? 11. Jonathan likes Playstatlcn games {P} and Hot Pockets {H}. Playstation games cost $40. Hot Pockets cost $2. donathan's monthly budget for these items is 31 0t]; and his utility function is. UfF. H) = P'H'\". Find Jonathan's utility-maximizing bundle and his level of utility. 12. Caitlin likes to go to the mall to buy sandals {3} and handbags [H]. Her utility function is U[S. H} = SmH\". The price of sandals is $1 a, and the price of handbags is can. How much money should Caitlin bring with her if she wishes to receive a utility level of 16 from her trip to the mall? 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. Katrina (who owns a cat} has the following utility function. U: F+ M where F= cans of Friskies cat food and N: cans of Nine Lives cat food. The price of Friskies is $1 per can. The price of Nine Lives is $2 per can. How much of each will Katrina buy if she has $20 to spend on cat food? Boris has an income of $100 per month. Initially the price of food is $1 per bag, the price of prune juice is $2 per bottle, and Boris buys no prune juice. Then the California prune growers launch a very slick advertising campaign convincing Boris that prunejuice is very hip, so he starts buying 10 bottles per month. Boris's income, the price of food, and the price of prune juice have all remained the same. Show graphically why and how Boris has changed his consumption bundle. Bulk Phone Inc. offers a discount for bulk purchases. Calls cost 10 cents per minute, but if you call for 100 minutes or more. you get a 10 percent discount on your entire phone bill. Draw the budget constraint facing the firm's customers. Bonus Phone Inc. offers a bonus to frequent callers. Calls cost 10 cents per minute. but for every 100 minutes that you call during that month, you receive 100 free 'bonus' minutes. Draw the budget constraint facing the firm's customers. How many minutes would you select if faced with this budget constraint? A newspaper article says, 'Sales of SU'v's have plunged in recent months as the price of gasoline has soared. Manufacturers have noticed this change in tastes for SUVs and have begun pouring their resources into producing more fuelefficient vehicles.' Do you agree with the article that consumers' 'tastes' for SUlv's have changed? Explain. LaTonya's utility function is U: 5.4532. The price of A is pa: $10, the price of His on: $5, and 10 her income, if is $200. What is her optimal consumption bundle? How much utility does she receive from this bundle? If her utility function was U: 10ADE', how would her consumption decision change? Use an indifference mapping to show Blanchflower and Oswald's finding about happiness (from the Application at the beginning of this chapter} that 'to \"compensate\" men for unemployment would take a rise in income of approximately $60,000 per annum.' a. Lauren is at the grocery store, where there is a sale on cereal. Cereal is only $1 per box, but next week it will be $2 per box. Lauren has $20 to spend on cereal in this two-week period. Show her cereal budget constraint and predict the point on the budget constraint that she'll select. b. Lauren is at the grocery store, where there is a sale on bananas. Bananas are only 25 cents per pound, but next week they will be 50 cents per pound. Lauren has $1 to spend on bananas in this two-week period. Show her banana budget constraint and predict the point on the budget constraint that she'll select. Explain why this is likely to differ from the point that she selected on her cereal budget constraint. Addie can buy vitamins at the corner store for $5 per bottle or over the Internet at $4 per bottle. (The vitamins are identical.) The $4 per bottle includes the shipping cost, but there is a $5 fee for handling each order on the lntemet. Draw a budget constraint showing the tradeoffs she faces, then explain, using indifference curves, where she'll buy the vitamins. Suppose that Zach's monthly income is 31000, the price of food is $10 per unit, and the price of housing is $50 per unit. He initially consumes 50 units of food each month and 10 units of housing. Then Zach's income climbs to $1200 per month, the price of food climbs to $13.33 per unit, and the price of housing falls to $40 per unit. Show how these changes shift Zach's budget constraint. Is he better off before or after the shift in the budget constraint? The Hormsbury family's income is $3000 per month. They purchase two things, doctor visits. Bid and other stuff, 03 Doctor visits cost $100 each and other stuff costs $1 per unit. Originally no medical insurance is available. but then a plan is offered that costs $300 per month and pays 00 percent of the cost of doctor visits, up to 10 visits per month. Show how the availability of this medical insurance will affect the Hormsbury's budget constraint. l 1. Graph a typical indifference curve for the following utility functions and determine whether they obey the assumption of diminishing MRS. Pick a utility such as 10. a. U(x, y) = 3x + y b. U( x, )) = xy c. U(x, ) ) = Vx2 + 2 d. U(x,)) = Vx' - y2 e. U(x, J) = x2/3 1/3 f. U(x, )) = logx + log y where log is the natural log (In) 2. Suppose a consumer's preferences for two goods can be represented by the Cobb- Douglas utility function U(x, J) = Ax-J', where A, a, and Bare positive constants. a. What is MRS ? b. Is MRS. , diminishing, constant, or increasing as the consumer substitutes x for y along an indifference curve? c. On a graph with x on the horizontal axis and y on the vertical axis, draw a typical indifference curve. Indicate on your graph whether the indifference curve will intersect either or both axes. 3. Ch 3, Problem 3.6 For the following sets of goods draw two indifference curves, U, and U2, with U2 > Up. Draw each graph placing the amount of the first good on the horizontal axis. a. Hot dogs and chili (the consumer likes both and has a diminishing marginal rate of substitution of hot dogs for chili) b. Sugar and Sweet'N Low (the consumer likes both and will accept an ounce of Sweet'N Low or an ounce of sugar with equal satisfaction) C. Peanut butter and jelly (the consumer likes exactly 2 ounces of peanut butter for every ounce of jelly) d. Nuts (which the consumer neither likes nor dislikes) and ice cream (which the consumer likes) Econ 3070 Prof. Barham 4. Repeat Problem 2 for the quasi-linear utility function U(x, y) = 2x + y. Chapter 4 Problems: 5. Julie has preferences for food, F, and clothing, C, are derived by a utility function U(F,C)=FC. Food costs $1 a unit and clothing costs $2 a unit. Julie has $12 to spend on food and clothing. a. Give the equation for Julie's budget line. If food is on the vertical axis, what is the slope of the budget line? b. Graph Julie's budget line. Place food on the vertical axis and clothing on the horizontal axis. c. On the same graph, draw an indifference curves that is tangent to his budget line. d. Julie is a utility maximize, write the objective function. e. Write down the full optimization problem with the objective function and the Constraint d. Using calculus and algebra, find the basket of food and clothing that maximizes Julie's utility (ie. solve the maximization problem you wrote down in e) (Assume Julie can purchase fractional amounts of both goods.) Do not solve this using the tangency condition taught in the book solve it like in class