Question 1. A risk averse individual with preferences U=W^1/2 appears as a contestant on a new television game show. At the start of the show the TV host gives the contestant $10,000 in cash. The contestant is then given the opportunity to trade the $10,000 in exchange for one of two risky propositions that are denoted "A" and "B".
- In "Proposition A" the contestant will be asked to roll a fair six sided dice. If the dice shows the number ONE the contestant will win the grand price valued at "A" dollars. If the number on the dice is not ONE the contestant wins nothing. What is the minimal value for "A" that would entice this person to trade in their $10,000 cash and play "Proposition A"?
- In "Proposition B" the contestant will be allowed to draw a ball from a large urn. One of the balls in the urn will be worth $4,000,000. The other balls will be worth nothing. Because each ball has an equal likelihood of winning the person's chances of getting $4 million will be inversely related to the number of balls in the urn. What it the largest number of balls in the urn that would entice this person to trade in their $10,000 cash and play "Proposition B"?
- Suppose the game show started differently. Instead of being given the $10,000 the contestant was offered a risky proposition to toss a fair coin: Heads you win $20,000 Tails you win nothing. Explain how would the minimal prize determined in "Proposition A" and the maximal number of balls in determined in "Proposition B" be affected if we added risk to the opening of the game show? Why does this result make sense in this context? Why wouldn't this change affect a risk neutral person in the same way?
Question 2. Bob has $25 in a savings account and a 1982 Honda worth $200. His preferences are given by U=W^1/2. He purchases an insurance premium for $14.75 that promises to pay him $200 if he wrecks the Honda. Assuming he acts to maximize his expected utility, what is the lowest probability that Bob attaches to his chances of wrecking the car? Explain his rationale in terms of expected utilities and expected losses.
Question 3. Amber has $25 cash and a $200 phone she bought from Rogers. She is risk averse with U = √W. There is a 10 percent chance that the phone will break. It can't be fixed so she'd lose the $200. No diagrams are required. Rogers offers an insurance plan for their phones. If anything goes wrong, they'll replace it. What is the maximum amount that Amber would pay for this insurance? Rogers also offers a different insurance plan; this one comes with a deductible. Amber will have to pay the first D dollars if her phone breaks but then Rogers will cover the rest of the cost. This plan is cheaper; only $14.75. What is the largest deductible that Amber would accept for this plan?
Question 4. After five years or marriage you've decided to murder your husband. His life insurance policy pays $10000; but the amount increases to $1 million in the event of accidental death. You've thought about poisoning his beer tonight but know there is at least a 10 percent chance the insurance company will find out that it wasn't accidental. A friend knows this guy from Etobicoke who can "make anything look like an accident" but he'll demand to be paid $250,000 for his services. You're risk averse with U=W^1/2.What is the most you'll be willing to pay to have your husband killed? Would you be better off doing it yourself? Explain the economics underlying your decision.
Question 5. A coffee addicted teaching assistant who studies in the Kaneff Centre is desperate for a refill. Walking to the North Building Tim Horton's and back will always take her 20 minutes. A round trip to the Davis Building Tim Horton's will take her 10 minutes if the lineup is short, but 40 minutes if the lineup is long. Her travel time, denoted T, affects her happiness: U=2500-T^2
1. Denote the probability of a long lineup at the Davis Building as Π. What is the Expected Value associated with the two options? Use your diagram from Part a) to explain why this calculation tells you that our teaching assistant is risk averse.
2. The North Building Tim Horton's has closed for the day but a third option is available. An unreliable friend offers to bring a coffee to Kaneff. He says that it will only take 10 minutes, but there is a 50% chance that it will take him 30 minutes. Explain why the availability of this risky option increases our teaching assistant's calculation of π from Part a). No diagram required.
Question 6. A risk averse investor has utility function is (W)=W^1/2 and her initial wealth is $225. For a price of $200 she can re-open an old diamond mine. There is a 60 percent chance that her venture in the diamond mine will be fruitless and her wealth will be $25. There is a 40 percent chance that the business will succeed, she will recover her initial $200 and earn an additional $400; this means a wealth of $625. Assess whether she should engage in this risky venture. Provide a labelled diagram. Suppose that she also has the option of taking on three partners in this venture; Eaton & Eaton call this a syndicate. With four equal partners each invests $50 = $200/4 and they share equally in the profits. Assess whether our investor would favor the syndication option over going it alone.
You are an expected utility maximizing, risk averse micro student with U=W^1/2. After some effort you have narrowed your job search down to two possibilities. Jean Machine at The Dixie Mall will pay 10 per hour. Based on 40 hours a week your weekly wealth could be W = 10 x 40 = $400 and you'd get U = 20 units of happiness. The Sheridan Reptile Emporium also offers 40 hours a week, but there is an 80 percent chance you will be eviscerated by some 900 kg lizard named Fifi. The blood loss associated with such an encounter would leave you too weak to work so your wealth would be zero. Assume that selling skin tight Parasucos is a completely risk-free endeavor.
- What is the lowest hourly wage you would be willing to accept to work at the Emporium?
- The Emporium will pay you the wage you've calculated above. For a fee of F dollars per week you can be fully insured against reptilian related losses of income. What is the maximum amount you'd pay to participate in this plan? Explain why this is such a huge amount.
Question 7. If you invest your entire wealth of $12 it should be possible to setup a marijuana growing operation in one of the MaGrath Valley townhouses here at UTM. If successful, the investment could be worth $64 by the end of the summer. There is a however a 60 percent chance that the operation will be raided by the UTM Police in which case your wealth would be $0. Your utility of wealth is given byU(W) = W1/2.
- If your goal is to maximize the expected utility of your wealth should you make this investment? What is the most you would invest for a 40% chance of getting $64?
- Three friends from your ball hockey team also have preferences like U=W^1/2 persons have expressed interest in forming a syndicate to make investments. Would you be happier undertaking this venture as one of four equal partners?
- A member of the UTM Police has indicated that if you were to make a "donation" that the possibility of being raided would drop to zero. What is the most that your syndicate would pay for this bribe? Show this in your diagram from Part b.
Question 8. Rana and Saralivein Oakville. Driving to UTM via the QEW takes only 10minutes, but when there is an accident, it takes 40 minutes. Accidents occur with probability π. Driving to UTM along Dundas Street takes 20 minutes under all conditions. Rana is risk averse expected utility maximizer. Her utility from the time spent driving to school, variable T, is given by the utility unction U(T) = 2,500 - T^2. Sara is risk neutral.
- Solve for the value of π that will leave Rana indifferent between routes, and the value of π that will leave Sara indifferent between routes. Explain why Rana's probability is lower. No diagram is required.
- Rana's neighbor has identical preferences and must always drive to UTM every day. Would car pooling be like a syndicate to affect the probability you calculated in part a? No diagram is required.
- Their brother is a risk lover. Does this mean he will drive to UTM along the QEW for any value of π just to get his thrills? No diagram is required.
- Rana can drive the QEW route a fraction of α days a week and take Dundas a fraction of 1 - α days a week. What value of α will maximize her expected utility? How many days a week should she take the QEW?
Question 9. Investors with preferences for risk σ and return μ described by the utility function U = μ- σ^2 can diversify by holding a fraction of their portfolio α in a risk-free government bond that pays a return of μ = 2 percent and a fraction (1 - α) of their wealth in a market index that has return μ = 10 percent but imposes risk of σ = 4 percent.
- Provide a labelled Indifference Curve Diagram that shows the utility maximizing portfolio as bundle "a".
- International financial reforms reduce risk. The market index now has return μ = 10 percent and risk of σ = 2.5 percent. Decompose the utility maximizing response into a substitution effect "a" to "b" and income effect "b" to "c". Show these bundles in your diagram from Part a).
- Does the income effect in your diagram suggest that risk in an Inferior Good? Explain.
Question 10. Bob is a risk averse investor with U = lnWwill invest in a portfolio consisting of Security A and Security B. The performance of these assets depends on whether a certain tax law is passed. If the law is passed Security A will pay $8 and Security B will pay $6. If the law is not passed Security A will pay $10 and Security B will pay $12. There is a 60% chance that the law will not pass. State contingent payoffs are given below.
- Calculate the mean and variance for each security. Calculate the covariance of returns.
- If Bob wishes to maximize his expected value, what portion of his portfolio should be held in Security A?
- What portion of the portfolio should be held in Security A to maximize expected utility.
Question 11. How are convexity and diminishing marginal productivity related? Does diminishing marginal productivity necessarily result in convex Isoquants? Can we have convex Isoquants without diminishing marginal productivity?
Question 12. A utility maximizing consumer believes Goods X, Y and Z are perfect complements. She always combines 2 units of X with one unit of Y and 4 units of Z. Prices are =$1andshehasanincomeof $24. She has the option of joining a price club where all three goods can be purchased for $1 but she would have to pay a membership fee. What is the most she would pay to join this club? No diagram is required.
Question 13. You and a friend named Annika each spend $1440 a month on Tennis, T and Golf, G. You do fine playing her in tennis. Golf if a different matter. You have identical preferences U = TG. Annika is a member of the Royal Mississauga Golf Club and must both Calculate the maximum amount that you would pay to join the golf club and the minimum amount that Annika would accept to sell her membership.
- Is there any chance that the two of you could work out a deal where she sells you her membership?
- What would happen to the maximum amount you would be willing to pay to join the club if your monthly spending was higher than $1440? [Don't recalculate numbers this is a theoretical answer]. How does your answer depend on Golf being a Normal Good?
Question 14. The UTM Faculty Club sells steak dinners D for a price of $64 and wine W for $4 a glass. An economics professor withwith preferences U = D^2/3W^1/3 spends $480 a week at this establishment. Joining the Faculty Club is currently free.
1. Calculate the professor's utility maximizing choices.
2. The Faculty Club has proposed that they will lower the price of steak dinners to only $8 but will implement a membership fee. The price of wine will remain unchanged. Calculate the maximum fee that this professor will pay to join.
3. Does the amount the professor pay get larger or smaller when the steak dinners are an inferior good? Why?
Question 15. It's unbelievable! You've just discovered those $400 designer jeans you've been trying on at Holt's are on sale at an outlet mall in New York City. Even with the exchange rate they'd only cost you $100. Dad is away so the new Lexus is all yours. He'll never notice the extra 5,000 km on the odometer but MapQuest says it will cost you $600 in gas to drive there and back and you've already maxed Dad's Shell card. Your preferences are measured by the utility function U = JS where Good J is jeans and Good S is designer sandals Ps=$100. Your monthly budget for sandals and jeans is $800.
- Provide calculations to assess whether you should spend the $600 and drive to NYC. Briefly explain your results.
- A girlfriend from eco class has also heard about those jeans and says she'd come with you. She's low on cash but could pay at least something towards the gas. Calculate the minimum amount that your friend would have to contribute towards gas to make the NYC trip cost effective for you. Briefly explain your results.
- Your girlfriend can't go. You've just discovered that designer sandals are way cheaper in NYC. Calculate the maximum price that you would pay for these sandals in NYC given that it will cost you $600 to travel. The jeans will still cost you only $100. Briefly explain your results.
Question 16. A utility maximizing consumer with preferences described by the utility function U = 9X^2 +4Y^2 spends $24 to purchase an addictive good X at a price Px=$4 and and a regular economic good Y at a price Py=$2. This person can join a price club where they could purchase good X for Px=$2.
- Provide a fully labelled diagram and supplementary calculations that illustrate the maximum amount this person would pay to join this price club. On the same diagram, show the minimum amount that a person with similar preferences and $24 income would accept to sell their membership in this club. Clearly label the CV and the EV in your diagram.
- Explain why the CV and EV will never be the same amount of money for this utility function. Which is larger?
Question 17. An expensive night club sells only Champagne Cand Caviar V to customers, who want to drink, dine and dance all night in Downtown Toronto. The typical patron of the club has preferences given by U=CV on these goods. Currently the club charges Pc=$160 per bottle and Pv=$80 per ounce. Club management has recently decided to implement a new pricing scheme. They will introduce a Cover Charge (admission fee) but also plan on reducing the price of customer's utility maximizing bundle at the old set of prices. Calculate the maximum Cover Charge that a typical customer would be willing to pay.
Question 18. In an Edgeworth Box model of exchange Adam with utlility U=X^4/5 Y^1/5 is endowed with Fa=(1,6) while Bob with utility U=X^1/5Y^4/5 is endowed with Fb=(3,2). Provide a labelled diagram showing the initial equilibrium F, Pareto Preferred Region, Contract Curve, Core, final allocation E and the price ratio p*. Now switch the endowments to Fa=(3,2( andFb=(1,6). Provide a second labelled diagram showing the initial equilibrium F, Pareto preferred region, Contract Curve, Core, final allocation E and the price ratio p*. Compare the results.
Question 19. In an Edgeworth Box economy initial endowments are Xa=4, Xb=6, Ya=3, Yb=1 and utility functions are Ua=2Ya, Ub=Xb+2Yb. Provide a labelled diagram showing the initial endowment; Pareto preferred region, contract curve and core. Calculate bounds for the equilibrium price ratio.
Question 20. Adam, who believes X and Y are perfect complements Ua-min(2Ya,Xa) is edowed with Fa=(2,2) while Eve, who has preferences Ue=15yE is endowed with Fe=(6,2). Provide an Edgeworth Box diagram that shows the PPR, CC, Core and p, the equilibrium price ratio. Demonstrate your knowledge of the concepts for the PPR, CC, Core and p. Do this by citing the definition, or idea or principle that you used to choose the area that you did for the PPR, or the CC or the Core or the p. Explain why Ea=(3,11/2), Ee=( 5,21/2) with p* = 2.00 could not be an equilibrium outcome.
Question 21. The Cycle of Life Model suggests that life consists of two periods.InPeriod1youareyoungandableto earn income. In Period 2 you are retired. The model usually assumes that you can borrow and/or save at the bank but sometimes there are no banks. Suppose you find yourself stranded on an island. Your only companion is a five-year-old named Simba. You and Simba both have symmetric Cobb Douglas preferences. Because you are a healthy, strong adult you are able to hunt and collect 8 units of food per day; young Simba can only collect 2. You and Simba are both getting older. Simba is getting stronger every day; but sadly, you are losing your abilities, losing your hair and even losing your teeth. In Period 2 you anticipate that you will only be able to collect 3 units of food per day but a healthy, strong and adult Simba will be able to collect 12. In the absence of a banking sector, but with endowments of (8, 3) and (2, 12) what is the pareto optimal strategy that you and he should follow? Explain why this strategy is pareto optimal. Provide a labelled diagram that illustrates how you and Simba will behave.
Question 22. A firm with production function q=K^0.25L^0.25 hires labour for w=1 and capital for r=0.25
- Construct an Isoquant Diagram to illustrate how this cost minimizing firm would produce q = 2 units of output as bundle "a", how the firm would implement a short-run increase in output to q = 4 units when capital is fixed at the level chosen for q = 2 as bundle "b" and how this firm would implement a long-run increase in output to q = 4 when capital in not fixed as bundle "c"
- Provide a Total Cost Curve Diagram to sketch the long-run total cost C = C(q, w, r) and short-run total cost SC = SC(q, K, w, v) curves at q = 0, q = 2, and q = 4.
- Underneath the total cost curve diagram provide and Average Cost Curve Diagram to sketch the long-run AC curve and the short-run SATC, SAVC and SAFC curves at q = 0, q = 2, and q=4.
Question 23. Uncle John lives in a small village. He grows his own tomato andp roduce"UncleJohn'SecretTomato Sauce" which he sells for $5 a can. The firm produces 20 cans of fresh tomato sauce per day, with production function q = min (2K, 5L) and the cost of capital is $4 and cost of labour is $8.
- Provide a labelled Isoquant Diagram showing the cost minimizing combination of labour and capital as bundle A.
- During the summer, a new firm moved into the village and produce organic tomato sauce which gets most of Uncle John's costumer. Therefore, Uncle John must reduce the output to 10 cans a day. In the short run, capital is fixed. On the same diagram show John's short-run response as Bundle B.
- On the same diagram show Uncle John's long-run cost minimizing choices for q = 10 as Bundle C.
- Uncle John has a fixed-proportions production function. Explain why the gap between long-run and short-run costs would be smaller if he operated with a CD production function.
Question 24. A firm with production function q=4K+5L pays input pries Pl=$4 and Pk=$2. The firm currently produces under a quota set at 100 units of output. Beginning next month, the quota will be increased to 200 units. During the first few months the firm will not be able to change the amount of capital used. In the long run both inputs can be varied. Provide a fully labelled Isoquant and Isocost Diagram and the basic calculations to demonstrate that expansion is more expensive in the short run than it is in the long run. Provide a second diagram showing the firms LTC and STC curves from this example.
Question 25. A cost minimizing firm operates with production function Y=K^1/3 L^1/3. The firm purchases capital f or $2per unit and labour for $0.5 per unit. At a price of $6 they sell 4 units of output. Provide a fully labelled Isoquant / Isocost Diagram, supplementary calculations to show the cost minimizing solution. Using the same diagram explain how this cost minimizing firm would respond if they were now restricted to earn no more than $2.50 per unit of capital. The firm continues to produce 4 units of output.
Question 26. A firm with production function Q = KL produces 16 units of output which itsells at a price of $4.50 The firm pays $4 per unit for labor and $4 for capital but faces a regulatory constraint which limits returns to $8 per unit of capital.
- Provide a fully labeled Isoquant Diagram showing the firm's unregulated optimum as "A" and the response to this regulation as "E".
- The A.J. effect tells us that firms facing rate of return regulation will over-use capital. Making reference to your diagram in Part a), explain how this degree of over-utilization will depend on σ the elasticity of substitution.
Question 27. A firm with production function q = min(100K, 50L) hires labour and capital at Pl=$4 and Pk=$2. Producing 200 units of output the firm earns total revenues of $40. Regulators impose a Rate of Return Constraint which restricts the return on capital to $4. Provide one fully labelled diagram comparing the firm's cost minimizing optimum (before regulation) to the firm's behaviour after the constraint is imposed.
Question 28. I've heard that Xiaowen is opening two marijuana grow houses. At the Schreiber wood house the production function is q=2K^1/4L^1/4 while at the MaGrath Valley house the production function is q=4K^1/4L^1/4. In both cases Pl=$16 and Pk=$16. Hopefully she will produce 200 kilograms of marijuana in time for the Christmas bash at the eco department. How should she allocate these 200 units of production between the two operations if she wishes to minimize costs? No diagram is required.
Question 29. An off-campus a gency promises to provide your sociology professor with anun for get table surprise.This firm produces results using RottweilersR and Pit Bulls B as inputs. The production function is q=R^1/3B^1/3. They purchase Rottweilers for $400 and Pit Bulls for $100. Output is sold in a competitive market for $1200.
1. Derive the long-run marginal cost curve for this process.
2. Assume profit maximization and calculate the choices for output. Graph AC, MC and profits.
3. How many dogs are hired and the level of profits. Provide an isoquant diagram.
Question 30. A firm produced with technology given by q={K-8]^1/2 [L-16]^1/2. Note that if K<8 OR L<16 then the firm cannot produce a positive amount of output. Competitively determined factor prices are Pl=$5 and Pk=$5. and the firm sells its product at competitively determined market price of $P. In the short-run capital is is fixed at K = 9 units. Operating under the rules of perfect competition, calculate the lowest market price for output $P at which this firm will continue to supply output in the short-run (not shut down). Calculate how much labor will be demanded at this price and the firm's profits. Provide a fully labeled diagram.
A firm with production function q=K^1/3L^1/3 for $4 an hour and capital for $4 an hour and sells output for $24. The price of capital falls to $1. Provide a fully labelled Isoquant Diagram showing the Substitution Effect and Output Effect for this input price change as "A", "B" and "C".
Question 31. You are the manager of 2 small stores with production functions q = K^1/4L^1/4 and a larger store with production function q = 2K^1/4L^1/4. You hire capital with for $4, labour for $1. When you took over this role, your boss told you that Q = 24 was the profit maximizing output for this multi-plan firm: 24 = q1 + q2 + q3. Now, the price of labour rises to $4. Provide (i) Isoquant/Isocost diagrams, (ii) Total Cost and (iii) Marginal Cost diagrams. Illustrate the substitution effect (point a to b) and output effect (point b to c) on these diagrams. Explain why your firm uses less capital even when the price of labour increases. (September 2010)
Question 32. A constant costs industry is initially in long- run competitive equilibrium. All firms in this industry have long-run total cost functions given by C = 2q^2-30q+800. Market demand initially given by Q=1800-4P decreases to Q1=1200-4P. Solve the equilibrium model.
A constant costs industry is comprised of many identical firms with C = q^2-5q+16. Due to changing consumer tastes market demand initially given by Q = 200 - 40P increases to Q = 300 - 40P. Provide two fully labelled diagrams (typical firm and industry) showing the short-run and long-run responses to this change in tastes. Your answer should provide numerical values for P, q, Q, and n in each of the three equilibria. Briefly indicate how your numerical answers would have differed if this were a decreasing costs industry.
Question 33. A Perfectly Competitive Industry faces market demand Q=24-2P and consists of many identical firms each with total costs C = q^2-nq+16. Provide a pair of fully labelled diagrams and supplementary calculations to illustrate the impact of a $2 per unit subsidy introduced for this industry. Why does the price paid by consumers fall by more than $2?
Question 34. A Perfectly Competitive Industry facesmarket demandQ=14-P and consists of many identical firms each with costs C = q^2-nq+9. Provide a pair of fully labelled diagrams and supplementary calculations to assess the impact of a $7 lump sum tax introduced in this industry. Explain why the tax makes price increase by more in this decreasing cost industry than it would in a constant costs case.
Question 35. A monopolist has costs given by C = 4Q^2. and faces demand curve P = 180 - Q. Provide a labeled diagram that shows the monopolist's profit maximizing level of output, price and profits. Calculate the per-unit subsidy required to eliminate the Efficiency loss and show it in your diagram. Does your diagram suggest that this would be a sensible way to eliminate the Efficiency loss?
Question 36. A Yonge Street store has exclusive rights to sell a brand of snow board. During the summer months,the price elasticity of demand is -6.00 but during the winter the price elasticity of demand is -4.00. It is the store's policy to offer a discount to consumers buying a snowboard during the summer months. What discount (in percentage terms) is consistent with the model of ordinary price discrimination?
Question 37. The Rat Man School of Accountancy offers courses in Scarborough, Mississauga and Downtown Toronto. The school has total cost function C = 100Q + 200,000. The relationship between enrollment Q and tuition fees P is given by the demand curve: in Scarborough Q = 800 - 2P, in Mississauga Q = 1400 - 2P and in downtown Toronto Q = 2000 - 2P. Provide ONE diagram for all parts of this question. (August 2006) The School practices Ordinary Price Discrimination in setting tuition fees. How many students will attend the school in each market and what prices will be charged? Calculate profits. The CICA has ruled that the RatMan School must reduce enrollment to 900 students. They have been instructed to close the Mississauga and Scarborough campuses. Calculate enrollments and profits under this plan. Rather than close the two campuses there is an efficient economic way to restrict output. Demonstrate how this will work. Explain the principles behind this more profitable way to restrict output. Compare profits to Part b.
Question 38. A firm with production function Q = K^1/4L^1/4 pays input prices Pl=$4 and Pk=$1. Demand in Market A is given by Qa=80 - 0.1P while demand in market B is given by Qb=160 - 0.4P. The firm has monopoly power in both markets. Derive the monopolist's long run marginal cost curve. Solve for prices, quantities, labour, capital and profits if the firm practices Ordinary Price Discrimination. Provide a fully labelled diagram showing this result. The threat of arbitrage allows the firm to price discriminate only up to a $100 gap in prices. Re-calculate the profit maximizing prices, quantities, labour, capital and profits. No diagram is required.
Question 39. A firm with production function Q = K^1/4l^1/4 has applied to sell high speed cable internet service in the Toronto market. The firm hires capital and labour competitively for $0.50 per unit but also incurs fixed costs of $3600 to lease the fiber optic lines from Rogers. Demand is given by D = 300 - 2P. Concerned about the Efficiency loss, a regulatory board gives the firm 3 options. Either: (i) operate as a single-price (basic) monopoly, or (ii) implement a two-part tariff, or (iii) accept a Pigouvian per-unit subsidy and produce at the efficient level. Provide ONE fully labelled diagram to assess these options. Calculate and show, price, output, profits and the Efficiency loss under each of these options. Which of these options would be best for society?
Question 40. A campus restaurant can act as a monopolist selling meals to students,with demandQ=100-2P and to professors who have demand Q = 140 - 2P. The firm has total costs given by C = 0.5Q^2. No diagrams are required. If the restaurant cannot price discriminate, how many meals will they sell? What price will be charged? To price discriminate, the restaurant will need to hire a bouncer who will ensure that no professors try to pay the lower student price. Hiring a bouncer will cost $25. Is it worthwhile to price discriminate? While the restaurant is still able to price discriminate, a problem occurs because fire regulations only allow them to serve 32 customers. What is the profit maximizing strategy that you would recommend for the restaurant?
Question 41. A little restaurant around the corner offers this incredible seven course Italian dinner for only $30. At this price, I figure that the restaurant barely covers their costs. I don't mind paying $50 for a bottle of wine, even though I know this bottle is only worth $20, because I get such a great price on the food. At $50, I'd really rather just buy a couple of glasses, but the restaurant makes customers buy the whole 750 ml bottle. Being an economist I understand why. Provide diagrams to illustrate how the two goods Dinner and Wine, can be viewed as Tied Sales. Further explain how the restaurant has implemented an All-or- Nothing Pricing Plan for the Wine because they force me to buy the entire bottle. With explicit reference to your diagrams, clearly explain why a customer who buys an entire bottle of wine when dinner is priced at $30 might no longer be willing to buy an entire bottle of wine if the restaurant increased the price of their dinner. (April 2007)
Question 42. An enterprising Commerce student runs a phone sex business. His typical customer, a 40-something divorcee, has demand given by QD = 120 - P where P is measured in dollars per minute. Since Mom pays his cell phone bill the costs of production are zero. As an ordinary monopolist he can follow the MR = MC rule. What price per minute should he charge? How long would the typical phone conversation last? What would he earn as profit? Show how he could further maximize profits through a Block Pricing Scheme where he would charge a high price of PH dollars per minute but his customers could get a discounted price of PL dollars per minute if they stay on the phone for more than L minutes.
Question 43. Suppose your demand for long distance minutes is QD=120-40 P and your provider currently charges you $2 per minute. Your provider has implemented a block pricing scheme. If you purchase 60 minutes at the "Standard Price" of $2 you are allowed to purchase additional time for a "Bonus Price" of only 50 cents a minute. Should you participate in this plan? Provide a diagram. Suppose that the phone company now thinks that the "Bonus Price" of 50 cents might be too generous and they are going to increase it. What is the highest "Bonus Price" that would still induce you to purchase the full 60 minutes at the "Standard Price" of $2 per minute? Provide a diagram
Question 44. A price discriminating monopolist has total costs C= 2Q^2. The firm sells to students, who have elasticity E1= -5 and to professors who have elasticity E2=- 2.00. The firm wishes to sell precisely 100 units of output. What prices should be charged? Provide a labelled diagram showing prices, quantities and profit.
Question 35. The cost to provide a university course are C = 0.05Q^2+ 200,000. The variable Q is the number of students. Domestic students have demand Q = 20,000 - 10P and international students have demand Q = 28,000 - 10P.
- Compute tuition fees, enrollment, and the efficiency loss under an Ordinary Price Discrimination Plan.
- Compute tuition fees, enrollment, and the efficiency loss if the university continued to price discriminate but also introduced a Two Part Tariff and charged each group of students an Activity Fee to extract their consumer surplus.
- Provide a set of diagrams comparing the results from Part a) and Part b). Be sure to show the efficiency loss.
- Foreign enrollment increases but domestic enrollment does not. Will this always happen when a 2PT is introduced for a firm practicing OPD? Explain.