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eco200y-a09 - UNIVERSITY OF TORONTO Faculty of Arts and...

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Unformatted text preview: UNIVERSITY OF TORONTO Faculty of Arts and Science AUGUST EXAMINATIONS 2009 ECONOMICS 200Y Duration: 2 hours Aids Allowed: Non-Programmable Calculator STUDENT INFORMATION: NAME (print) FIRST LAST STUDENT # SECTION (circle): Wolfson/Wang Deferred Exam: Your professor’s name INSTRUCTIONS: The exam consists of two parts. Part A: Select 2 of 3 questions. Part B: Select 3 of 4 questions. All questions are worth 20 marks. You select a total of 5 @ 20 marks each. All answers are to be written on this examination paper. Show your work clearly in all your answers. PART A: SELECT 2 OF 3 QUESTIONS 1. Indifference Theory 1.1 (9) Lily has a bread budget of $1 (I = income). She consumes either white bread (W) or brown bread (B), at fixed prices (Pw and PB). Her Utility Function is U(W, B) = 1W + 2B. a) What can you deduce about the relationship between W and B? b) What is Lily’s Marginal Rate of Substitution (MRSw/B)? MRSW/B = c) Lily’s indifference curves are (convex / linear / L—shaped / concave). c) What is Lily’s demand function for white bread? Show the demand function in the form of quantity as a function of the price. Consider all possibilities. [You can use a diagram in your answer, but it is not essential to do so.] 1.2 (l 1) Driver Dave consumes gasoline and other goods (i.e., the composite good Y, with a b) d) d) price of $1). Dave has a utility function U(G, Y) = G*Y. His income is $1000. Initially the price of gasoline is $4 per unit and he consumes 125 units of gasoline. (Call this Point A). In an effort to conserve gasoline and reduce pollution, the government imposes a tax on gasoline that raises its price to $5 per unit (and Dave’s equilibrium moves to Point B). It is an election year, and the government appeases Dave by also giving him a lump sum subsidy such that his satisfaction remains at the original level prior to the tax (now his equilibrium is Point C). Calculate the quantity of gasoline Dave consumes at both Point B and Point C. [For ease of future calculations, round your answers to the nearest 10 e. g., 152.5 would become 150.] Gasoline at Point B = Gasoline at Point C = For Dave, gasoline is a (normal / inferior / income-independent / inferior—Giffen good). What is the amount of the lump sum subsidy provided by the government? Amount of lump sum subsidy = What is the name given by economists to the change in gasoline consumed between B and C? If there is no special name, say so. 2. Work-Leisure and Index Numbers 2.1 (10) Walid Worker has a Utility Function U(L, I) = 4L”2 + 11/2 where L is leisure hours and I is income earned from work. His wage rate is $w per hour and he can freely choose the number of hours he works in a day (24 hours maximum). a) What is Walid’s budget constraint? b) What is his Marginal Rate of Substitution (MRS Ln)? MRS L/I = c) Walid’s indifference curves are (convex / linear / L-shaped / concave). d) What is his Labour Supply function? Show the Supply function in the form of number of hours worked as a function of the wage rate. ' e) How many hours will he work if the wage rate is $16? Hours worked = b) d) (10) Rachel spends all her income on X and Y. In period 1, she bought 20 units of X at $5 per unit and 15 units of Y at $5 per unit. In period 2, she bought 30 units of X at $5 per unit and 10 units of Y at $10 per unit. What is the value of the Laspeyres quantity index (LQI)? LQI= What is the value of the Paasche quantity index (PQI)? PQI= Assuming that her tastes did not change, What can you say, using these indices, about whether she is better off in period 2 vs. period 1? In period 2, I conclude she is (better off / worse off / same satisfaction / can’t determine). My explanation, using the indices is: Use an indifference diagram, with indifference curves that exhibit diminishing MRS, to illustrate your answer to part c) above. (Free—hand of course, not to scale! Label Year 1 consumption bundle as Point 1 and Year 2 consumption bundle as Point 2. To save time, you do NOT need to show precise values of intercepts or consumption bundles. However, you should note the following fact in constructing your diagram: 2 p2 q1 = 2 p1 ql). Y 3. Revealed Preference and Uncertainty 3.1 (9) Consider the following quotation about a consumer who buys only two goods X and Y, spending all her income in both years: “With my income this year, I could just buy what I bought last year, but I chose not to. I am better ofi’ this year even though my income and the prices of the goods have changed from last year. ” a) Using a diagram and Revealed Preference only, determine whether you agree or disagree with the above statement. Use Point 1 for last year and Point 2 for this year. Explain. Y I (agree / disagree). Explanation: b) What is the name given by economists to the change in Good X consumed between Point 1 and Point 2 in this particular case? If there is no special name, say so. 3.2 (11) Harper has $160,000 (her only wealth). She thinks the Canadian team at the Vancouver Olympics in 2010 has a great opportunity to win the most medals ever in the country’s athletic history. She is considering a $70,000 investment in a business that will produce and sell Olympic T-shirts with the message “Canada Did It!”. If Canada does it, she will get back the $70,000 investment plus she will earn an additional $90,000 in profits. If Canada is not successful, she will lose her investment completely. Harper has a utility function of U(W) = w“. She thinks the odds that Canada will do it are 3 to 2 (odds in this question are measured as probability of doing it to probability of not doing it). a) Analyze carefully whether Harper will make this investment. I conclude Harper (will / will not) make this investment. b) Draw a diagram of Harper’s Utility Function that fully demonstrates your answer. part c) on next page Harper’s cousin Jamie runs an insurance business. He is willing to sell Harper an insurance policy that will pay her $160,000 if Canada does not do it (equal to her initial investment plus the expected profits). He thinks that Canada is more likely to do it than she does. He places the odds at 3 to 1. He is willing to sell Harper a $160,000 policy at actuarial cost (based on 3 to 1 odds) plus $10,000. Analyze in detail Whether Harper will buy this insurance. I conclude Harper (will / will not) buy this insurance. Part B SELECT 3 OUT OF 4 QUESTIONS 1. Long Run Equilibrium in Perfectly Competitive Market (20 marks) Consider the market for bakery products in a small town. There are many local bakeries and the market is perceived to be perfectly competitive. The daily demand for bakery products is mm = 180 — lOP. (a) (8 marks) Suppose input prices are constant and all the local bakeries have the same long run total cost function C (q) = 4 + 2g + qz. The associated marginal cost function is M C(q) = 2 + 2g and the average cost function is AC(q) = g + 2 + q. What is the long run equilibrium price? Market output? Each individual bakery’s output? The number of bakeries? Show your work and put your answers in the table below. Individual Bakery Output _ Number of Bakeries _ (b) (12 marks) Suppose only 5 bakeries have access to locally produced milk. They have the cost structure shown in question (a). Other bakeries need to purchase milk from farms further away and their long run total costs function is C(q) = 5 + 2q+ 5q2.The associated marginal cost function is M Ch(q) = 2 + 10q, where h denotes high costs. The average cost function is ACh(q) = g + 2 + 5q. What is the long run equilibrium price? Market output? Each low costs individual bakery’s output? Each high costs individual bakery‘s output? Number of high costs bakeries? What is the maximum the high cost bakeries would be Willing to pay (on top of milk costs) for a monthly supply contract with local milk farmers (for 30 days supply)? Show your work and put your answers in the table below. Market Price Individual Output (local milk) _ Market Output Number of High Cost Bakeries - Individual Output (further away) Payment for 30 Days Supply Con- tract (net of milk costs) 2. Second Degree Price Discrimination (Block Pricing) (20 marks) Sports Supplements Guru (SSG) is thinking about the pricing of its new product, a better tasting protein bar branded No Compromise (NC Bar). SSG’s estimate of a gym lover’s monthly demand for NC bar is Qd(P) = 60 — 15P. The marginal cost of producing a bar is $1. (a) (6 marks) SSG is now considering block pricing and wants to set the first block price at P1 = $2.50. Is P1 the profit maximizing uniform monopoly price? (Yes / No). Show your work. (Marks are only given to correct or partially correct reasoning.) Diagram for 2(b): P1 (b) (14 marks) Given P1, what is the optimal second block price P2? Show your work and put your answer in the table below. Also show in the diagram (on the previous page) how you find P2 and hatch the area representing SSG’s surplus. 3. Third Degree Price Discrimination (Market Segments) (20 marks) Software company StatGenii has recently developed a new product of statistical software and named it StatGenius. StatGenii believes the demand schedule of institutions for StatGenius is Q1 T(P) = 10—5P and the demand schedule of individuals is Q1 D (P) = 20—20P. Both quantities are in thousands of licenses and prices are in thousands of dollars. The cost of issuing license of StatGenius to an additional user is $0. StatGenii has incurred $5M of costs to develop the software before a single sale was made. (a) (10 marks) If StatGenii is not allowed to charge different prices to institutional and individual users, what price should StatGenii charge per license to maximize profits? How many licenses will be purchased? What are StatGenii’s profits from StatGenius? Show your work and put your answers in the table below. Number of Licenses Price per License (b) (6 marks) What is the efficient amount of licenses? What is the deadweight loss from undersupply? (Marginal cost / Average cost) pricing rule can eliminate deadweight loss. What is the problem with this pricing rule? Show your work and put your answers in the table below. Efficient Amount of Licenses _ Deadweight Loss — (c) (2 marks) Explain (no calculation required) how StatGenii is going to price StatGenius if price discrimination among institutional and individual users is allowed. (d) (2 marks) StatGenii knows that certain functions of StatGenius are attractive to advanced users who are less price sensitive. Beginning users are generally more price sensitive and they are less likely to use these functions. Is there anything that StatGenii can do to make more profits from StatGenius than in (c)? 4. Bertrand Price Competition Between Horizontally Differentiated Products (20 marks) There are two restaurants nearby each other. Supreme Sushi and Truly Thai. Each of them has its own signature lunch specials and compete for lunch customers on price. Demand for Supreme Sushi’s lunch special Q3 depends on Supreme Sushi’s price P3 and Truly Thai’s price Pt as follows: Q5(Ps; Pt) = 150 -— 15Ps + NB. Similarly the demand for Truly Thai’s lunch special is Qt(Pt; P5) = 150 — 15Pt +10Ps. The marginal cost of one lunch special is $4 for both restaurants. (a) (11 marks) Derive the reaction function of Supreme Sushi P5 (Pt) and the reaction function of Truly Thai Pt(Ps) and find the Bertrand equilibrium prices P* and Pg“. Show your 8 work and put your answers in the table below. Ps(Pt) = Pt(Ps) = P: -P: _ (b) (3 marks) Sketch the reaction functions you derived in (a) in the diagram. Clearly label the curves representing reaction functions Pt(Ps) and P5 (Pt) respectively. Show the equi- librium point E0. (The diagram does not need to be precise but should show the right shape.) Ps Pt (c) (3 marks) Supreme Sushi’s marginal cost has increased because salmon is getting more expensive. Show the effect on the reaction function of Supreme Sushi in the diagram and label the new equilibrium point with E1. Explain the change from E0 to E1. (d) (3 marks) Another Sushi restaurant is opened on a street 15 minutes of walk away. As a result, people become more sensitive to Supreme Sushi’s price, i.e, the magnitude of the coefficient of P8 in Q8 becomes larger than 15. Show the effect on the reaction function of Supreme Sushi in the diagram and label the new equilibrium point with E2. Explain the change from E0 to E2. (This is a separate question from (c), i.e, there has been no change in the price of salmon.) ...
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