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University of Toronto Scarborough
Economics for Management Studies

UNIVERSITY OF TORONTO SCARBOROUGH DEPARTMENT OF MANAGEMENT MGEB02: Price Theory: A Mathematical Approach Instructor: A. Mazaheri Sample Test-1.1 (Solutions) Instructions: This is a closed book test. You have 2 Hours. Good Luck! Last Name: First Name: ID FOR MARKERS ONLY: Q1 Q2 Q3 Q4 Q5 Total Marks Earned Maximum Marks 40 15 15 18 12 100 Possible Page 1 of 15 Answer all following 5 questions: Question-1 [40 Points] Answer the following Short Questions: a) [4 points] You are analyzing the market for Crude oil in the last decade or so, you know that the price has risen from $20 or so to $100+ during this period. Show what must have happened to the demand and supply to lead to such an equilibrium. Demand shifts right, P & Q increase b) [6 Points] In the following, the initial equilibrium is given. Suppose price of X declines. Assuming X is Giffen, draw the new equilibrium. On the same graph show the income and the substitution effects. Y X SE IE Page 2 of 15 c) [6 Points] Draw representative indifference curves for the followings: i) Sandra has a strange habit and she insists on it; she likes to eat an apple and two bananas together. Perfect complement: Apple 1 Banana 2 ii) Adam does not care about orange juice or apple juice as long as he has juice. Perfect Substitute: Orange Juice 1 Apple Juice 1 Page 3 of 15 d) [6 Points] Assume you have a fixed budget of $10. Further assume that you spend your entire budget. Both good X and good Y cost $1 each. You are spending all your money on X. At this bundle, your marginal utility of X is 10 while your marginal utility of Y is 5. Are you optimizing your utility? Why or why not? Using a graph explain your answer. Solution: (1) spend your entire income because you are on the budget line (2) The MRS = 10/5=2 > 1, or (MU x/ Px) > (MU y Py). That is, the marginal utility of X per dollar spent is higher than that of Y. However, you already gave away all Y and cannot get more X. Therefore your optimal consumption bundle is a corner solution where you consume no Y. Y X Page 4 of 15 e) [8 Points] Assume a utility function that is given by U(X,Y) = X Y . Further assume a budget of $50. When the prices wherX P and PY=1, you consumed X= 25 and Y = 25, while when the prices changed tX P =2 anY P =1, you consumed X= 12.5 and Y = 25. With the help of the following graph decompose the total effect of the price change into the substitution and income effects. Solution: We know TE = 25-12.5. We need to find the SE. Having SE we can solve for IE as TE=SE+IE. SE is the change in the quantity of x demanded, if (1) the individual remains at the same indifference curve and (2) if MRS is equal to the new price ration. 0.5 0.5 0.50.5 1:U = 25 ×25 = 50 = X Y Y 2 2 :MRS = = => Y = 2X X 1 (1),(2) => 25 =X 0.(2X) 0.=> X =17.68 SE =17.68 − 25 = −7.32 IE =12.5−17.68 = −5.18 Graphically: 50 25 SE IE 12.5 17.68 25 50 Page 5 of 15 f) [5 Points] You have 5 spent on two products, a composite product (Y) with a price of p = 1 y and coffee (X) with a price of px = 1. If you purchase three cups of coffee, you will be offered one coffee for free and a 50% discount on each additional cup of coffee purchased. Show graphically how this affects your budget line. y 5 x 3 4 8 Page 6 of 15 g) [5 Points] Ahmed only consumes hamburger (Y) and coffee (X). He wants two cups of coffee. If he gets less than two cup of coffee he will not care about anything else and if he is given more than two cups of coffee he will discard it. Graph his representative indifference map. Hamburger Coffee 2 Page 7 of 15 Question-2 [15 Points] As a manufacturer you are interested in obtaining quick estimates of the supply and demand curves for your product. You have done some research and you know that for your product the elasticity of supply is 2, the elasticity of demand is -1.5. You also know that the current price and quantity are $50 and 1,000, respectively. Assume that both demand and supply are linear. a) [6 Points] What is the supply and demand curves at the current price and quantity. b) [4 Points] What impact would a 10% decline in demand have on the equilibrium price and quantity? d) [5 Points] Ignore part (b). Suppose the government subsidizes your product by 5 dollars per unit. What would be the new
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