HW3_anskey_tutorial_2015 (3) - 1 Solutions to Tutorial 3...

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1 Solutions to Tutorial 3: ECO 204Y (2015-2016) 1. Ms. Caffeine enjoys coffee (C ) and tea (T) and where the marginal utility from enjoying a cup of coffee is 3 while tea is 4 for all amounts of tea or coffee. If coffee and tea cost $3 each and Ms. Caffeine has $12 to spend on these products, how much coffee and tea should she buy to maximize her utility? Depict your answer graphically as well. How would her demands change if the price of tea fell to $2? Solutions 1. We are talking here about perfect substitutes where the marginal utilities of both goods are constant (marginal utilities do not vary with the amount of either good) MRS = ¾ U = 3C + 4T Pc/Pt =1. MRS < Pc/Pt marginal value of C relative to T is less than the actual cost of C relative to T. Hence only T will be purchased, C=0, T>0 T=12/3 =4 units. If the price fell to $2 then Pc/PT= 3/2> MRS. Use the same reasoning to justify why demand pattern (C=0, T>0). The amount of T increases to 6 units. 2. Suppose Sunil loves bagels for breakfast and MUST have 1/2 a stick of butter (t) and 3 small trays of jam (j) and 1.5 small cups of coffee (c) per bagel (b). No other combination per bagel will work for Sunil. Changing any one of those condiments will not change Sunil’s satisfaction. Suppose that each bagel costs $1, butter costs $.5 a stick, a tray of jam costs $.25 and coffee costs $.80 per small cup. Sunil has $8 to spend per day on his breakfast. a) Express Sunil’s preferences as a utility function. Remember to show your reasoning. b) Find Sunil’s equilibrium consumption bundle of each good given the prices and his allowance. What is the level of satisfaction/utility? Solutions: 2. a) The proportion of consumption is as follows: b/t = 1/1/2 = 2 b/ j = 1/ 3 b/c = 1/3/2 = 2/3 Hence b/t = 2, b/j = 1/3 and b/c = 2/3 or b=2t, b=j/3, and b=(2/3)c U = min{b, 2t, j/3, 2/3c} Case of perfect complements as these goods are taken in the same proportions – and changing consumption of a good does not change the consumption of the other. b) m = p b b + p t t +p c c + p j j 8 = (1) b + 0.5 t + 0.25j+0.8c = b + 0.5 (b/2) + 0.25 (3b) + 0.8(3/2b) = b + b/4 + 3b/4 + 6/5b
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2 40 = 10b+6b b=2.5, t=1.25, j=15/2, c=15/4 U =2.5 3. Jon is always willing to trade one can of Coke for one can of Sprite, or one can of Sprite for one can of Coke. You may put Coke on the Yaxis. a. What can you say about Jon’s marginal rate of substitution? b. Draw a set of indifference curves for Jon. c. Suppose Jon’s budget is $4.00 and Coke costs $1.00 and Sprite costs $2.00. How much of each does Jon afford? d. What happens to the marginal rate of substitution as you move along a convex indifference curve? A linear indifference curve? e. Explain why an MRS between two goods must equal the ratio of the price of the goods for the consumer to achieve maximum satisfaction. Solution: 3. Jon is always willing to trade one can of Coke for one can of Sprite, or one can of Sprite for one can of Coke.
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