Tutorial 3 Solutions - EC202 PDF

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--------------------------------------------------------------------------------------------------------------------EC202: Intermediate Microeconomics Semester 2, 2019 Tutorial 3 Solutions (Week 4) --------------------------------------------------------------------------------------------------------------------Question 1 Suppose Michael purchases only two goods, hamburgers (H) and Cokes (C). a) What is the relationship between MRSH,C and the marginal utilities MUH and MUC ? MRSH ,C 

MU H MUC

b) Draw a typical indifference curve for the case in which the marginal utilities of both goods are positive and the marginal rate of substitution of hamburgers for Cokes is diminishing. Using your graph, explain the relationship between the indifference curve and the marginal rate of substitution of hamburgers for Cokes.

C

H The indifference curve in this case will be convex toward the origin. The marginal rate of substitution is measured as the absolute value of the slope of a line tangent to the indifference curve. As can be seen in the graph above, this slope becomes less negative as we move down the indifference curve, implying a diminishing MRS. c) Suppose the marginal rate of substitution of hamburgers for Cokes is constant. In this case, are hamburgers and Cokes perfect substitutes or perfect complements? If the MRS was constant, this would imply that at any consumption level the consumer would be willing to trade a fixed amount of one good for a fixed amount of the other. This occurs with perfect substitutes.

d) Suppose that Michael always wants two hamburgers along with every Coke. Draw a typical indifference curve. In this case, are hamburgers and Cokes perfect substitutes or perfect complements? If the consumer wishes to always consume goods in a fixed ratio, then the goods are perfect complements. In this case, the indifference curves will be L-shaped. Question 2 Carlos has a utility function that depends on the number of musicals and the number of operas seen each month. His utility function is given by U = xy2, where x is the number of movies seen per month and y is the number of operas seen per month. The corresponding marginal utilities are given by: MUx = y2 and MUy = 2xy. a) Does Carlos believe that more is better for each good? By plugging in ever higher numerical values of x and ever higher numerical values of y, it can be verified that Carlos’ utility goes up whenever x or y increases. b) Does Carlos have a diminishing marginal utility for each good? First, consider the marginal utility of x, MUx. Since x does not appear anywhere in the formula for MUx, MUx is independent of x. Hence, the marginal utility of movies is independent of the number of movies seen, and so the marginal utility of movies does not decrease as the number of movies increases. Next, consider the marginal utility of y, MUy. Notice that MUy is an increasing function of y. Hence, the marginal utility of operas does not decrease in the number of operas seen. In this case, neither good, movies or operas, exhibits diminishing marginal utility. Question 3 Adam likes his café latte prepared to contain exactly 1/3 espresso and 2/3 steamed milk by volume. On a graph with the volume of steamed milk on the horizontal axis and the volume of espresso on the vertical axis, draw two of his indifference curves, U1 and U2, with U1 > U2.

Volume of Espresso 3 U2 2

U1

1

1

2

3

4

5

6

Volume of Steamed Milk

Question 4 Pedro is a college student who receives a monthly stipend from his parents of $1,000. He uses this stipend to pay rent for housing and to go to the movies (you can assume that all of Pedro’s other expenses, such as food and clothing have already been paid for). In the town where Pedro goes to college, each square foot of rental housing costs $2 per month. The price of a movie ticket is $10 per ticket. Let x denote the square feet of housing, and let y denote the number of movie tickets he purchases per month. a) What is the expression for Pedro’s budget constraint? 2x + 10y ≤ 1000 or 2x + 10y = 1000 b) Draw a graph of Pedro’s budget line.

c) What is the maximum number of square feet of housing he can purchase given his monthly stipend? The maximum amount of housing Pedro can purchase is his budget divided by the price of housing: $1,000/$2 per square feet = 500 square feet. d) What is the maximum number of movie tickets he can purchase given his monthly stipend? The maximum number of movie tickets Pedro can purchase is his budget divided by the price of a movie ticket: $1,000/$10 per tickets = 100 tickets. e) Suppose Pedro’s parents increase his stipend by 10 percent. At the same time, suppose that in the college town he lives in, all prices, including housing rental rates and movie ticket prices, increase by 10 percent. What happens to the graph of Pedro’s budget line? His budget line does not change at all. Initially, the budget line (with x on the horizontal axis and y on the vertical axis) has a horizontal intercept equal to 1000/2 = 500 and a vertical intercept equal to 1000/10 = 100. The slope of the budget line is -2/10 = - 0.20 (the price of housing divided by the price of movie tickets). With the increase in Pedro’s stipend and the increases in prices we have:  Horizontal intercept of budget line: 1000(1.10)/(2(1.10)) = 500  Vertical intercept of budget line: 1000(1.10)/(10(1.10)) = 100  Slope of budget line: -2(1.10)/(10(1.10)) = - 0.20. These are the same as before and thus the budget line does not change.

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