EC212 Tutorial 2 Week 4 with answers PDF

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EC212 Tutorial 2 Week 4 with answers...

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EC212 Microeconomics 2, Tutorial 2, Week 4 1.

T F If someone has a utility function U = 2 min{x, y}, then x and y are perfect complements for that person. ANSWER: T Plot some representative indifference curves.

2.

T F A person with the utility function U(x, y) = y + x2 has convex preferences. ANSWER: F Find two consumption bundles that lie on the same indifference curve. Is the average bundle on a higher indifference curve? No, therefore preferences are not convex. E.g., (1,16) and (4,1) have same utility of 17. Average is (2·5 , 8·5) which has utility 14·75.

3.

T F Max Gross has the utility function U(x, y) = max{x, y}. If the price of x is the same as the price of y, Max will buy equal amounts of x and y. ANSWER: F Max will buy only one product. Draw the indifference curves.

4.

T F Millie’s utility function is U(x, y) = min{x, y}. She maximizes her utility subject to a budget constraint. The price of x is the same as the price of y. If the price of x rises and both the price of y and her income remain constant, then her consumption of y will certainly decrease. ANSWER: T Goods x and y are perfect complements, so both goods are needed in the same quantity. Millie’s original consumption bundle is no longer affordable, so she cuts back on consumption of both x and y (keeping x = y).

5.

Paw Broon’s utility function is U(x, y) = xy. Horace’s utility function is U(x, y) = 1000xy + 2000. Daphne’s utility function is U(x, y) = xy(1 − xy). Joe’s utility function is U(x, y) = −1 ∕ (10 + 2xy). Maggie’s utility function is U(x, y) = x(y + 1000). Hen’s utility function is U(x, y) = 0·5xy − 10000. The Twins’ utility function is U(x, y) = x ∕ y. Maw Broon’s utility function is U(x, y) = −xy. a. Who has the same preferences as Paw Broon? b. Who has the same indifference curves as Paw Broon? c. Explain why the answers to (a) and (b) differ.

ANSWER: a. Horace, Hen and Joe have the same preferences as Paw Broon since their utility functions are monotonic transformations of Paw Broon’s. Joe's utility function is both the negative and the inverse of Paw Broon's—together making a monotonic transformation. b. Horace, Hen, Joe, Daphne, and Maw Broon have the same indifference curves as Paw Broon, but Daphne and Maw Broon have different preferences. To check that the indifference curves are the same, choose consumption baskets that have the same utility for Paw Broon and confirm that they lie on the same indifference curve for the others as well (e.g. (1,12), (2,6), (3,4), (4,3),... ) c. Maw Broon's utility function is a decreasing transformation of Paw Broon’s, so he orders his indifference curves in the opposite way. Daphne's utility function is a transformation of Paw Broon’s but is sometimes increasing and sometimes decreasing. 6.

Max has the utility function U(x, y) = x(y + 1). The price of x is £2 and the price of y is £1. Income is £10. How much x does Max demand? How much y? If his income doubles and prices stay unchanged, will Max’s demand for both goods double? ANSWER: To set his MRS equal to the price ratio, Max sets (y + 1)/x = 2. His budget constraint is 2x + y = 10. Solve these two equations to find that x = 11∕4 and y = 9∕2. If his income doubles and prices stay unchanged, his demand for both goods does not double. A quick way to see this is to note that if quantities of both goods doubled, the MRS would not stay the same and hence would not equal the price ratio, which has stayed constant.

7.

T F Fiery Demon is a rotgut whisky made in Kentucky. Smoothy is an unblended malt whisky imported from Scotland. Ed regards these brands as perfect substitutes. When he goes into a bar, he sometimes buys only Fiery Demon. Other times he buys only Smoothy. This shows that Ed has unstable preferences. ANSWER: F Ed will choose to consume only the cheaper whisky and will change brands depending on which whisky has the lower price.

8.

Martha has the utility function U = min{4x, 2y}. Write down her demand function for x as a function of the variables m, px, and py, where m is income, px is the price of x, and py is the price of y. ANSWER:

x = m∕(px + 2py)...