8. (25 points) With some services (e.g. checking accounts, phone service, or pay TV), a consumer is offered a choice of two or more payment plans. One can either pay a high entry fee and get a low price per unit of service or pay a low entry fee and a high price per unit of service. Suppose you have an income of $100. There are two plans. Plan A has an entry fee of $20 with a price of $2 per unit. Plan B has an entry fee of $40 with a price of $1 per unit for using the service. Let x be expenditure on other goods and y be consumption of the service. Explain your answer. (i) Write down the budget equation that you would have after you paid the entry fee for each of the two plans. (ii) If your utility function is u(x, y) = xy, how much y would you choose in each case? (iii) Which plan would you prefer? Explain.

(D)

2. Utility maximization - Trading off labor and leisure The indifference curves on the following graph show Amy's preferences for leisure and consumption for increasing levels of utility, such that her utility increases in both consumption and leisure. Assuming that Amy spends 68 hours each week sleeping, she has a maximum of 100 hours available to her for leisure if she does not work at all. Initially, she works 45 hours (and thus has 55 hours of leisure) and earns $250 per week. Use the grey point (star symbol) to indicate Amy's initial leisure/consumption bundle. Dashed drop lines will automatically extend to both axes. CONSUMPTION (Dollars per week) 1000 900 800 700 600 500 400 300 200 100 0 0 + 10 20 30 40 50 60 70 80 LEISURE (Hours per week) 90 U3 100 110 Initial bundle + $200 Unemployment Benefits Equivalent Bundle, $100 Unemployment Benefits Equivalent Bundle ?

4. Kay lives in a city where housing costs $1 per square foot. They have a monthly budget of$1,000, of which they decide to allocate $500 to rent a 500 sqft. apartment and spend teother $500 on consumption. A generous relative offers Kay a deal on a 400 sqft. apartmentfor only $200 per month, which they accept. What is the equivalent variation of this transferfor Kay, in dollars per month? (Select one)(a) More than $300: Kay gets utility from both consumption and the new apartment.(b) $300: That is how much more Kay can consume with the new cost of rent.(c) $250: That is how much less Kay’s old bundle would have cost at the new prices.(d) Between $0 and $250: Kay would substitute away from her old bundle at the new prices.(e) $200: That is the additional cost of Kay’s new bundle at the old prices.(f) Between $0 and $200: Kay may prefer to substitute away from her new bundle at theold prices.(g) $100: That is the differential cost of the new apartment at the old prices.(h) $0: The new…

5. (12) Max is stocking up on ice cream and cookies; ice cream costs $2 and cookies cost 50 cents ($.50). The marginal utility gained from each treat is given in the table below. If Max is a rational utility maximizer and has $8 to spend, how many of each treat will they purchase, and in what order? Show your work. Qice cream MU of ice Qcookies MU of cream cookies 1234567 40 1 9 32 2 9 26 3 7 18 4 5 8 5 3 6 6 3 4 7 1

6. For your birthday, you receive a hamper from your friend, which contains food and drink. They have chosen to buy you 8 packs of hot chocolate and 10 packs of luxury biscuits. Unfortunately, the hot chocolate is not milk chocolate and the biscuits are chocolate chip and not your favourite ginger biscuits! They haven't provided the receipt, but you return to the shop where the hamper was bought and ask to exchange the items. Each pack of hot chocolate was priced at £5 and each pack of biscuits was priced at £6. You face a utility function of U (Hċ, B) = H²B. When you return to the shop, you see that all of the biscuits are now half price, but all of the types of hot chocolate haven't changed in price. You are able to exchange your biscuits and hot chocolate, but can only receive a refund based on the current marked price of the products in the shop. Given this information and assuming hot chocolate is on the horizontal axis and your aim to maximise utility, what should you do? (a) You…

1. Suppose that you are in charge of purchasing for a U.S. corporation that is planning to acquire a large number of new computers. The company's computer specialist has identified two models, one Japanese-made and one U.S.-made, that meet the necessary specifications. Since the two models are essentially equivalent, the company will buy the one with the lower price. Suppose the U.S.-made computer costs $2,400, and a similar Japanese-made computer costs 242,000 yen. If the nominal exchange rate is 110 yen per dollar, which computer is a better buy? (Hint: calculate the real exchange rate for computers)

PROBLEM (1) (Rational Choice) Suppose your friend is about to buy a digital camera. A digital camera is identified with three dimensions; 1) resolution (in megapixels), 2) optical zoom (a real number) and 3) battery life (a number of hours). For example, A = (8, 4, 20) is a camera with 8mp resolution and x4 optical zoom and 20 hours of battery life. When he goes into a store, he faces a menu of cameras. When comparing two cameras if camera A is weakly better than B on at least 2 dimensions, it is weakly preferred to the other; written A ≥preferred B. a) Is this preference relation complete? Transitive? Prove it or show an example where the property doesn't hold. b) Suppose the agent chooses from any menu of cameras, a camera that is (weakly) preferred to all other cameras in the menu. Would this choice function be rational, given (a)? Briefly explain your reasoning.