# Test 1 10 October Assume that tea and lemons are complements and that coffee and tea are substitutes.

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1 Eco 301 Name Test 1 10 October points. Please write all answers in ink. Please use pencil and a straight edge to draw graphs. Allocate your time efficiently. 1. Assume that tea and lemons are complements and that coffee and tea are substitutes. a. How, if at all, will the imposition of an effective ceiling price on tea affect the price of lemons? Explain. The imposition of the ceiling price on tea causes a reduction in the quantity of tea bought, from Q1 to Q2 (left panel). The result is a leftward shift in the demand for lemons, resulting in a reduction in both price and quantity (right panel). b. How, if at all, will the imposition of an effective ceiling price on tea affect the price of coffee? Explain. The ceiling price for tea lowers the quantity people are able to buy from Q1 t to Q2 t. There is excess demand for tea at the ceiling price P2 t, and some of this excess demand spills over to substitute products such as coffee. The result is that the equilibrium price of coffee rises. (Note: This result may seem inconsistent with the claim that a fall in the price of a good's substitute reduces the demand for that good. But this claim refers to a fall in the equilibrium price of the good, not a price reduction caused by a ceiling. Because of the quantity reduction caused by the ceiling, tea buyers would be willing to pay P3 t for tea. So the price ceiling actually raises the opportunity cost of additional units of tea.)

2 2. Suppose demand for seats at football games is P = 1900 (1/50)Q and supply is fixed at Q = 90,000 seats. a. Find the equilibrium price and quantity of seats for a football game (using algebra and a graph). The equilibrium quantity is Q = 90,000 seats and the equilibrium price is P = 1900 (1/50)(90,000) = = \$100. b. Suppose the government prohibits tickets scalping (selling tickets above their face value), and the face value of tickets is \$50 (this policy places a price ceiling at \$50). How many consumers will be dissatisfied (how large is excess demand)? At a price ceiling of P = \$50, quantity demanded is found by solving 50 = 1900 (1/50)Q for Q = 92,500 seats. Since the stadium only holds Q = 90,000 seats, there will be 92,500 90,000 = 2,500 dissatisfied fans who want to buy a ticket at P = \$50 but cannot find one available. c. Suppose the next game is a major rivalry, and so demand jumps to P = (1/50)Q. How many consumers will be dissatisfied for the big game? Quantiy demanded for the higher demand is found by solving 50 = 2100 (1/50)Q for Q = 102,500 seats. Now there will be 102,500 90,000 = 12,500 dissatisfied fans who want to buy a ticket at P = \$50 but cannot find one available. The excess demand is 12,500 2,500 = 10,000 seats more than for the not so big game. 3. Two types of radar weather-detection devices are available for commercial passenger aircraft: the "state-of-the-art" machine and another that is significantly less costly, but also less effective. The Federal Aviation Administration (FAA) has hired you for advice on whether all passenger planes should be required to use the state-of-the-art machine. After careful study, your recommendation is to require the more expensive machine only in passenger aircraft with more than 200 seats. How would you justify such a recommendation to an FAA member who complains that all passengers have a right to the best weather-detecting radar currently available? A plane of either type--large or small--should use the state-of-the-art device if the extra benefits of that device exceed its extra costs. Because the device will save more lives in large planes than in small planes, its benefits are larger in large planes than in small ones. Your original recommendation was presumably based on the calculation that the benefits for the larger planes justified the extra cost, but did not do so in the case of the smaller planes. Airline passengers are like other people insofar as their willingness to invest in extra safety is constrained by other pressing uses for their scarce resources.

3 Where extra safety is relatively cheap, as in large planes, they will rationally choose to purchase more than when it is relatively more expensive, as in small planes. 4. When the price of gasoline is \$l/gal, you consume 1000 gal/yr. Then two things happen: (1) The price of gasoline rises to \$2/gal and (2) a distant uncle dies, with the instruction to his executor to send you a check for \$1000/yr. If no other changes in prices or income occur, do these two changes leave you better off than before? Assume the consumer's original income was M. His original budget constraint is a; after the gas price increase, it is b; and after the money from his uncle it is c. At the very end, he can afford the original bundle he bought. But his indifference curve at the original optimum is below his new budget constraint. By decreasing his gas consumption and increasing other goods consumption, he can reach a higher indifference curve. (see dotted indifference curve)

4 Eco 301 Name Test 1 10 October points. Please write all answers in ink. Please use pencil and a straight edge to draw graphs. Allocate your time efficiently. 1. Hardware and software for computers are complements. Draw a graph and discuss the effects on the equilibrium price and quantity. a. In the software market, when the price of computer hardware falls. b. In the hardware market, when the price of computer software rises. A reduction in the price of hardware would raise demand for software and thus cause equilibrium price and quantity of software to rise. On the other hand, a rise in the price of software would reduce demand for hardware and thus cause the equilibrium price and quantity of hardware to fall. 2. Jones spends all his income on two goods, X and Y. The prices he paid and the quantities he consumed last year are as follows: P x = 15, X = 20, P y = 25, and Y = 30. If the prices next year are P x = 6 and P Y = 30, and Jones's income is 1020, will he be better or worse off than he was in the previous year? (Assume that his tastes do not change.) The two budget lines and last year's optimal bundle are shown in the diagram. A closer look at the tangency point for last year's bundle shows that this year Jones can afford a bundle he prefers to last year's. 3. The market for DVDs has supply and demand curves given by P = 2Q S and P = 42 Q d, respectively. a. How many units will be traded at a price of \$35? At a price of \$14? Which participants will be dissatisfied at these prices? At prices of 35 and 14, there will be 7 DVDs traded in the market. At P=35, sellers are dissatisfied. They would like to sell 17.5 units. At P=14, buyers are dissatisfied, because they would like to buy 28 units.

5 b. What quantity of DVDs at what price will be sold in equilibrium? The supply and demand curves, shown in the diagram, intersect at P=28, Q=14 c. What is the total revenue from DVD sales? Total revenue is (28)(14) = Consider the following two scenarios: a. You have just purchased a house for \$200,000. The very next day, the prices of all houses, including the one you just bought, double. b. You have just purchased a house for \$200,000. The very next day, the prices of all houses, including the one you just bought, fall by half. In each case, how does the price change affect your welfare? (Are you better off before the price change or after?) When the price of housing doubles, your budget constraint becomes B 2, which also contains your original bundle A Because C, the optimal bundle on B 2, lies on a higher indifference curve than A the effect of the housing price increase is to make you better off.

6 When the price of housing falls by half, your budget constraint becomes B 3, which also contains your original bundle A. Because D, the optimal bundle on B 3, lies on a higher indifference curve than A, the effect of the housing price drop is to make you better off.

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