Microeconomics, Problem Set
MPA 2460 -Microeconomics Prof. Bryce Steinberg Watson Institute Brown University MPA 2460 Problem Set #1 Summer 2024 Due Sunday 6/23/2023, 11:59 PM EDT in Gradescope Last Name: First Name: Group members with whom you worked: 1 MPA 2460 -Microeconomics Prof. Bryce Steinberg Watson Institute Brown University 1. Annual demand for US wheat is: QD = 3600 – 300P. Annual supply of U.S. wheat is: QS=1800 + 300P. P is the price, in dollars. a. Draw a supply and demand diagram representing this system. b. What is the price for wheat in equilibrium? c. Government sometimes regulates the price of food. Imagine that government introduces a short-term restriction that you cannot sell wheat at more than $2 per unit. What will happen to the market? Illustrate using your supply and demand graph. 2. Use supply and demand curves to illustrate the effects of the following actions on the quantity and price of tea: a. b. c. d. An increase in the price of sugar. An increase in the price of coffee. An increase in income levels. An announcement from scientists that coffee contains very effective antioxidants. 3. TRUE, FALSE or UNCERTAIN (explain your answers): a. The elasticity of demand is the same as the slope of the demand curve. b. The supply of apartments is more inelastic in the short run than in the long run. c. Demand for Dell computers is less elastic than demand for all desktop computers. 4. The rent control agency of Providence has found that the aggregate demand for apartments, measured in tens of thousands of apartments, is QD = 160-8P Price, which is the monthly rental rate, is measured in hundreds of dollars. The supply of apartments, in the same units, is: QS = 70+7P a. What is the free market price of apartments? How much will population change (assume two people per apartment) if the rent control agency sets a 2 MPA 2460 -Microeconomics Prof. Bryce Steinberg Watson Institute Brown University maximum average monthly rent of $300 and everyone who can’t find an apartment leaves the city? b. What would you actually expect to happen in this case? Would everyone leave the city? What if this example was in New York: do you think the effects of rent control would be the same or different in the two places? Why? (1-2 paragraphs). 5. Disney World is trying to decide how to set the pricing for its rides. Suppose that it can operate rides costlessly, regardless of how many people take the rides. Everyone who visits the park has a daily demand for rides given by the following equation: qD = 20 − 0.8P a. Suppose rides are free. How many rides will each person take in a given day? b. How much will consumer surplus fall if the price per ride is increased from $0 to $1? c. An alternative pricing regime is to sell a daily pass and let people ride all the rides for free. What is the most Disney could charge for the daily pass? 6. Researchers have estimated the long run demand elasticity for almonds is -0.47, and the long run supply elasticity is 12.0. The short run demand elasticity for almonds is -0.30, and the short run supply elasticity is 0.5. The government is considering a tax on almonds. What share will be paid by the consumer in the long run? How about the short run? Provide some intuition for why these are different. 7. Louis has stable preferences and consumes two goods, wine and cheese. In 1994, the price of wine was $4/glass and the price of cheese was $2/ounce. Louis’s income was $60 and he bought 12 glasses of wine and 6 ounces of cheese. In 1995, wine costs $2/glass and cheese costs $4/ounce. Louis’s income is still $60. a. Draw both years’ budget lines. Where do they cross? b. What is Louis’s marginal rate of substitution of wine for cheese in 1994? [hint: you can’t use calculus] c. True or false. Explain carefully. In 1995, Louis will definitely not buy exactly 10 glasses of wine. 8. Tickets to a Providence Bruins game are sold out and available only on a blackmarket basis. Sally and Mike are big Bruins fans and work together at a local bar. Mike tells Sally that he will go buy some tickets and asks her how many she wants. 3 MPA 2460 -Microeconomics Prof. Bryce Steinberg Watson Institute Brown University Sally replies: “If the price per ticket is $150, buy one ticket for me. If the price per ticket is $100, buy two tickets for me. And, if the price per ticket is $50, buy three tickets for me.” Mike responds: “What are you talking about? You’re saying you’re willing to pay more in total for two tickets than for three. You are behaving irrationally.” Evaluate Mike’s statement. Is Sally behaving irrationally? 9. Andy purchases only two goods, apples (a) and kumquats (k). He has an income of $40 and can buy apples at $2 per pound and kumquats at $4 per pound. His utility function is U(a,k)= 3a + 5k. a. What is his marginal utility for apples and his marginal utility for kumquats? b. What bundle of apples and kumquats should he purchase to maximize his utility? 4
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