Microecon_ps2_sol_fall2011

# Microecon_ps2_sol_fall2011 - Department of Economics...

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Department of Economics W3211 Columbia University Fall 2011 SO LUTIO NS T O Probl e m S e t 2 Int e rm e diat e Mi c ro ec onomi c s Prof . S e yhan E Arkona c 1. Suppose that a consumer’s annual demand for office visits is described by the equation Q 8 0.1 p . If office visits cost \$30, and the consumer has no health insurance (i.e., the consumer pays full price), how many office visits will she make? What is the elasticity of demand for office visits at this point? Suppose a health insurance plan is instituted that pays for one-third of each office visit. How would this affect the quantity and the demand elasticity at the new equilibrium? Answer: If the consumer has no health insurance, she will make 5 office visits per year, and the elasticity of demand is 0.6. If an insurance plan covers one- third of the cost of an office visit, the consumer’s quantity will increase and price sensitivity will decrease. By substituting 0.667 p into the demand equation, we can see that the elasticity will fall, as the consumer now reduces visits by 0.0667 when price increases by \$1, rather than 0.1. The result is the same as if the price were \$20 per visit instead of \$30. The new equilibrium quantity is 6 visits per year, and the elasticity falls to 0.33 [ 0.0667(30/6)]. 2. A consumer faces prices for hot dogs and hamburgers of \$1 each. Consumption of the two commodities at various weekly income levels is shown below. a. Use the information to sketch the income consumption curve on a graph. b. Draw the Engel curves for hot dogs and hamburgers. Income Hot Dogs Hamburgers \$10 3 7 15 6 9 20 10 10 c. What is the income elasticity of hot dogs for this consumer as income increases from \$10 to \$15?

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Answer: a. See Figure below b. See Figures below
c. (3/5)(10/3) 2

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3. Draw a graph with arcade games on the horizontal axis and newspapers on the vertical axis. Joe has \$10 per week to allocate between these commodities. The price of newspapers is \$0.50. At the initial price for arcade games of \$0.25, Joe purchases 10 newspapers and plays 20 games. When the price of games increases to \$0.50, Joe purchases 8 newspapers and plays 12 games. When the price of games increases again to \$0.75, Joe buys 5 papers and plays 8 games. a. Use this information to draw the utility maximizing points on a graph. b. Draw the price-consumption curve. c. Draw the individual demand curve for arcade games. d. Use the information given to calculate Joe’s elasticity of demand for arcade games between \$0.25 and \$0.50, and between \$0.50 and \$0.75. Answer: a. See Figure below b. See Figure above c. See Figure below
d. 1 (8/ 0.25)(0.25/20) 0.4. 2 (4/ 0.25)(0.50/12) 0.66 4. Sarah allocates her income of \$5.00 between the consumption of donuts and coffee. Her tastes and preferences are indicated by the indifference curves shown in Figure 4.1. The price of donuts is \$0.50 each. Initially the price of coffee is \$1.00 per cup. Subsequently, the price of coffee falls to \$0.50 per cup. On the graph below, show the initial utility maximizing position, the new utility maximizing position, and separate the income and substitution effects. For Sarah, is coffee a normal

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Microecon_ps2_sol_fall2011 - Department of Economics...

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