Homework 2: Demand (to be handed in on Thursday February 5th 2004)
- How is an individual demand curve different from a market demand curve? Which curve is likely to be more price elastic? Is the demand for a particular brand of product, such as Head skis, likely to be more price elastic or price inelastic than the demand for the aggregate of all brands of downhill skis? Explain (1 point)
- By observing how Bill behaves, determine the relevant income elasticities of demand for each good (i.e. whether the good is normal or inferior) (1 point)
a) Bill spends all of his income on coffee and books. He finds $20 while rummaging through a used paperback bin at the bookstore, and immediately buys a new hardcover book of poetry.
b) Being bohemian becomes the latest teen fad. As a result, coffee and book prices both rise 25%. Bill lowers his consumption of both goods by the same percentage.
- Suppose that Anna’s price elasticity of demand for food = -1.0. Suppose also that she spends $10,000 a year on food, and that that the price of food is $2. If a $2 sales tax on food were to cause the price of food to double, what would happen to Anna’s consumption (Hint: as a large price change is involved, you should use an arc elasticity, rather than a point elasticity). (1 point)
- Consumption of pounds of hamburger per year by a typical consumer has been estimated as follows (2 points):
Price ($) / Income
$20,000 per year $30,000 per year
0.50 / 1,000 lbs / 1,500 lbs
1.00 / 900 / 1,100
1.50 / 800 / 900
a) Estimate the arc price elasticities of demand when I = $20,000, and when I = $30,000. What pattern do you observe?
b) Sketch the Engel curves implied by these data.
- Suppose that the average household consumers 500 gallons of gas per year. A 10-cent gasoline tax is introduced, combined with a $50 annual tax rebate per household. Will the household be worse or better off after the new program is introduced? (1 point)
- Assume orange juice and apple juice are perfect substitutes. Draw the appropriate price-consumption curve (for a variable price of orange juice), and income-consumption curve (1 point)
- Suppose you are in charge of a toll bridge that is essentially cost free. The demand for bridge crossings is given by P = 12 - 2Q (2 points)
a) Draw the demand curve for bridge crossings.
b) How many people would cross the bridge if there were no toll?
c) What is the loss of consumer surplus associated with the charge of a $6 toll.
- Vera has decided to upgrade the operating system on her new PC. She hears that the new Linux system is technologically superior to Windows, and is significantly cheaper. However, when she asks her friends, it turns out they all use Windows. They agree Linux is more appealing, but add they see relatively few copies of Linux on sale at local retail software stores. Based on what she learns and observes, Vera chooses to upgrade her PC with Windows. Can you explain her decision? (1 point)