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Unformatted text preview: Homework 3 Sample Solution 1. Suppose the demand function for beef can be expressed (in the relevant region) as Q: 130+ l.5M—6p+5p2
where Q is the quantity of beef demanded (in millions of kilograms per year), M is average
household income in thousands of dollars per year,p is the price of beef in dollars per kilogram,
and p2 is the price of pork in dollars per kilogram. Calculate the own—price elasticity of demand for beef when M = 40,p = 10, and p2 = 8. .0 BQ 3Q The own price elasticity of demand is 8 = —— . For our problem, p = 10, — = ~— 6,
Q Bp 3}?
and Q = 130 + 1.5(40) — (6)(10) + 5(8) = 130 + 60 — 60 + 40 = 170, so the own price elasticity of
demand for beef is 8 = ﬂ —6) z "0.35 .
(170) 2. The own price elasticity of demand for coffee is — 0.6 and the cross price (tea price)
elasticity of demand for coffee is 0.1. Starting from a coffee price of $8 per kilogram, a tea price
of $4 per kilogram, and a quantity demanded of 20,000 kilograms per month, if the price of
coffee decreases to $5 per kilogram, does the quantity of coffee demanded increase or decrease, and by how much? The coffee price is changing, so the own price elasticity of demand for coffee, — 0.6, is
the relevant elasticity. The coffee price is decreasing by $3, from $8 to $5, for a 37.5% decrease.
The percentage change in the quantity of coffee demanded is (— 0.6)( ~ 37.5%) = + 22.5%. Thus
the quantity of coffee demanded increases by 22.5% (or 4,500 Kg per month) from 20,000 Kg per month to 24,500 Kg per month. 3. The own-price elasticity of demand for cigarettes is — 0.107 [Pagoulatos and Sorensen,
a. If a tax change leads to an increase in all cigarette prices from $4 to $5 per pack, what would you predict to happen to the quantity of cigarettes demanded per month? Predict a 2.675 % decrease in quantity demanded. A 25% increase in price leads to a
(— 0.107)(25%) change in quantity. b. Suppose the producers of Kent brand cigarettes decide to change its price from $4 to $5
per pack, but other cigarette brands keep their prices at $4 per pack. What wouid you predict to
happen to the quantity of Kent brand cigarettes demanded per month? Predict a decrease of much more than 2.675% because this is a brand—level, not market-
level, price change. 4. The price and quantity information below is from the 1989 US market for sugar. The
price elasticity of demand in the US has been estimated to be - 0.3 while the price elasticity of
US supply has been estimated to be 1.54. US sugar production: 13.7 billion pounds in 1989 US sugar consumption: 17.5 billion pounds in 1989 US price in 1989: $0.23 per pound
Using the 1989 price and quantities along with the elasticity estimates, find linear
approximations to the US supply and US demand curves. [Find the formulas to use in the region where price and quantity are positive .] For both supply and demand, let us measure prices in dollars per pound and quantities in billion pounds per year.
Because it is linear, the demand function will have form Q = b — mp where b and m are constants whose values we seek. The appropriate quantity is from US consumption, 17.5 billion dQ_ pounds. Then :1— — — m and by the elasticity formula evaluated at the known point,
- 0.3 = 35-9 = Mkm) or m 2 228. Thus Q = b — 22.8p. Again using the known point,
Q dp (17.5) 17.5 = b — 22.8(023) or b 2 22.7. The unique linear demand function consistent with our original
information is Q = 22.7 — 22.8p. [Your exact answer will depend on the approximate values you use.] Because it is linear, the supply function will have form Q = b + mp where b and m are
constants whose values we seek. The appropriate quantity is from US production, 13.7 billion pounds. Then 5:2 = m and by the elasticity formula evaluated at the known point,
1.54 = ﬂig— = w(m) or m x 91.7. Thus Q = b + 91.7p. Again using the known point,
Q do (137) 13.7 = b + 91 .7(0.23) or b 2 — 7.4. The unique linear demand function consistent with our
original information is Q = — 7.4 + 91.7p. [Your exact answer will depend on the approximate values you use.] ...
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- Spring '08