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Chapter 4 Q6, Q8 and Q9
Question 6
a) The concept is that of the own-price elasticity of demand, since we are considering
changes in the price and quantity of ticket sales. The measure of elasticity in this case is
the percentage change in quantity demanded divided by the percentage change in price.
The average quantity is 1275 and the average price is $12.50. Thus, we have:
 = (150/1275)/(3/12.50) = 0.49
b) The concept is that of the income elasticity of demand because we are relating changes
in income to changes in quantity demanded. The measure of income elasticity is the
percentage change in quantity demanded divided by the percentage change in income.
The average quantity is 61,500. Note that we are given the percentage change in income
equal to 10 percent or 0.10. Thus we have:
Y = (11,000/61,500)/(0.10) = 1.79
The positive sign reveals that Toyota Camrys are a normal good since a rise in income
leads to an increase in quantity demanded.
c) The concept is that of the cross-price elasticity of demand because we are relating
changes in the price of coffee to changes in the quantity demanded of tea. The measure of
cross-price elasticity is the percentage change in the quantity demanded of tea divided by
the percentage change in the price of coffee. The average coffee price is $3.90 and the
average quantity of tea is 7 750 kg. Thus we have:
XY = (500/7,750)/(1.80/3.90) = 0.14
The positive sign reveals that coffee and tea are substitute goods since a rise in the price
of coffee (which presumably reduces the quantity demanded of coffee) leads people to
demand more tea.
d) The concept is the Canadian own-price elasticity of supply because we are relating
changes in the world price of pulp to changes in the quantity of pulp supplied by
Canadian firms. The measure of supply elasticity is the percentage change in (Canadian)
quantity supplied divided by the percentage change in the world price. The average
quantity is 9.5 million tons. Note that we are given the percentage increase in the price
equal to 14 percent, or 0.14. Thus we have:
S = (3/9.5)/(0.14) = 2.26
Question 8
a) The four scale diagrams are shown below. Note that all four diagrams have the same
scale on the vertical axes but different scales on the horizontal axes.
b) The own-price elasticity of supply is equal to the percentage change in quantity supplied
divided by the percentage change in the price. The calculations for cases (i) through (iv)
are :
i)
ii)
iii)
iv)
average p = $30, average Q = 15.
average p = $30, average Q = 7.5.
average p = $30, average Q = 6.
average p = $30, average Q = 3.
S = (10/15)/(20/30) = 1
S = (5/7.5)/(20/30) = 1
S = (4/6)/(20/30) = 1
S = (2/3)/(20/30) = 1
Note that in each case the supply curve is a straight line from the origin. As we mentioned
in footnote #1 in the chapter, the elasticity of all such supply curves, no matter what the
slope, is equal to one.
c) As we saw in part (b), the elasticity of supply of each of the four supply curves is one.
But the slopes of the four curves are different. The slope of the curve is measured by the
change in price per unit change in quantity supplied. The slopes are: (i) 20/10 = 2; (ii) 20/5
= 4; (iii) 20/4 = 5; and 20/2 = 10. The difference between slope and elasticity is that the
first is measured in absolute changes whereas the second is measured as percentage
changes. This question should make it clear that this difference matters!
Question 9
a) The appropriate scale diagram is shown below.
b) The equilibrium price and quantity can be determined algebraically by solving the
demand and supply system — 2 equations and 2 unknown variables. The equilibrium is
where the two curves intersect. Algebraically, this occurs where the price on the demand
curve is equal to the price on the supply curve. Thus, we set
80 – 5QD = 24 + 2QS
But at the equilibrium, the quantity on the demand curve will also equal the quantity on the
supply curve, thus we set QD = QS = Q*. Our equation becomes
56 = 7Q*  Q* = 8 (million litres per month)
Substituting this value for Q* back into either the demand curve or supply curve we can
solve for the equilibrium price, p*. Using the demand curve, we get
p* = 80 – (58) = 40 (cents per litre)
c) With a tax of 14 cents per litre, there will be a 14-cent wedge between the price the
consumer pays (the consumer price) and the price received by the producer (the seller
price). Algebraically, we can solve for the new equilibrium by rewriting the demand and
supply curves in terms of the consumer price (pC) and the seller price (pS). The demand and
supply functions are now:
pC = 80 – 5QD and pS = 24 + 2QS
To solve for the equilibrium quantity in the presence of the tax, note that the consumer
price minus the 14-cent tax must exactly equal the seller price. Thus, pC – 14 = pS. This
gives:
80 – 5Q* – 14 = 24 + 2Q*  42 = 7Q*  Q* = 6
To solve for the consumer and seller prices, simply substitute this value of Q* into the
demand and supply curves. The consumer and seller prices are
pC = 80 – (56) = 50 and pS = 24 + (26) = 36
The gasoline tax raises revenue equal to the number of litres sold (6 million litres per
month) times the unit tax (14 cents per litre). Thus, the monthly tax revenue is $840,000.
What share is paid by consumers and what share is paid by producers? The tax has raised
the consumer price from 40 cents per litre to 50 cents per litre. Thus consumers are
‘paying’ 10 cents of each 14 cents of tax, or 71% of the total tax. The seller price fell from
40 cents per litre to 36 cents per litre, so they are ‘paying’ 4 cents of each 14 cents of tax, or
29% of the total tax.