Chapter 4 - Practice Problems
True, False, or Uncertain
Explain why each of the following statements is True, False, or Uncertain according to economic
principles. Use diagrams where appropriate. Unsupported answers would receive no marks. It
is the explanation that is important.
True, False, or Uncertain
4-1. A per bottle tax on beer raises more tax revenue, and consumers pay more of it, the more elastic is
the demand curve for beer.
Problems
4-2. Suppose that the daily supply and demand curves for pizzas in Kingston are given by the following;
QS = -10 + 3p
QD = 15 - 2p
where QS and QD are quantities in thousands and p is the price.
(a) Graph the supply and demand curves. Identify the p and Q intercepts demand and the p
intercept for supply. Calculate and show the equilibrium price and quantity.
(b) Calculate both the demand and supply elasticity around the equilibrium point.
(c) Suppose several new pizza shops open in the city so that the supply curve shifts to:
QS = -5 + 3p
Find the new equilibrium and illustrate it on your diagram.
(d) Has total spending on pizza increased or decreased? Explain how you could have predicted
this without knowing precisely the new equilibrium point. Will a further shift out in the
supply curve result in more or less total spending on pizza?
Chapter 4 - Solutions
True, False, or Uncertain
4-1.
False.
See the figure below. The "t" dollars per unit excise tax shifts the supply curve up by "t" from S to
S’. If demand is relatively elastic as characterized by DE,, the equilibrium price rises from p to p’,
and the quantity falls to Q’. If demand is relatively inelastic as characterized by DI,, the
equilibrium price rises to p”, and the quantity falls only to Q”. Thus, for the more elastic demand
(DE), the tax revenue (txQ’) and the consumer portion of the tax (p’ - p0), are both less than they
are for the less elastic demand (DI).
p
S'
t
p"
p'
p
S
DE
DI
Q'
Q" Q
Q
Problems
4-2.
(a)
Supply curve, for p intercept, let Q = 0 and solve for p = 3.33.
Demand curve, for p intercept, let Q = 0 and solve for p = 7.50, for Q intercept, let p = 0
and solve for Q = 15.
To solve for the equilibrium price set QS equal to QD :
-10 + 3p = 15 - 2p
5p = 25
p=5
To solve for the equilibrium quantity plug this value into supply or demand (actually you
should do both as a check).
Q = -10 + 3(5) = 5
See point A in the figure below.
p
S(a)
7.5
S(c)
A
5
C
3.33
0
(b)
5
10
15
Supply Elasticity:
Demand Elasticity:
ES = {%ΔQS / %Δp}
ED = - {%ΔQD / %Δp}
= {ΔQS /Δp}Η{p/Q}
= - {ΔQS /Δp}Η{p/Q}
= 3 x {5/5} = 3
= - (-2) x {5/5} = 2
Q
Note: You can also answer this part by choosing prices (or quantities) just above and just
below the equilibrium levels and using the average arc method. As long as the prices are
the same level above and below (say 4.90 and 5.10) then the appropriate base P and Q
are the equilibrium values and you will get the same answer as using the point method.
For example, for the demand elasticity:
@ p = 4.90, QD = 15 - 2(4.90) = 5.2 Æ Point 1: {4.90, 5.2}
@ p = 5.10, QD = 15 - 2(5.10) = 4.8 Æ Point 2: {5.10, 4.8}
Q − Q1 p1 + p 2
− .4 10 .4 10
4.8 − 5.2
4.9 + 5.10
=−
× = × =2
×
ED = − 2
×
=−
5.10 − 4.90 5.2 + 4.8
.2 10 .2 10
p 2 − p1 Q1 + Q2
(c)
To solve for the new equilibrium price set the new QS equal to QD :
-5 + 3p = 15 - 2p
5p = 20
p=4
To solve for the equilibrium quantity plug this value into supply or demand (actually you
should do both as a check).
Q = 15 - 2(4) = 7
See point C in the figure.
(d)
Total spending has increased. At the old equilibrium it was 5x5 = 25 thousand dollars. At
the new equilibrium it is $28 thousand. This could have been predicted by looking at the
elasticity of demand at the original equilibrium. Since it was equal to 2, then the
percentage increase in quantity would be greater than the percentage decrease in price.
Thus total expenditure (price times quantity) would be certain to increase with a
downward movement along the demand curve.
By the same logic, since the elasticity of demand at the new equilibrium point is equal to
8/7 (= -(-2)x(4/7)) -- still greater than one -- a further shift of the supply curve will result
in a further increase in total spending on pizza.