Lecture 3 Problems and Solutions
Q1 - Demand Analysis. The demand for housing is often described as being highly cyclical and very sensitive to
housing prices and interest rates. Given these characteristics, describe the effect of each of the
following in terms of whether it would increase or decrease the quantity demanded or the demand
for housing. Moreover, when price is expressed as a function of quantity, indicate whether the
effect of each of the following is an upward or downward movement along a given demand curve
or involves an outward or inward shift in the relevant demand curve for housing. Explain your
answers.
A.
B.
C.
D.
E.
An increase in housing prices
A fall in interest rates
A rise in interest rates
A severe economic recession
A robust economic expansion
SOLUTION
A.
An increase in housing prices will decrease the quantity demanded and involve an upward
movement along the housing demand curve.
A fall in interest rates will increase the demand for housing and cause an outward shift of the
housing demand curve.
A rise in interest rates will decrease the demand for housing and cause an inward shift of the
housing demand curve.
A severe economic recession (fall in income) will decrease the demand for housing and result in an
inward shift of the housing demand curve.
A robust economic expansion (rise in income) will increase the demand for housing and result in
an outward shift of the housing demand curve.
B.
C.
D.
E.
Q2 - Market Equilibrium. Various beverages are sold by roving vendors at Busch Stadium, home of the St. Louis
Cardinals. Demand and supply of the product are both highly sensitive to changes in the weather. During hot
summer months, demand for ice-cold beverages grows rapidly. On the other hand, hot dry weather has an
adverse effect on supply in that it taxes the stamina of the vendor carrying his or her goods up and down many
flights of stairs. The only competition to this service are the beverages that can be purchased at kiosks located
throughout the stadium.
Demand and supply functions for ice-cold beverages per game are as follows:
QD = 20,000 - 20,000P + 7,500PK + 0.8Y + 500T
(Demand)
QS = 1,000 + 12,000P - 900PL - 1,000PC - 200T
(Supply)
where P is the average price of ice-cold beverage ($ per beverage), P K is the average price of beverages sold at
the kiosks ($ per beverage), Y is disposable income per household for baseball fans, T is the average daily high
temperature (degrees), PL is the average price of unskilled labor ($ per hour), and P C is the average cost of capital
(in percent).
A.
When quantity is expressed as a function of price, what are the ice-cold beverage demand and supply
curves if P = $5, PK = $4, Y = $62,500, T = 80 degrees, P L = $10, and PC = 12%.
B.
Calculate the surplus or shortage of ice-cold beverage when P = $4, $5, and $6.
C.
Calculate the market equilibrium price-output combination.
ANS:
A.
When quantity is expressed as a function of price, the demand curve for ice-cold beverages per game
is:
QD = 20,000 - 20,000P + 7,500PK + 0.8Y + 500T
= 20,000 - 20,000P + 7,500(4) + 0.8(62,500) + 500(80)
QD = 140,000 - 20,000P
When quantity is expressed as a function of price, the supply curve for ice-cold beverages per game
is:
QS = 1,000 + 12,000P - 900PL - 1,000PC - 200T
= 1,000 + 12,000P - 900(10) - 1,000(12) - 200(80)
QS = -36,000 + 12,000P
B.
The surplus or shortage can be calculated at each price level:
Price
(1)
$4
$5
$6
C.
Quantity
Supplied
(2)
QS = -36,000+12,000(4)
= 12,000
QS = -36,000+12,000(5)
= 24,000
QS = -36,000+12,000(6)
= 36,000
Quantity
Demanded
(3)
QD = 140,000-20,000(4)
= 60,000
QD = 140,000-20,000(5)
= 40,000
QD = 140,000-20,000(6)
= 20,000
Surplus (+) or
Shortage (-)
(4) = (2) - (3)
-48,000
-16,000
+16,000
The equilibrium price is found by setting the quantity demanded equal to the quantity supplied and
solving for P:
QD = Q S
140,000 - 20,000P = -36,000 + 12,000P
32,000P = 176,000
P = $5.50
To solve for Q, set:
Demand:
QD = 140,000 - 20,000(5.50) = 30,000
Supply:
QS = -36,000 + 12,000(5.50) = 30,000
In equilibrium, QD = QS = 30,000.
Q3 - Cross-Price Elasticity. Surgical Systems, Inc., makes a proprietary line of disposable surgical stapling
instruments. The company grew rapidly during the 1990s as surgical stapling procedures continued to gain
wider hospital acceptance as an alternative to manual suturing. However, price competition in the medical
supplies industry is growing rapidly in the increasingly price-conscious new millennium. During the past year,
Surgical Systems sold 6 million units at a price of $14.50, for total revenues of $87 million. During the current
year, Surgical Systems' unit sales have fallen from 6 million units to 3.6 million units following a competitor
price cut from $13.95 to $10.85 per unit.
A.
Calculate the arc cross price elasticity of demand for Surgical Systems' products.
B.
Surgical Systems' director of marketing projects that unit sales will recover from 3.6 million
units to 4.8 million units if Surgical Systems reduces its own price from $14.50 to $13.50
per unit. Calculate Surgical Systems' implied arc price elasticity of demand.
C.
Assuming the same implied arc price elasticity of demand calculated in Part B, determine
the further price reduction necessary for Surgical Systems to fully recover lost sales (i.e.,
regain a volume of 6 million units).
SOLUTION
A.
EPX
=
Q Y 2 - Q Y1 P X 2 + P X1
x
P X 2 - P X1 Q Y 2 + Q Y1
=
3, 600, 000 - 6, 000, 000
$10.85 + $13.95
x
$10.85 - $13.95
3, 600, 000 + 6, 000, 000
= 2 (Substitutes)
B.
EP
Q 2 - Q1 P 2 + P1
x
P 2 - P1 Q 2 + Q1
4,800, 000 - 3, 600, 000
$13.50 + $14.50
=
x
$13.50 - $14.50
4,800, 000 + 3, 600, 000
=
= -4 (Elastic)
C.
EP
-4
-4
-36P2 + $486
37P2
P2
Q 2 - Q1 P 2 + P1
x
P 2 - P1 Q 2 + Q1
6, 000, 000 - 4,800, 000
P 2 + $13.50
=
x
6, 000, 000 + 4,800, 000
P 2 - $13.50
P 2 + $13.50
=
9(P 2 - $13.50)
=
= P2 + $13.50
= $472.50
= $12.77
This implies a further price reduction of 73 cents because:
ΔP = $12.77 - $13.50 = -$0.73.
Q4 - Income Elasticity. Ironside Industries, Inc., is a leading manufacturer of tufted carpeting under the
Ironside brand. Demand for Ironside's products is closely tied to the overall pace of building and
remodeling activity and, therefore, is highly sensitive to changes in national income. The carpet
manufacturing industry is highly competitive, so Ironside's demand is also very price-sensitive.
During the past year, Ironside sold 30 million square yards (units) of carpeting at an
average wholesale price of $15.50 per unit. This year, household income is expected to expected
to surge from $55,500 to $58,500 per year in a booming economic recovery.
A.
Without any price change, Ironside's marketing director expects current-year sales to soar
to 50 million units because of rising income. Calculate the implied income arc elasticity of
demand.
B.
Given the projected rise in income, the marketing director believes that a volume of 30
million units could be maintained despite an increase in price of $1 per unit. On this basis,
calculate the implied arc price elasticity of demand.
C.
Holding all else equal, would a further increase in price result in higher or lower total
revenue?
SOLUTION
A.
EI =
=
B.
 Q I 2 + I1
x
 I Q 2 + Q1
50 - 30
$58,500 + $55,500
x
$58,500 - $55,500
50 + 30
= 9.5
Without a price increase, sales this year would total 50 million units. Therefore, it is appropriate to
estimate the arc price elasticity from a before-price-increase base of 50 million units:
EP =
=
C.
 Q P 2 + P1
x
 P Q 2 + Q1
30 - 50
$16.50 + $15.50
x
$16.50 - $15.50
30 + 50
= -8 (Elastic)
Lower. Since carpet demand is in the elastic range, E P = -8, an increase (decrease) in price will
result in lower (higher) total revenues.