Microeconomics 7th Edition By R. Glenn Hubbard - Test Bank

Microeconomics 7th Edition By R. Glenn Hubbard – Test Bank

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112) The monthly supply of desktop personal computers is given by the equation
QS = 15,000 + 43.75P. At a price of $800, what is the price elasticity of supply?
Answer: At a price of $800, the quantity supplied is 50,000. The price elasticity of supply is
ES = P
Q
ΔQ
ΔP = 800
50,000 43.75 = 0.7
Diff: 1
Section: 2.4
113) The demand for tickets to the Daytona 500 NASCAR event is given by the equation
QD = 350,000 – 800P. The supply of tickets to the event is given by the capacity of the Daytona
track, which is 150,000. What is the equilibrium price of tickets to the event? What is the price
elasticity of demand at the equilibrium price? What is the price elasticity of supply at the
equilibrium price?
Answer: Consumers are willing to pay P = 200,000
800 = $250 per ticket. The price elasticity of
demand at $250 is ED = P
Q
△Q
△P = 250
150,000 –800 = –1 1
3 . The price elasticity of
supply is ES = P
Q
△Q
△P = 250
150,000 0 = 0.
Diff: 2
Section: 2.4
114) Midcontinent Plastics makes 80 fiberglass truck hoods per day for large truck manufacturers.
Each hood sells for $500.00. Midcontinent sells all of its product to the large truck
manufacturers. Suppose the own price elasticity of demand for hoods is 0.4 and the price
elasticity of supply is 1.5.
a. Compute the slope and intercept coefficients for the linear supply and demand equations.
b. If the local county government imposed a per unit tax of $25.00 per hood manufactured,
what would be the new equilibrium price of hoods to the truck manufacturer?
c. Would a per unit tax on hoods change the revenue received by Midcontinent?
Answer: Given: P* = $500 Q* = 80 hoods per day
Ed = –0.40 Es = 1.5
a. Demand: Qd = a0 + a1P Supply: Qs = b0 + b1P
Use: E = P
Q × ΔQ
ΔP to compute a1 and b1.
–0.4 = 500
80 a1 1.5 = 500
80 b1
a1 = –0.064 b1 = 0.24
Solve for a0 and b0
Qd = a0 + a1P Qs = b0 + b1P
80 = a0 + –0.064(500) 80 = b0 + 0.24(500)
a0 = 112b0 = –40
Qd = 112 – 0.064P Qs = –40 + 0.24P
47

b. The tax represents a price increase to the purchaser regardless of the current
price. Thus, the supply curve will be adjusted vertically upward by $25.
Qs = –40 + 0.24P or
P = 166.67 + 4.17 Qs, then
Pt = P + $25 = 166.67 + 25 + 4.17Qs
Pt = 191.67 + 4.17Qs or
Qs = –45.96 + 0.24P
The new equilibrium price will be:
New Supply = Demand
Qs = –45.96 + 0.24P = 112 – 0.064P = Qd
Solving yields P = $519.60 per truck hood
c. Since the new selling price in (c) is $519.60 and the tax is $25 per hood,
Midcontinent would receive only $494.6 per hood. As quantity sold has
fallen too, revenues would fall.
Diff: 3
Section: 2.6
115) Suppose that a small market Major League Baseball team currently charges $12 for a ticket. At
this price, they are able to sell 12,000 tickets to each game. If they raise ticket prices to $15,
they would sell 11,053 tickets to each game. What is the price elasticity of demand at $12? If
the demand curve is linear, what is the algebraic expression for demand?
Answer: The price elasticity of demand is E = P
Q
△Q
△P = 12
12,000
–947
3 = –0.316. If the
demand curve is linear, it is in the form of QD = a + bP. Also, we know that
E = b P
Q ⇔ b = E Q
P = –0.316 12,000
12 = –316. Rearranging the linear expression for
demand allows us to solve for a as follows: a = QD – bP ⇒ a = 12,000 + 316(12) = 15,792.
We may now write the linear expression for demand as QD = 15,792 – 316P.
Diff: 2
Section: 2.6
48

116) Suppose that the short–run world demand and supply elasticities for crude oil are –0.076 and
0.088, respectively. The current price per barrel is $30 and the short–run equilibrium quantity
is 23.84 billion barrels per year. Derive the linear demand and supply equations.
Answer: If the demand curve is linear, it is in the form of QD = a + bP Also, we know that
E = b P
Q ⇔ b = E Q
P = –0.076 23.84
30 = –0.060. Rearranging the linear expression for
demand allows us to solve for a as follows:
a = QD – bP ⇒ a = 23.84 + 0.060(30) = 25.640. We may now write the linear expression
for demand as QD = 25.640 – 0.060P. If the supply curve is linear, it is in the form of
QS = c + dP. Also, we know that E = d P
Q ⇔ d = E Q
P = 0.088 23.84
30 = 0.070.
Rearranging the linear expression for demand allows us to solve for c as follows:
c = QS – dP ⇒ c = 23.84 – 0.070(30) = 21.740. We may now write the linear expression
for supply as QS = 21.740 + 0.070P.
Diff: 2
Section: 2.6
117) Suppose that the long–run world demand and supply elasticities of crude oil are –0.906 and
0.515, respectively. The current long–run equilibrium price is $30 per barrel and the
equilibrium quantity is 16.88 billion barrels per year. Derive the linear long–run demand and
supply equations. Next, suppose the long–run supply curve you derived above consists of
competitive supply and OPEC supply. If the long–run competitive supply equation is:
SC = 7.78 + 0.29P, what must be OPECʹs level of production in this long–run equilibrium?
Answer: If the demand curve is linear, it is in the form of QD = a + bP. Also, we know that
E = b P
Q ⇔ b = E Q
P = –0.906 16.88
30 = –0.510. Rearranging the linear expression for
demand allows us to solve for a as follows:
a = QD – bP ⇒ a = 16.88 + 0.510(30) = 32.180. We may now write the linear expression
for demand as QD = 32.18 – 0.510P. If the supply curve is linear, it is in the form of
QS = c + dP. Also, we know that E = d P
Q ⇔ d = E Q
P = 0.515 16.88
30 = 0.290.
Rearranging the linear expression for demand allows us to solve for c as follows:
c = QS – dP ⇒ c = 16.88 – 0.290(30) = 8.18. We may now write the linear expression for
supply as QS = 8.18 + 0.290P. OPECʹs supply is the difference between the world
supply and competitive supply at $30. We know that world supply at $30 is 16.88.
Competitive supply at $30 is 7.78 + 0.29(30) = 16.48. This implies that OPECʹs supply is
0.4 billion barrels per year at $30 in this long –run equilibrium.
Diff: 3
Section: 2.6
118) The U.S. Department of Agriculture is interested in analyzing the domestic market for corn.
The USDAʹs staff economists estimate the following equations for the demand and supply
curves:
Qd = 1,600 – 125P
Qs = 440 + 165P
Quantities are measured in millions of bushels; prices are measured in dollars per bushel.
a. Calculate the equilibrium price and quantity that will prevail under a completely free
49

market.
b. Calculate the price elasticities of supply and demand at the equilibrium values.
c. The government currently has a $4.50 bushel support price in place. What impact will this
support price have on the market? Will the government be forced to purchase corn under a
program that requires them to buy up any surpluses? If so, how much?
Answer: a. Set Qd = Qs to determine price.
1600 – 125P = 440 + 165P
1160 = 290P
P = 4
Obtain Q by substituting into either expression.
Qd = 1600 – 125(4)
Qd = 1600 – 500
Q = 1100
P* = $4, Q* = 1100
b. For the Own Price Elasticity of Demand E = –125 × 4
1100 = –0.45 (approximately)
For the Own Price Elasticity of Supply E = –165 × 4
1100 = 0.60
c. Calculate Qd and Qs at the $4.50 price
Qd = 1600 – 125(4.5)
Qd = 1037.5
Qs = 440 + 165(4.5)
Qs = 1182.5
surplus = Qs – Qd = 1182.5 – 1037.5 = 145
The support price would create an excess supply of 145 million bushels that
the government would be forced to buy.
Diff: 2
Section: 2.7
50

119) The market for gravel has been estimated to have these supply and demand relationships:
Supply P = 10 + 0.01Q
Demand P = 100 – 0.01Q,
where P represents price per unit in dollars, and Q represents sales per week in tons.
Determine the equilibrium price and sales. Determine the amount of shortage or surplus that
would develop at P = $40/ton.
Answer: The equilibrium price can be found by equating S to D in terms of Q.
10 + 0.01Q = 100 – 0.01Q
0.02Q = 90
Q = 4,500 tons/week
P = 10 + 0.01(4,500) = $55/ton.
At P = $40/ton, the quantity demanded is:
40 = 100 – 0.01Q – or – Q = 6,000 tons/week
The quantity supplied is:
40 = 10 + 0.01Q – or – Q = 3,000 tons/week
The shortage is 3,000 tons/week.
Diff: 2
Section: 2.7
120) American Mining Company is interested in obtaining quick estimates of the supply and
demand curves for coal. The firmʹs research department informs you that the elasticity of
supply is approximately 1.7, the elasticity of demand is approximately –0.85, and the current
price and quantity are $41 and 1,206, respectively. Price is measured in dollars per ton,
quantity the number of tons per week.
a. Estimate linear supply and demand curves at the current price and quantity.
b. What impact would a 10% increase in demand have on the equilibrium price and
quantity?
c. If the government refused to let American raise the price when demand increased in (b)
above, what shortage is created?
Answer: a. First we estimate the demand curve
Q = a0 – b0P
Elasticity of demand = b0 × P
Q
.85 = b0 × 41
1206
–1025.1 = b0 × 41
b0 = 25
Q = a0 – b0P
1206 = a0 – 25(41)
1206 = a0 – 1025
a0 = 2231
Q0 = 2231 – 25P
Next, we estimate the supply curve
Q = a1 + b1P
Elasticity of Supply = b1 × P
Q
51

1.7 = b1 × 41
1206
2050.2x = b1 × 41
b1 = 50
Q = a1 + b1P
1206 = a1 + 50(41)
a1 = –844
Qs = –844 + 50P
Check to see if correct:
Set Qs = Qd
2231 – 25P = –844 + 50P
3075 = 75P
P = 41
The equations are correct.
b. Multiply demand equation by 1.10
1.10 (2231 – 25P)
Qdʹ = Qs and solve
Qs = –844 + 50P
Set Qdʹ = Qs and solve.
2454.1 – 27.5P = –844 + 50P
3298.1 = 77.5P
P = 42.56
Substitute P into Qdʹ to find quantity demanded
Qdʹ = 2454.1 – 27.5(42.56)
Qdʹ = 1283.7 or 1284
c. Since price cannot rise, the shortage will be the quantity demanded with
the new demand minus the quantity supplied with the unchanged supply
Quantity demanded: Q = 2454.1 – 27.5(41) = 1326.6
Quantity supplied: Q = –844 + 50(41) = 1206.0
Shortage = 1326.6 – 1206.0 = 120.6 tons per week.
Diff: 3
Section: 2.7
121) In a city with a medium sized population, the equilibrium price for a city bus ticket is $1.00,
and the number of riders each day is 10,800. The short–run price elasticity of demand is –0.60,
and the short–run elasticity of supply is 1.0.
a. Estimate the short run linear supply and demand curves for bus tickets.
b. If the demand for bus tickets increased by 10% because of a rise in the world price of oil,
what would be the new equilibrium price of bus tickets?
c. If the city council refused to let the bus company raise the price of bus tickets after the
demand for tickets increases (see (b) above), what daily shortage of tickets would be created?
d. Would the bus company have an incentive to increase the supply in the long run given the
city councilʹs decision in (c) above? Explain your answer.
52

Answer: Given: P* = $1.00 per ticket Q* = 10,800
Ed = –0.60 Es = 1.0
a. Demand: Qd = a0 + a1P Supply: Qs = b0 + b1P
Use: E = P
Q × ΔQ
ΔP to compute a1 and b1.
Ed = 1
10,800 a1 Es = 1
10,800 b1
–0.60 = 1
10,800 a1 1.0 = 1
10,800 b1
a1 = –6,480 b1 = 10,800
Solve for a0
Qd = a0 + a1P
Solve for b0
Qs = b0 + b1P
10,800 = a0 – 6,480.00(1.0) 10,800 = b0 + 10,800.00(1.0)
a0 = 17,280 b0 = 0.0
Qd = 17,280 – 6,480P Qs = 0.0 + 10,800P
b. New demand = (1.10)Qd = (17,280 – 6,480P)(1.10)
Qdʹ = 19,008.00 – 7,128P
Equate Qdʹ to Qs to get new equilibrium price.
19,008 – 7,128P = 0.0 + 10,800 P
P* = $1.06 per ticket
c. The shortage would be the quantity demanded at P = $1.00
minus the quantity supplied at P=$1.00
Qd = 19,008 – 7,128($1.00) = 11,880
Qs = 0.0 + 10,800($1.00) = 10,800
Shortage = 11,800 – 10,800 = 1,080 rides per day
d. No. The bus company has no incentive to supply more than 10,800 rides
per day, as long as the price is restricted at $1.00.
Diff: 3
Section: 2.7

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