CHAPTER 16: Equilibrium
TRUE/FALSE
1. If the supply curve is vertical, then the amount supplied is independent of price.
2. If the supply is perfectly elastic, then an upward shift of the demand curve will lead to a higher price
and a higher quantity in equilibrium.
3. The supply curve slopes up and to the right. If the demand curve shifts upward to a new curve which is
everywhere higher than the old curve (but possibly of different slope) and if the supply curve does not
shift, then the equilibrium price and quantity must necessarily increase.
4. Supply and demand theory shows us that the burden of a sales tax is shared equally by suppliers and
demanders whether the tax is collected from the sellers or collected from the buyers.
5. An economic situation is Pareto optimal only if there is no way to make someone better off.
6. The amount of a good supplied is independent of the price. If a sales tax is imposed on the good, then
the price paid by consumers will not change at all.
7. If a quantity tax is collected from competitive suppliers of a good, placing a tax on the good causes the
price paid by consumers to increase more than if the tax had been collected directly from the buyers.
8. The demand curve, which is a downward-sloping straight line, crosses the supply curve, which is an
upward-sloping straight line. If a tax is introduced where sellers must pay a tax of $2 per unit sold,
then the equilibrium price paid by demanders will rise by more than $1 if the absolute value of the
slope of the demand curve is greater than the absolute value of the slope of the supply curve.
MULTIPLE CHOICE
1. The demand for pickles is given by p = 131 − 2q and the supply is given by p = 5 + 7q. What is the
equilibrium quantity?
a.
11
b.
14
c.
19
d.
103
e.
None of the above.
2. The demand for pickles is given by p = 167 − 3q and the supply is given by p = 5 + 6q. What is the
equilibrium quantity?
a.
15
b.
23
c.
113
d.
18
e.
None of the above.
3. The demand function for fresh strawberries is q = 200 − 5p and the supply function is q = 60 + 2p.
What is the equilibrium price?
a.
$10
b.
$20
c.
$40
d.
$50
e.
None of the above.
4. The inverse demand function for mangos is defined by the equation p = 91 − 5q, where q is the number
of crates that are sold. The inverse supply function is defined by p = 3 + 6q. In the past there was no
tax on mangos but now a tax of $44 per crate has been imposed. What are the quantities produced
before and after the tax was imposed?
a.
5 crates before and 5 crates after
b.
16 crates before and 9 crates after
c.
14 crates before and 7 crates after
d.
8 crates before and 4 crates after
e.
None of the above.
5. The inverse demand function for lemons is defined by the equation p = 120 − 11q, where q is the
number of crates that are sold. The inverse supply function is defined by p = 8 + 3q. In the past there
was no tax on lemons but now a tax of $84 per crate has been imposed. What are the quantities
produced before and after the tax was imposed?
a.
4 crates before and 3 crates after
b.
8 crates before and 2 crates after
c.
16 crates before and 5 crates after
d.
16 crates before and 5 crates after
e.
None of the above.
6. The inverse demand function for eggs is p = 84 − 9q, where q is the number of cases of eggs. The
inverse supply is p = 7 + 2q. In the past, eggs were not taxed, but now a tax of 33 dollars per case has
been introduced. What is the effect of the tax on the quantity of eggs supplied?
a.
Quantity drops by 2 cases.
b.
Quantity drops by 3 cases.
c.
Quantity drops by 6 cases.
d.
Quantity drops by 4 cases.
e.
None of the above.
7. The inverse demand function for eggs is p = 125 − 6q, where q is the number of cases of eggs. The
inverse supply is p = 5 + 6q. In the past, eggs were not taxed, but now a tax of 72 dollars per case has
been introduced. What is the effect of the tax on the quantity of eggs supplied?
a.
Quantity drops by 7 cases.
b.
Quantity drops by 5 cases.
c.
Quantity drops by 6 cases.
d.
Quantity drops by 12 cases.
e.
None of the above.
8. The inverse demand function for cases of whiskey defined by p = 160 − 6q, and the inverse supply
function is defined by p = 61 + 3q. Originally there was no tax on whiskey. Then the government
began to tax suppliers of whiskey $27 for every case they sold. How much did the price paid by
consumers rise when the new equilibrium was reached?
a.
It rose by $27.
b.
It rose by $29.
c.
It rose by $18.
d.
It rose by $16.
e.
None of the above.
9. The inverse demand function for cases of whiskey defined by p = 186 − 6q, and the inverse supply
function is defined by p = 90 + 2q. Originally there was no tax on whiskey. Then the government
began to tax suppliers of whiskey $32 for every case they sold. How much did the price paid by
consumers rise when the new equilibrium was reached?
a.
It rose by $32.
b.
It rose by $24.
c.
It rose by $22.
d.
It rose by $34.
e.
None of the above.
10. The inverse demand function for cigars is defined by p = 240 − 2q, and the inverse supply function is
defined by p = 3 + q. Cigars are taxed at $4 per box.
a.
The after-tax price paid by consumers rises by more than $2, and the after-tax price
received by suppliers falls by less than $2.
b.
The after-tax price paid by consumers goes up by less than $2, and the after-tax price
received by suppliers rises.
c.
Consumers and suppliers share the cost of the tax equally.
d.
The after-tax price paid by consumers rises by $4, and the after-tax price received by
suppliers stays constant.
e.
The after-tax price paid by consumers rises by less than $2, and the after-tax price
received by suppliers stays constant.
11. Xaquane and Yullare are obscure but talented eighteenth-century painters. The world’s stock of
Xaquanes is 100 and the world’s stock of Yullares is 70. The demand for each painter’s work depends
on its own price and the price of the other painter’s work. If Px is the price of Xaquanes and Py is the
price of Yullares, the demand function for Xaquanes is 101 − 3Px + 2Py and the demand function for
Yullares is 72 + Px − Py. What is the equilibrium price for Yullare’s paintings?
a.
$5
b.
$11
c.
$12
d.
$7
e.
None of the above.
12. In a certain kingdom, the demand function for rye bread was q = 381 − 3p and the supply function was
q = 5 + 7p, where p is the price in zlotys and q is loaves of bread. The king made it illegal to sell rye
bread for a price above 32 zlotys per loaf. To avoid shortages, he agreed to pay bakers enough of a
subsidy for each loaf of bread so as to make supply equal demand. How much would the subsidy per
loaf have to be?
a.
21 zlotys
b.
14 zlotys
c.
8 zlotys
d.
20 zlotys
e.
None of the above.
13. In a certain kingdom, the demand function for rye bread was q = 181 − 8p and the supply function was
q = 13 + 6p, where p is the price in zlotys and q is loaves of bread. The king made it illegal to sell rye
bread for a price above 6 zlotys per loaf. To avoid shortages, he agreed to pay bakers enough of a
subsidy for each loaf of bread so as to make supply equal demand. How much would the subsidy per
loaf have to be?
a.
21 zlotys
b.
20 zlotys
c.
14 zlotys
d.
14 zlotys
e.
None of the above.
14. The demand function for orange juice is q = 269 − 9p and the supply function is q = 9 + 4p, where q is
the number of units sold per year and p is the price per unit, expressed in dollars. The government
decides to support the price of orange juice at a price floor of $24 per unit by buying orange juice and
destroying all that it has purchased. How many units must the government destroy per year?
a.
52
b.
56
c.
25
d.
61
e.
57
15. The demand function for orange juice is q = 247 − 8p and the supply function is q = 19 + 4p, where q
is the number of units sold per year and p is the price per unit, expressed in dollars. The government
decides to support the price of orange juice at a price floor of $27 per unit by buying orange juice and
destroying all that it has purchased. How many units must the government destroy per year?
a.
105
b.
104
c.
40
d.
96
e.
101
16. The demand function for rental apartments is q = 960 − 7p and the supply function is q = 160 + 3p.
The government makes it illegal to charge a rent higher than $35. How much excess demand will there
be?
a.
149
b.
450
c.
364
d.
726
e.
245
17. The demand function for abalone is q = 30 − 9p and the supply function is q = 6p. Suddenly the
yuppies discover abalone. The quantity demanded at every price doubles. The supply function,
however, remains the same as before. What is the effect on the equilibrium price and quantity?
a.
The price doubles and the quantity remains constant.
b.
The quantity doubles and the price remains constant.
c.
Both price and quantity double.
d.
Both price and quantity increase but neither doubles.
e.
None of the above.
18. Remember King Kanuta and his tropical island? The demand function for coconuts by his subjects on
the island is D(p) = 1,200 − 100p and the supply function is S(p) = 100p. The law used to be that any
subject who consumed a coconut had to pay another coconut to the king. King Kanuta then ate all the
coconuts he got. But now the king, apparently fed up with coconuts, decides to sell the coconuts that
he collects in the local market at the going selling price, ps. In equilibrium, the number of coconuts that
will now be produced is
a.
100.
b.
200.
c.
600.
d.
400.
e.
300.
19. The inverse demand function for video games is p = 240 − 2q and the inverse supply function is p = 3
+ q. When the government imposes a $6 tax on each video game purchased,
a.
consumer’s surplus falls by more than producer’s surplus.
b.
producer’s surplus falls by more than consumer’s surplus.
c.
consumer’s surplus and producer’s surplus fall by the same amount.
d.
consumer’s surplus falls and producer’s surplus increases.
e.
producer’s surplus falls and consumer’s surplus increases.
20. The demand function for corn is q = 200 − p and the supply function is q = 50 + .5p. The government
sets the price of corn at $150 and agrees to purchase and destroy any excess supply of corn at that
price. How much money does it cost the government to buy this corn?
a.
$11,250
b.
$18,750
c.
$7,500
d.
$10,750
e.
$14,500
21. The market for tennis shoes has a horizontal supply curve and a linear, downward-sloping demand
curve. Currently the government imposes a tax of t on every pair of tennis shoes sold and does not tax
other goods. The government is considering a plan to double the tax on tennis shoes, while leaving
other goods untaxed. If the tax is doubled, then
a.
the total deadweight loss caused by the doubled tax will be exactly twice the original
deadweight loss.
b.
the total deadweight loss caused by the doubled tax will be more than twice the original
deadweight loss.
c.
the total deadweight loss caused by the doubled tax will be less than twice the original
deadweight loss.
d.
to know if doubling the tax would more than double the deadweight loss, we would have
to know the slope of the demand curve.
e.
None of the above.
22. The demand curve for rutabagas is a straight line with slope 23 and the supply curve is a straight line
with slope 2. Suppose that a new tax of $3 per sack of rutabagas is introduced.
a.
The total number of rutabagas purchased increases.
b.
The price paid by demanders rises by the same amount as the price received by suppliers
falls.
c.
The price received by suppliers falls by more than the price paid by demanders rises.
d.
The price paid by demanders rises by more than the price received by suppliers falls.
e.
The price paid by demanders rises by more than $3.
23. The demand curve for rutabagas is a straight line with slope 26 and the supply curve is a straight line
with slope 2. Suppose that a new tax of $3 per sack of rutabagas is introduced.
a.
The price received by suppliers falls by more than the price paid by demanders rises.
b.
The total number of rutabagas purchased increases.
c.
The price paid by demanders rises by the same amount as the price received by suppliers
falls.
d.
The price paid by demanders rises by more than the price received by suppliers falls.
e.
The price paid by demanders rises by more than $3.
24. The quantity q of grapefruits demanded at price p is given by q = 30 − 3p and the supply schedule by q
= 6p. The government imposes a quantity tax at some rate t, which it collects from buyers. What is the
smallest tax rate that will result in no grapefruits being bought or sold?
a.
10%
b.
3.33%
c.
3.67%
d.
11.50%
e.
13%
25. The quantity q of apricots demanded at price p is given by q = 36 − 4p and the supply schedule by q =
2p. The government imposes a quantity tax at some rate t, which it collects from buyers. What is the
smallest tax rate that will result in no apricots being bought or sold?
a.
6.67%
b.
9%
c.
6%
d.
10.50%
e.
12%
26. The demand function for x is D(p) = 65 − 2p and the supply function is S(p) = 20 + p. The price that
should be set to restrict the quantity supplied to 30 units is closest to
a.
$5.
b.
$10.
c.
$15.
d.
$50.
e.
$55.
27. The inverse demand function for apples is defined by the equation p = 214 − 5q, where q is the number
of units sold. The inverse supply function is defined by p = 7 + 4q. A tax of $36 is imposed on
suppliers for each unit of apples that they sell. When the tax is imposed, the quantity of apples sold
falls to
a.
23.
b.
14.
c.
17.
d.
19.
e.
21.
28. The inverse demand function for cantaloupes is defined by the equation p = 305 − 5q, where q is the
number of units sold. The inverse supply function is defined by p = 8 + 4q. A tax of $45 is imposed on
suppliers for each unit of cantaloupes that they sell. When the tax is imposed, the quantity of
cantaloupes sold falls to
a.
28.
b.
33.
c.
21.75.
d.
26.
e.
30.50.
29. In a crowded city far away, the civic authorities decided that rents were too high. The long-run supply
function of two-room rental apartments was given by q = 14 + 5p, and the long-run demand function
was given by q = 329 − 5p, where p is the rental rate in crowns per week. The authorities made it
illegal to rent an apartment for more than 25 crowns per week. To avoid a housing shortage, the
authorities agreed to pay landlords enough of a subsidy to make supply equal to demand. How much
would the weekly subsidy per apartment have to be to eliminate excess demand at the ceiling price?
a.
6.50 crowns
b.
10 crowns
c.
13 crowns
d.
26 crowns
e.
19.50 crowns
30. In a crowded city far away, the civic authorities decided that rents were too high. The long-run supply
function of two-room rental apartments was given by q = 5 + 2p, and the long-run demand function
was given by q = 225 − 4p, where p is the rental rate in crowns per week. The authorities made it
illegal to rent an apartment for more than 30 crowns per week. To avoid a housing shortage, the
authorities agreed to pay landlords enough of a subsidy to make supply equal to demand. How much
would the weekly subsidy per apartment have to be to eliminate excess demand at the ceiling price?
a.
10 crowns
b.
17 crowns
c.
20 crowns
d.
40 crowns
e.
30 crowns
31. The price elasticity of demand for a certain agricultural product is constant (over the relevant range of
prices) and equal to −1.50. The supply elasticity for this product is constant and equal to 4. Originally
the equilibrium price of this good was $15 per unit. Then it was discovered that consumption of this
product was unhealthy. The quantity that would be demanded at any price fell by 11%. The percent
change in the long-run equilibrium consumption of this good was
a.
−11%.
b.
−8%.
c.
−2%.
d.
−12%.
e.
There is not enough information to determine the answer.
32. The price elasticity of demand for a certain agricultural product is constant (over the relevant range of
prices) and equal to −2. The supply elasticity for this product is constant and equal to 3. Originally the
equilibrium price of this good was $45 per unit. Then it was discovered that consumption of this
product was unhealthy. The quantity that would be demanded at any price fell by 100%. The percent
change in the long-run equilibrium consumption of this good was
a.
−100%.
b.
−64%.
c.
−20%.
d.
−60%.
e.
There is not enough information to determine the answer.
33. Suppose that King Kanuta, whom you met in your workbook, demands that each of his subjects give
him 1 coconut for every coconut that they consume. The king puts all of the coconuts that he collects
in a large pile and burns them. The supply of coconuts is given by S(ps) = 100ps, where ps is the price
received by suppliers. The demand for coconuts by the king’s subjects is given by D(pd) = 1,500 −
100pd, where pd is the price paid by consumers. In equilibrium, the price received by suppliers will be
a.
$6.
b.
$9.
c.
$7.50.
d.
$15.
e.
None of the above.
34. Suppose that King Kanuta, whom you met in your workbook, demands that each of his subjects give
him 2 coconuts for every coconut that they consume. The king puts all of the coconuts that he collects
in a large pile and burns them. The supply of coconuts is given by S(ps) = 100ps, where ps is the price
received by suppliers. The demand for coconuts by the king’s subjects is given by D(pd) = 6,000 −
100pd, where pd is the price paid by consumers. In equilibrium, the price received by suppliers will be
a.
$30.
b.
$18.
c.
$90.
d.
$27.
e.
None of the above
35. Schrecklich and Lamerde are two obscure modernist painters, who are no longer alive but whose
paintings are still enjoyed by persons of dubious taste. The demand function for Schrecklichs is 200 −
4PS − 2PL and the demand function for Lamerdes is 200 − 3PL − PS, where PS and PL are respectively
the price of Schrecklichs and Lamerdes. If the world supply of Schrecklichs is 110 and the world
supply of Lamerdes is 110, then the equilibrium price of Schrecklichs is
a.
$9.
b.
$22.50.
c.
$36.
d.
$27.
e.
$18.
36. Schrecklich and Lamerde are two obscure modernist painters, who are no longer alive but whose
paintings are still enjoyed by persons of dubious taste. The demand function for Schrecklichs is 200 −
4PS − 2PL and the demand function for Lamerdes is 200 − 3PL − PS, where PS and PL are respectively
the price of Schrecklichs and Lamerdes. If the world supply of Schrecklichs is 100 and the world
supply of Lamerdes is 70, then the equilibrium price of Schrecklichs is
a.
$46.
b.
$4.
c.
$25.
d.
$42.
e.
$8.
37. Daily demand for gasoline at Billy-Bob’s Mobile Station is described by Q = 776 − 200p, where Q are
gallons of gasoline sold and p is the price in dollars. Billy-Bob’s supply is Q = 2890 + 1,500p. Suppose
the state government places a tax of 20 cents on every gallon of gasoline sold. What is the deadweight
loss resulting from this tax?
a.
3.53 dollars
b.
3.11 dollars
c.
0.42 dollars
d.
96.12 dollars
e.
34.59 dollars
38. Daily demand for gasoline at Billy-Bob’s Mobile Station is described by Q = 980 − 300p, where Q are
gallons of gasoline sold and p is the price in dollars. Billy-Bob’s supply is Q = 22,980 + 3,000p.
Suppose the state government places a tax of 18 cents on every gallon of gasoline sold. What is the
deadweight loss resulting from this tax?
a.
4.02 dollars
b.
0.40 dollars
c.
4.42 dollars
d.
93.42 dollars
e.
58.91 dollars
PROBLEM
1. Use supply and demand analysis to examine the following statement: “The practice of giving food
stamps is self-defeating. Food stamps effectively lower the price of food. When food becomes
available at lower prices, demand will increase thereby forcing the price up to its initial level.” Is this
reasoning correct? Draw supply and demand curves to illustrate your answer.
2. Long ago, a kindly prince noticed the misery of his subjects. His subjects all had the same preferences
and the same low incomes. The demand function of each subject for bread was q = 26 − p, where p is
the price of bread and q is the number of loaves per week. The supply of bread per capita per week was
given by the function q = .3p. The king declared since his subjects did not even get a loaf of bread per
day, he would help them by making it illegal to sell bread for more than 10 groschens per loaf.
Unhappily, a bread shortage arose and people waited in long lines to get bread.
a. Draw a graph to show why. Put numerical labels on the important points on your graph.
b. If the citizens could earn 4 groschens per hour at work that was exactly as unpleasant as waiting in
line, what would be the equilibrium waiting time for a loaf of bread?