CHAPTER 14: Consumer’s Surplus
TRUE/FALSE
1. Consumer’s surplus is another name for excess demand.
2. There is a positive consumer’s surplus when the total amount the consumer pays for something is less
than the amount she would be willing to pay rather than do without it altogether.
3. The equivalent variation in income from a tax is the amount of extra income that a consumer would
need in order to be as well off after the tax is imposed as he was originally.
4. With quasilinear preferences, the equivalent variation and the compensating variation in income due to
a tax are the same.
5. Producer’s surplus at price p is the vertical distance between the supply curve and the demand curve at
price p.
6. If somebody is buying 10 units of x and the price of x falls by $3, then that person’s net consumer’s
surplus must increase by at least $30.
7. If somebody is buying 10 units of x and the price of x falls by $4, then that person’s net consumer’s
surplus must increase by at least $40.
8. If there is Cobb-Douglas utility, compensating and equivalent variation are the same.
9. Bernice has the utility function U(x, y) = minx, y. The price of x used to be 3 but rose to 4. The price
of y remained at 1. Her income is 12. The price increase was as bad for her as a loss of $3 in income.
10. If there is a price increase for a good that Marilyn consumes, her compensating variation is the change
in her income that allows her to purchase her new optimal bundle at the original prices.
11. If there is a price increase for a good that Susan consumes, her compensating variation is the change in
her income that allows her to purchase her new optimal bundle at the original prices.
12. Bernice’s utility function is U(x, y) = minx, y. The price of x used to be 3 but rose to 4. The price of
y remained at 1. Her income is 12. She would need an income of $15 to be able to afford a bundle as
good as her old one at the new prices.
MULTIPLE CHOICE
1. Ella’s utility function is min5x, y. If the price of x is $10 and the price of y is $15, how much money
would she need to be able to purchase a bundle that she likes as well as the bundle (x, y) = (10, 25)?
a.
$209
b.
$440
c.
$425
d.
$475
e.
$85
2. Ella’s utility function is min5x, y. If the price of x is $20 and the price of y is $20, how much money
would she need to be able to purchase a bundle that she likes as well as the bundle (x, y) = (7, 15)?
a.
$440
b.
$360
c.
$177
d.
$372
e.
$72
3. Reginald is fond of cigars. His utility function is U(x, c) = x + 10c − .5c2, where c is the number of
cigars he smokes per week and x is the money that he spends on the consumption of other goods.
Reginald has $200 a week to spend. Cigars used to cost him $1 each, but their price went up to $2
each. This price increase was as bad for him as losing income of
a.
$5.
b.
$7.25.
c.
$9.
d.
$8.
e.
$8.50.
4. Sam’s utility function is U(x, y) = 2x + y, where x is the number of x’s he consumes per week and y is
the number of y’s he consumes per week. Sam has $200 a week to spend. The price of x is $4. Sam
currently doesn’t consume any y. Sam has received an invitation to join a club devoted to the
consumption of y. If he joins the club, Sam can get a discount on the purchase of y. If he belonged to
the club, he could buy y for $1 a unit. How much is the most Sam would be willing to pay to join this
club?
a.
Nothing
b.
$100 a week
c.
$50 a week
d.
$40 a week
e.
None of the above.
5. Yoram’s utility function is U(x, y) = 2x + 5y. The price of x is $4 and the price of y is $15. Yoram has
$150 a week to spend on x and y. Yoram is offered a chance to join a club of y consumers. If he joins,
he can get y at a price of $10. What is the most that Yoram would be willing to pay to join the club?
a.
Nothing
b.
$30 a week
c.
$50 a week
d.
$75 a week
e.
None of the above.
6. Minnie gets 4 tapes for her birthday, but they are currently useless to her because she doesn’t have a
tape recorder and she cannot return them for a refund. Her utility function is U(x, y, z) = x + f(y)z5,
where z is the number of tapes she has, y is the number of tape recorders she has, and x is the money
she has to spend on other stuff. Let f(y) = 0 if y 1 and f(y) = 7 otherwise. The price of tapes is $7.99.
What is her reservation price for a tape recorder?
a.
$20
b.
$7
c.
$24
d.
$0
e.
None of the above.
7. Izaak likes to eat pizza and to fish. The more fishing he does the happier he is, up to 8 hours a day. If
he fishes longer than 8 hours he gets a sore back and is less happy than if he hadn’t fished at all. For y
less than or equal to 8, his utility function is U(x, y) = x + 3y, where x is money spent on pizza and y is
hours per day spent fishing. His income is $40 a day and he has no expenses other than pizza. The
Bureau of Fisheries has just decided to allow people without fishing licenses to fish only 3 hours a day.
But if you buy a fishing license, you can fish as many hours as you wish. How much is Izaak willing
pay for a license?
a.
$15
b.
$24
c.
$18
d.
$13
e.
$0
8. Izaak likes to eat pizza and to fish. The more fishing he does the happier he is, up to 8 hours a day. If
he fishes longer than 8 hours he gets a sore back and is less happy than if he hadn’t fished at all. For y
less than or equal to 8, his utility function is U(x, y) = x + 6y, where x is money spent on pizza and y is
hours per day spent fishing. His income is $45 a day and he has no expenses other than pizza. The
Bureau of Fisheries has just decided to allow people without fishing licenses to fish only 3 hours a day.
But if you buy a fishing license, you can fish as many hours as you wish. How much is Izaak willing
pay for a license?
a.
$33
b.
$30
c.
$48
d.
$28
e.
$0
9. Ellsworth’s utility function is U(x, y) = minx, y. Ellsworth has $150 and the price of x and the price
of y are both $1. Ellsworth’s boss is thinking of sending him to another town where the price of x is $1
and the price of y is $2. The boss offers no raise in pay. Ellsworth, who understands compensating and
equivalent variation perfectly, complains bitterly. He says that although he doesn’t mind moving for its
own sake and the new town is just as pleasant as the old, having to move is as bad as a cut in pay of
$A. He also says he wouldn’t mind moving if when he moved he got a raise of $B. What are A and B?
a.
A = 50 and B = 50.
b.
A = 75 and B = 75.
c.
A = 75 and B = 100.
d.
A = 50 and B = 75.
e.
None of the above.
10. Kristina consumes only goods X and Y. Her income is $600 and her utility function is U(x, y) = maxx,
y, where x is the number of units of X she consumes and y is the number of units of Y she consumes.
The price of good Y is 1. The price of good X used to be 1/2 but is now 2. The equivalent variation of
this price change for Kristina is
a.
$300.
b.
$600.
c.
$150.
d.
$800.
e.
None of the above.
11. Holly consumes only goods X and Y. Her income is $500 and her utility function is U(x, y) = maxx,
y, where x is the number of units of X she consumes and y is the number of units of Y she consumes.
The price of good Y is 1. The price of good X used to be 1/3 but is now 2. The equivalent variation of
this price change for Holly is
a.
$111.11.
b.
$1,566.67.
c.
$1,000.
d.
$333.33.
e.
None of the above.
12. Poindexter’s utility function is U(x, y) = minx + 2y, 3x + y, where x is butter and y is guns. If the
price of butter is $4 and the price of guns is $5, what would it cost Poindexter to buy the cheapest
bundle that he likes as well as 4 units of butter and 3 units of guns?
a.
$31
b.
$32
c.
$29
d.
$28
e.
None of the above.
13. Albin has quasilinear preferences and he loves pretzels. His inverse demand function for pretzels is
p(x) = 49 − 6x, where x is the number of pretzels that he consumes. He is currently consuming 8
pretzels at a price of $1 per pretzel. If the price of pretzels rises to $7 per pretzel, the change in Albin’s
consumer surplus is
a.
−$90.
b.
−$56.
c.
−$42.
d.
−$45.
e.
−$42.
14. Bernice’s preferences can be represented by the utility function, U(x, y) = minx, y. She faces prices
($2, $1), and her income is $12. If prices change to ($3, $1), the compensating variation
a.
equals the equivalent variation.
b.
is $2 greater than the equivalent variation.
c.
is $2 smaller than the equivalent variation.
d.
is $1 greater than the equivalent variation.
e.
There is not enough information to determine which variation is larger.
15. At the initial prices, Teodoro is a net seller of apples and a net buyer of bananas. If the price of apples
decreases and the price of bananas does not change,
a.
the compensating variation must be negative and the equivalent variation positive.
b.
the compensating variation must be positive and the equivalent variation negative.
c.
both the compensating variation and the equivalent variation must be positive.
d.
both the compensating variation and the equivalent variation must be negative.
e.
the compensating variation must be negative but the equivalent variation could be of either
sign.
16. Sam has quasilinear preferences and his demand function for x is D(p) = 15 − p/3. The price of x is
initially $15 per unit and increases to $24 per unit. Sam’s change in consumer’s surplus is closest to
a.
−168.
b.
−76.
c.
−27.
d.
75.
e.
Sam won’t consume x at either of the prices.
17. Sir Plus has a demand function for mead that is given by the equation D(p) = 100 − p. If the price of
mead is $60, how much is Sir Plus’s net consumer’s surplus?
a.
$40
b.
$800
c.
$1,600
d.
$400
e.
$3,900
18. Sir Plus has a demand function for mead that is given by the equation D(p) = 100 − p. If the price of
mead is $90, how much is Sir Plus’s net consumer’s surplus?
a.
$25
b.
$10
c.
$50
d.
$100
e.
$8,550
19. Quasimodo from your workbook has the utility function U(x, m) = 100x − x2/2 + m, where x is his
consumption of earplugs and m is money left over to spend on other stuff. If he has $10,000 to spend
on earplugs and other stuff and if the price of earplugs rises from $50 to $70, then his net consumer’s
surplus
a.
falls by 800.
b.
falls by 2,800.
c.
falls by 600.
d.
increases by 400.
e.
increase by 1,600.
20. Quasimodo from your workbook has the utility function U(x, m) = 100x − x2/2 + m, where x is his
consumption of earplugs and m is money left over to spend on other stuff. If he has $10,000 to spend
on earplugs and other stuff and if the price of earplugs rises from $50 to $75, then his net consumer’s
surplus
a.
falls by 937.50.
b.
increases by 468.75.
c.
falls by 2,937.50.
d.
falls by 625.
e.
increases by 1,875.
21. Bernice has the utility function u(x, y) = minx, y, where x is the number of pairs of earrings she buys
per week and y is the number of dollars per week she has left to spend on other things. (We allow the
possibility that she buys fractional numbers of pairs of earrings per week.) If she originally had an
income of $10 per week and was paying a price of $8 per pair of earrings, then if the price of earrings
rose to $13 per pair, the compensating variation of that price change (measured in dollars per week)
would be closest to
a.
$3.57.
b.
$5.56.
c.
$12.11.
d.
$11.11.
e.
$10.11.
22. Bernice has the utility function u(x, y) = minx, y, where x is the number of pairs of earrings she buys
per week and y is the number of dollars per week she has left to spend on other things. (We allow the
possibility that she buys fractional numbers of pairs of earrings per week.) If she originally had an
income of $18 per week and was paying a price of $6 per pair of earrings, then if the price of earrings
rose to $10 per pair, the compensating variation of that price change (measured in dollars per week)
would be closest to
a.
$20.57.
b.
$6.55.
c.
$10.29.
d.
$21.57.
e.
$19.57.
23. If Bernice (whose utility function is minx, y, where x is her consumption of earrings and y is money
left for other stuff) had an income of $15 and was paying a price of $8 for a pair of earrings, then if the
price of earrings went up to $13, the equivalent variation of the price change would be
a.
$5.36.
b.
$8.33.
c.
$16.67.
d.
$2.68.
e.
$6.85.
24. If Bernice (whose utility function is minx, y, where x is her consumption of earrings and y is money
left for other stuff) had an income of $12 and was paying a price of $4 for a pair of earrings, then if the
price of earrings went up to $6, the equivalent variation of the price change would be
a.
$4.80.
b.
$3.43.
c.
$1.71.
d.
$9.60.
e.
$4.11.
25. Lolita, the Holstein cow, has a utility function is U(x, y) = x − x2/2 + y, where x is her consumption of
cow feed and y is her consumption of hay. If the price of cow feed is $.30, the price of hay is $1, and
her income is $4, and if Lolita chooses the combination of hay and cow feed that she likes best from
among those combinations she can afford, her utility will be
a.
4.25.
b.
3.70.
c.
0.25.
d.
6.25.
e.
2.25.
26. Lolita, the Holstein cow, has a utility function is U(x, y) = x − x2/2 + y, where x is her consumption of
cow feed and y is her consumption of hay. If the price of cow feed is $.10, the price of hay is $1, and
her income is $2, and if Lolita chooses the combination of hay and cow feed that she likes best from
among those combinations she can afford, her utility will be
a.
1.90.
b.
3.40.
c.
2.40.
d.
0.40.
e.
1.40.
27. The number of “Gore in 2004” buttons demanded on a certain university campus is given by D(p) =
100 − p, where p is the price of buttons measured in pennies. The supply function is S(p) = p. The
current administration manages to enforce a price ceiling of 40A2 per button. The effect on net
consumer’s surplus is
a.
an increase of $5.50.
b.
an increase of $3.50.
c.
no change.
d.
a decrease of $3.50.
e.
a decrease of $5.50.
28. Pablo’s utility function is U(x, y) = x + 10y − y2/2, where x is the number of x’s he consumes per week
and y is the number of y’s he consumes per week. Pablo has $200 a week to spend. The price of x is
$1. The price of y is currently $5 per unit. Pablo has received an invitation to join a club devoted to the
consumption of y. If he joins the club, Pablo can get a discount on the purchase of y. If he belonged to
the club, he could buy y for $1 a unit. How much is the most Pablo would be willing to pay to join this
club?
a.
$8
b.
$28
c.
$36
d.
$56
e.
None of the above.
29. Herbie’s utility function is U(x, y) = x + 8y − y2/2, where x is the number of x’s he consumes per week
and y is the number of y’s he consumes per week. Herbie has $200 a week to spend. The price of x is
$1. The price of y is currently $4 per unit. Herbie has received an invitation to join a club devoted to
the consumption of y. If he joins the club, Herbie can get a discount on the purchase of y. If he
belonged to the club, he could buy y for $1 a unit. How much is the most Herbie would be willing to
pay to join this club?
a.
$33
b.
$21
c.
$4.50
d.
$16.50
e.
None of the above.
PROBLEM
1. The indirect utility function for a consumer with a utility function U(x1, x2) is defined to be a function
V(p1, p2, m) such that V(p1, p2, m) is the maximum of U(x1, x2) subject to the constraint that the
consumer can afford (x1, x2) at the prices (p1, p2) with income m.
a. Find the indirect utility function for someone with the utility function U(x, y) = 2x + y.
b. Find the indirect utility function for someone with the utility function U(x, y) = min2x, y.
Explain how you got your answers.