Deck 14: A: Consumers Surplus

Question 1

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

Answer 1

$15

Question 2

Bernice has the utility function U(x,y)=min{x,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.

Answer 2

False

Question 3

Ella's utility function is min{5x,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

Answer 3

$425

Question 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.

Question 5

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.

Question 6

If there is Cobb-Douglas utility,compensating and equivalent variation are the same.

Question 7

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.

Question 8

Bernice's utility function is U(x,y)=min{x,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.

Question 9

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 $\lt$ 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.

Question 10

With quasilinear preferences,the equivalent variation and the compensating variation in income due to a tax are the same.

Question 11

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.

Question 12

Producer's surplus at price p is the vertical distance between the supply curve and the demand curve at price p.

Question 13

Consumer's surplus is another name for excess demand.

Question 14

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.

Question 15

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.

Question 16

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.

Question 17

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.

Question 18

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.

Question 19

Ella's utility function is min{5x,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

Question 20

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

Question 21

Kristina consumes only goods X and Y.Her income is $600 and her utility function is U(x,y)=max{x,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.

Question 22

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

Question 23

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.

Question 24

Poindexter's utility function is U(x,y)=min{x+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.

Question 25

Holly consumes only goods X and Y.Her income is $500 and her utility function is U(x,y)=max{x,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.

Question 26

If Bernice (whose utility function is min{x,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.

Question 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.

Question 28

Bernice's preferences can be represented by the utility function,U(x,y)=min{x,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.

Question 29

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.

Question 30

Bernice has the utility function u(x,y)=min{x,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.

Question 31

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.

Question 32

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.

Question 33

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.

Question 34

If Bernice (whose utility function is minF{x,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.

Question 35

Bernice has the utility function u(x,y)=min{x,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.

Question 36

Ellsworth's utility function is U(x,y)F= min{x,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.

Question 37

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.

Question 38

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

Question 39

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.

Question 40

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.

Question 41

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)=min{2x,y}Explain how you got your answers.