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

Accepted Answer

To find out how much Izaak is willing to pay for a fishing license, we need to compare his utility with and without the license.

Without a license, he can fish for 3 hours a day, so his utility would be:

U(x, 3) = 10x + 3(3) = 10x + 9

With a license, he can fish for up to 8 hours a day, so his utility would be:

U(x, y) = 10x + 3y

If he chooses to fish for 3 hours a day with a license, then his utility would be the same as without a license:

U(x, 3) = 10x + 3(3) = 10x + 9

If he chooses to fish for more than 8 hours a day, then his utility would be less than if he didn't fish at all. So the only choice is to fish between 3 to 8 hours a day with a license.

To maximize his utility, we can take the partial derivative of U(x, y) with respect to y:

∂U/∂y = 3

This tells us that his marginal utility for fishing is a constant 3, regardless of how long he fishes.

Since he has $40 a day, he can spend on pizza and a license, we can set up the following equation to solve for the maximum amount he is willing to pay for a license:

10x + 3y = 40 - L

where L is the cost of the license.

Suppose he decides to fish for y hours a day with a license. Then his utility would be:

10x + 3y

And the amount he can spend on pizza and license would be:

40 - L

To find the maximum utility, we need to take the partial derivative of the amount he can spend with respect to y:

∂(40-L)/∂y = -L

To maximize his utility, we set the marginal utility for fishing (which is a constant 3) equal to the marginal cost of fishing (which is the cost of the license divided by the additional hours he can fish):

3 = L/(y-3)

Solving for L, we get:

L = 3y - 9

Substituting L back into the equation we set up earlier:

10x + 3y = 40 - (3y - 9)

10x + 6y = 49

5x + 3y = 24.5

To maximize his utility, he needs to choose the combination of x and y that satisfies the equation above and gives him the highest utility. We can solve for y in terms of x:

y = (24.5 - 5x)/3

Since y needs to be between 3 and 8 for him to buy the license, we can set up an inequality:

3 ≤ (24.5 - 5x)/3 ≤ 8

9 ≤ 24.5 - 5x ≤ 24

-15.5 ≤ -5x ≤ -0.5

0.1 ≤ x ≤ 3.1

We can plug in x = 0.1 and x = 3.1 into the equation for y to find the corresponding values for y:

y = (24.5 - 5(0.1))/3 ≈ 8.13

y = (24.5 - 5(3.1))/3 ≈ 3.83

We see that the optimal range for x is about $0.10 to $3.10, which means Izaak is willing to pay up to $3.00 for a license. However, the answer choices don't reflect this level of precision. The closest answer is A) $15, which is obviously too high. Therefore, we choose E) $0 as the best choice, since Izaak wouldn't buy a license in this case.

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.

Accepted Answer

Given Bernice's utility function U(x, y) = min{x, y}, her utility is determined by the lesser of x and y. Initially, with prices of x at 3 and y at 1, and an income of 12, she could afford 4 units of x (12/3) or 12 units of y (12/1), likely choosing a balanced bundle like 3x and 3y to maximize her utility given her utility function. After the price of x increases to 4, she can afford 3 units of x (12/4) or 12 units of y, potentially adjusting to 3x and 3y again or similar, to maintain utility. The price increase affects her ability to purchase x, but since her utility depends on the minimum of x and y, as long as she can afford equal quantities of x and y, her utility doesn't change. The comparison to a loss of $3 in income doesn't directly correlate without further information on how she allocates her budget. The impact of the price increase cannot be equated to a $3 loss in income without analyzing how the change affects her consumption bundle and utility, which depends on her initial consumption choice.

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

Accepted Answer

First, we need to calculate Ella's utility for the bundle (x,y) which is given by min(5x,5y) = 5x since x < y. So the utility of (x,y) is 5*10 = 50.
Now, we need to find the amount of money Ella needs to purchase a bundle that gives her the same level of utility as (x,y) i.e., 50. Let's assume that she purchases a bundle (x1,y1) where x1 and y1 are the quantities of x and y she purchases respectively. Then, we have:
min(5x1,5y1) = 50
Since x1 < y1, we have 5x1 = 50, which gives x1 = 10.
So, Ella needs to purchase 10 units of x and some units of y such that her utility is 50, which means she buys 5 units of y. Hence, the cost of this bundle is:
10*$10 + 5*$15 = $100 + $75 = $175
Therefore, Ella needs $175 to purchase a bundle that gives her the same level of utility as (x,y)F1F1F1S1F1F1F10 (10,25). 
But since she wants to purchase a bundle that she likes as well, she needs to spend more than $175. The only answer choice that is greater than $175 is C) $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.

Accepted Answer

The answer of Sam's utility function is U(x,y)=2x + y,where...

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.

Accepted Answer

This is the definition of consumer's surplus.

Question 6

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

Accepted Answer

The answer of If there is Cobb-Douglas utility,compensating and equivalent...

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.

Accepted Answer

The answer of Yoram's utility function is U(x,y)= 2x +...

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.

Accepted Answer

The answer of Bernice's utility function is U(x,y)=min{x,y}.The price of...

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.

Accepted Answer

The reservation price for a tape recorder is not directly given by the utility function or the information provided. The utility function shows that tapes (z) only add to Minnie's utility if she has a tape recorder (y > 0), with f(y) changing from 0 to 7 when she acquires a tape recorder. However, the price of tapes or the utility function does not directly provide a reservation price for the tape recorder itself. The reservation price would be the maximum amount Minnie is willing to pay for a tape recorder, considering it would make her tapes useful, but this cannot be determined with the given information.

Question 10

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

Accepted Answer

This is true because with quasilinear preferences, utility functions can be expressed as a linear function of a single good and thus the compensating variation and equivalent variation in income due to a tax would be 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.

Accepted Answer

The answer of If there is a price increase for...

Question 12

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

Accepted Answer

Producer's surplus at price p is the area above the supply curve and below the price level p, up to the quantity sold. It represents the difference between what producers are willing to accept for a good or service versus what they actually receive.

Question 13

Consumer's surplus is another name for excess demand.

Accepted Answer

Consumer's surplus refers to the difference between the maximum amount a consumer is willing to pay for a good or service and the actual price they pay. It is a measure of consumer satisfaction and welfare, not excess demand. Excess demand refers to a situation where the quantity demanded of a good or service exceeds the quantity supplied at a given price, leading to shortages and potentially higher prices.

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.

Accepted Answer

The answer of Reginald is fond of cigars.His utility function...

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.

Accepted Answer

Consumer surplus increases when the price of a good falls, but the increase in consumer surplus is not solely determined by the quantity bought multiplied by the price decrease. It also depends on the individual's demand curve for the product.

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.

Accepted Answer

The answer of If there is a price increase for...

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.

Accepted Answer

Consumer surplus is the difference between what consumers are willing to pay and what they actually pay. A decrease in price does not guarantee an increase in consumer surplus by a specific amount, as it depends on the demand curve and how much the consumer values additional units.

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.

Accepted Answer

The answer of The equivalent variation in income from a...

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

Accepted Answer

The answer of Ella's utility function is min{5x,y}.If the price...

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

Accepted Answer

To determine how much Izaak is willing to pay for a fishing license, we first calculate his utility from fishing for 3 hours without a license and then for 8 hours, which is his optimal fishing time. His utility function for fishing and pizza is U(x, y) = 10x + 6y, where x is the money spent on pizza and y is the hours spent fishing.Without a license, he can fish for 3 hours:U = 10x + 6(3) = 10x + 18.With a license, he prefers to fish for 8 hours:U = 10x + 6(8) = 10x + 48.His income is $45, and we assume all of it is spent on pizza (x) when not buying a license. Thus, without a license, his utility from spending all on pizza is 10(45) = 450. However, this isn't directly relevant as we're comparing utilities with different fishing hours.To find out how much he values the additional 5 hours of fishing (from 3 to 8 hours), we look at the increase in utility from those hours:Additional utility = 6(8) - 6(3) = 48 - 18 = 30.This means Izaak values the additional 5 hours of fishing at $30, which is the maximum he would be willing to pay for the fishing license to increase his fishing hours from 3 to 8.

Quiz 14:Consumers Surplus-Part A