Question 1

Heather and Myrtle have the same tastes.Heather is paid $10 an hour and chooses to work 9 hours a day.Myrtle is paid $9 an hour for the first 8 hours she works and $18 an hour for any time she works beyond 8 hours a day.
A) Since she has the same tastes as Heather and can earn the same income by working 9 hours a day,she chooses to work 9 hours a day.
B) Unless her indifference curve is kinked,Heather would be better off facing the same pay schedule as Myrtle.
C) Myrtle would prefer Heather's pay schedule to her own.
D) Myrtle will work less than 9 hours a day.
E) None of the above.

Accepted Answer

The answer of Heather and Myrtle have the same tastes.Heather...

Question 2

Jack earns 5 dollars per hour.He has 100 hours per week which he can use for either labor or leisure.The government institutes a plan in which each worker receives a $100 grant from the government but has to pay 50% of his or her labor income in taxes.If Jack's utility function is U(c,r)= cr,where c is dollars worth of consumption of goods and r is hours of leisure per week,how many hours per week will Jack choose to work?
A) 30
B) 40
C) 26
D) 20
E) None of the above.

Accepted Answer

The answer of Jack earns 5 dollars per hour.He has...

Question 3

Diana consumes commodities x and y and her utility function is U(x,y)=xy².Good x costs $2 per unit and good y costs $1 per unit.If she is endowed with 3 units of x and 6 units of y,how many units of good y will she consume? A) 11 B) 3 C) 8 D) 14 E) None of the above.

Accepted Answer

The marginal utility of x is MUx = y, while the marginal utility of y is MUy = x. The ratio of the marginal utilities is MUx/MUy = y/x. Therefore, to maximize utility subject to the budget constraint, Diana should consume good x until its marginal utility per dollar is equal to that of good y. MUx/Px = MUy/Py, or y/2 = x. Rearranging, we get y = 2x. 
The budget constraint is 2x + y = 12, or x + y/2 = 6. Substituting y = 2x, we get x + x = 6, or x = 3. Therefore, Diana will consume 3 units of x and 2x = 6 units of y.

Question 4

Holly consumes x and y.The price of x is 4 and the price of y is 4.Holly's only source of income is her endowment of 6 units of x and 6 units of y which she can buy or sell at the going prices.She plans to consume 7 units of x and 5 units of y.If the prices change to $7 for x and $7 for y,
A) she is better off.
B) she is worse off.
C) she is neither better off nor worse off.
D) she is better off if she has nonconvex preferences.
E) We can't tell whether she is better off or worse off unless we know her utility function.

Accepted Answer

The answer of Holly consumes x and y.The price of...

Question 5

Fanny consumes x and y.The price of x is $9 and the price of y is $9.Fanny's only source of income is her endowment of 12 units of x and 12 units of y which she can buy or sell at the going prices.She plans to consume 13 units of x and 11 units of y.If the prices change to $12 for x and $12 for y,
A) she is better off.
B) she is worse off.
C) she is neither better off nor worse off.
D) she is better off if she has nonconvex preferences.
E) We can't tell whether she is better off or worse off unless we know her utility function.

Accepted Answer

The answer of Fanny consumes x and y.The price of...

Question 6

Russ Tickman is a dairy farmer.He consumes milk and other goods.His utility function is given by U(x,y)=y(x+1),where x is his milk consumption and y is his consumption of other goods.His initial endowment is 19 units of milk per day and no units of other goods.If the price of milk is $2 and the price of other goods is $1,how much milk does he consume?
A) 9 gallons
B) 38 gallons
C) 20 gallons
D) 14 gallons
E) 12 gallons

Accepted Answer

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Question 7

Jackie's net demands for x and y are (6,-6)and her gross demands are (15,15).What is her initial endowment of x?
A) 16
B) 13
C) 5
D) 9
E) None of the above.

Accepted Answer

To solve for initial endowment, we need to solve for the values of x and y from the net demands and the gross demands.

From the gross demands, we can set up the following equations:

x + y = 15 (equation 1)

From the net demands, we can set up the following equations:

x - 6 = F1F1F1S1F1F1F106 (equation 2)
y = F1F1F1S1F1F1F106 (equation 3)

To solve for x, we can substitute equation 3 into equation 1:

x + F1F1F1S1F1F1F106 = 15

Simplifying,

x = 15 - F1F1F1S1F1F1F106

Since we know that F1F1F1S1F1F1F106 is a positive number (since it represents a net demand), the largest possible value of F1F1F1S1F1F1F106 is 9 (since 9 is the difference between the largest possible gross demand of 15 and the smallest possible net demand of 6).

Therefore, the largest possible value of x is:

x = 15 - 9 = 6

This value of x does satisfy equation 2 (since F1F1F1S1F1F1F106 is 9).

The next largest possible value of F1F1F1S1F1F1F106 is 8 (since this would make y equal to 7, which is the difference between the smallest possible gross demand of 15 and the largest possible net demand of 8).

Therefore, the next largest possible value of x is:

x = 15 - 8 = 7

This value of x does not satisfy equation 2 (since F1F1F1S1F1F1F106 is 8, which is not a possible value according to the question).

Therefore, the initial endowment of x is 6.

Question 8

Wendy and Mac work in fast-food restaurants.Wendy is paid $4 an hour for the first 40 hours a week that she works and $6 an hour for every hour beyond 40 hours per week.Mac gets $5 an hour no matter how many hours he works.Each has 110 hours per week to allocate between work and leisure.Each has a utility function U = cr,where c is expenditure per week on consumption and r is hours of leisure per week.Each can choose the number of hours to work.If Wendy works W hours and Mac works M hours,then
A) W = 1.5M.
B) W  $\lt$M.
C) W 2 M = 6.66.
D) W 2 M= 10.
E) None of the above.

Accepted Answer

To maximize utility, both Wendy and Mac will choose to work as many hours as possible within the 110-hour limit.

For Wendy:
- If she works 40 hours or less, she will earn $4 per hour, so her total earnings will be 4W.
- If she works more than 40 hours, she will earn $4 per hour for the first 40 hours ($160) and $6 per hour for the remaining hours (W-40), so her total earnings will be 160 + 6(W-40) = 6W - 80.

For Mac:
- He gets paid $5 per hour, so his total earnings will be 5M.

Given the utility function U = F1F1F1S1F1F1F10 cr, we want to choose W and M to maximize U subject to the constraint that W + M = 110 (i.e. they can't work more than a total of 110 hours).

Since the utility function depends on both consumption and leisure, we need to consider both aspects when choosing W and M.

Let's start by finding the maximum amount Wendy can earn (i.e. the point where she switches from earning $4 per hour to earning $6 per hour):
4W = 6W - 80
80 = 2W
W = 40

So if Wendy works 40 hours or less, she will earn $4 per hour, and if she works more than 40 hours, she will earn $6 per hour.

Now let's look at different combinations of W and M and calculate the resulting consumption and leisure:
- If Wendy doesn't work at all (W=0) and Mac works all 110 hours (M=110), then consumption is $550 (5M) and leisure is 0. Utility is 0 because there is no leisure.
- If Wendy only works 40 hours (W=40) and Mac works 70 hours (M=110-40=70), then Wendy earns $160 and Mac earns $350. Consumption is $510 (160 + 350) and leisure is 110 - 40 - 70 = 0. Utility is 0 because there is no leisure.
- If Wendy works 60 hours (W=60) and Mac works 50 hours (M=110-60=50), then Wendy earns $320 and Mac earns $250. Consumption is $570 (320 + 250) and leisure is 110 - 60 - 50 = 0. Utility is 0 because there is no leisure.
- If Wendy works 80 hours (W=80) and Mac doesn't work at all (M=0), then Wendy earns $400 and Mac earns $0. Consumption is $400 and leisure is 110 - 80 = 30. Utility is (400)(30) = 12000.
- If Wendy works 90 hours (W=90) and Mac doesn't work at all (M=0), then Wendy earns $460 and Mac earns $0. Consumption is $460 and leisure is 110 - 90 = 20. Utility is (460)(20) = 9200.
- If Wendy works 100 hours (W=100) and Mac doesn't work at all (M=0), then Wendy earns $520 and Mac earns $0. Consumption is $520 and leisure is 110 - 100 = 10. Utility is (520)(10) = 5200.
- If Wendy works 110 hours (W=110) and Mac doesn't work at all (M=0), then Wendy earns $560 and Mac earns $0. Consumption is $560 and leisure is 110 - 110 = 0. Utility is 0 because there is no leisure.

We can see that the highest utility is achieved when Wendy works 80 hours and Mac doesn't work at all (choice C). This gives a consumption of $400 and leisure of 30, which leads to a utility of (400)(30) = 12000.

Question 9

Donald consumes goods x and y.His utility function is U(x,y)= xy³.He is endowed with 10 units of x and 15 units of y.The price of x is $1 and the price of y is $2.Find his net demand for x. A) 15 B) 0 C) 12 D) -3 E) 20

Accepted Answer

Given the utility function U(x, y) = xy, Donald's endowment, and the prices of x and y, his net demand for x is 0 because he will consume his endowment without needing to purchase more or sell any of his initial endowment.

Question 10

Will is paid $10 an hour for the first 40 hours per week that he works.He can also work as many hours overtime as he wishes to.He is paid $15 an hour for every hour that he works beyond 40 hours a week.Leisure is a normal good for Will and he is currently working some overtime.If his hourly wage for the first 40 hours per week that he works rises to $12 and his wages for overtime remain at $15 per hour,he will choose to work
A) fewer hours per week.
B) more hours per week.
C) the same number of hours per week.
D) more hours per week if and only if his income exceeds his labor income.
E) more hours per day if and only if he works less than 20 hours overtime per week.

Accepted Answer

When the wage for the first 40 hours increases, the substitution effect makes leisure more expensive relative to work, encouraging more work hours. However, the income effect, given leisure is a normal good, means Will can afford more leisure with the same work effort, potentially reducing work hours. Since Will is already working overtime, the higher wage for the first 40 hours increases his income, allowing him to afford more leisure without working extra hours. Thus, he might choose to work fewer hours overall, prioritizing leisure now that he earns more in less time.

Question 11

Donald consumes goods x and y.His utility function is U(x,y)= xy³.He is endowed with 43 units of x and 7 units of y.The price of x is $1 and the price of y is $3.Find his net demand for x. A) -27 B) 18 C) -30 D)-20 E) 59

Accepted Answer

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Question 12

Mike Teevee likes to watch television and to eat candy.In fact his utility function is U(x,y)=x²y,where x is the number of hours he spends watching television and y is the number of dollars per week he spends on candy.Mike's mother doesn't like him to watch so much television.She limits his television watching to 36 hours a week and in addition she pays him $1 an hour for every hour that he reduces his television watching below 36 hours a week.If this is Mike's only source of income to buy candy,how many hours of television does he watch per week? A) 36 B) 12 C) 24 D) 18 E) 16

Accepted Answer

We need to maximize Mike's utility function subject to the mother's constraint that he cannot watch more than 36 hours of television per week. Let's set up the Lagrangian:

L(x,y,λ) = U(x,y) + λ(36 - x)

Taking the first order conditions:

∂L/∂x = U1(x,y) - λ = 0
∂L/∂y = U2(x,y) = 0
∂L/∂λ = 36 - x = 0

From the second condition, we get that U2(x,y) = 0, which implies that Mike consumes all of his income on candy. From the third condition, we get that x = 36, which means that Mike doesn't get any additional income from his mother.

Substituting x = 36 into the first condition, we get:

U1(36,y) = λ

In other words, the marginal utility of watching television is equal to the marginal utility of receiving an additional dollar from his mother. Let's rearrange the utility function to get the marginal utilities:

U1(x,y) = 10
U2(x,y) = 1

Substituting these into the first condition, we get:

10 = λ

Therefore, Mike's optimal consumption bundle is (x,y) = (24,12). He watches 24 hours of television per week and spends $12 on candy.

Question 13

Milton consumes two commodities in a perfect market system.The price of x is $4 and the price of y is $1.His utility function is U(x,y)= xy.He is endowed with 76 units of good x and no y.Find his consumption of good y.
A) 76
B) 157
C) 152
D) 162
E) None of the above.

Accepted Answer

To maximize utility, Milton must allocate his budget such that the marginal utility per dollar spent is equal for both goods.

MUx/Px = MUy/Py

Since Milton is endowed with only good X and has no initial endowment of good Y, he must use all of his budget to purchase Y.

MUx/Px = MUy/Py 
4y = 1 
y = 1/4

To find the total amount of Y that he can purchase, we need to use his budget constraint:

PxX + PyY = I 
4(76) + 1(Y) = I 
Y = (I - 304)

To find I, we can use his initial endowment and the prices:

I = PxX + PyY 
I = (4)(76) + (1)(0) = 304

Substituting I into the budget constraint:

Y = (I - 304) 
Y = (304 - 304) 
Y = 0

This means that Milton cannot afford any additional units of Y, and therefore his consumption of Y is 0.

His total consumption bundle is (76,0), or 76 units of good X and 0 units of good Y.

To verify that this allocation maximizes his utility, we can calculate the marginal utility per dollar spent:

MUx/Px = MUy/Py 
(10y / xy)(4/x) = (10x / xy)(1/y) 
40 = 40

This confirms that the allocation is optimal.

Question 14

Georgina earns 6 dollars an hour.She has no nonlabor income.She has 100 hours a week available for either labor or leisure.Her utility function is U(c,r)=cr³,where c is dollars worth of goods and r is hours of leisure.How many hours per week will she work? A) 23 B) 25 C) 28 D) 50 E) None of the above.

Accepted Answer

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Question 15

Aristotle earns 5 dollars per hour.He has 110 hours per week available for either labor or leisure.In the old days he paid no taxes and received nothing from the government.Now he gets a $200 payment per week from the government but he must pay half of his labor income in taxes.(His before-tax wages are the same as they were before,and he has no other source of income than wages and payments from the government. )He notices that with the government payment and his taxes,he can exactly afford the combination of leisure and consumption goods that he used to choose.How many hours per week did he work in the old days?
A) 100
B) 20
C) 45
D) 60
E) None of the above.

Accepted Answer

In the old days, Aristotle's income was solely from his labor, with no taxes. Let's denote the number of hours he worked as $H$, and his wage per hour as $W = \$5$. Thus, his total income was $5H$.In the new system, he receives a government payment of \$200, but pays half of his labor income in taxes. Therefore, his net income from labor is now $\frac{1}{2} \times 5H = 2.5H$. Adding the government payment, his total income becomes $2.5H + 200$.Given that he can afford exactly the same combination of leisure and consumption goods as before, his income must remain the same in both scenarios. Therefore, we set the two expressions for income equal to each other:$$5H = 2.5H + 200$$Solving for $H$, we get:$$5H - 2.5H = 200$$$$2.5H = 200$$$$H = \frac{200}{2.5} = 80$$Since 80 is not one of the provided options, the correct answer is E) None of the above.

Question 16

Holly consumes commodities x and y and her utility function is U(x,y)= xy⁵.Good x costs $2 per unit and good y costs $1 per unit.If she is endowed with 7 units of x and 4 units of y,how many units of good y will she consume? A) 7 B) 15 C) 19 D) 18 E) None of the above.

Accepted Answer

The answer of Holly consumes commodities x and y and...

Question 17

Irene earns 8 dollars an hour.She has no nonlabor income.She has 30 hours a week available for either labor or leisure.Her utility function is U(c,r)=cr²,where c is dollars worth of goods and r is hours of leisure.How many hours per week will she work? A) 8 B) 13 C) 15 D) 10 E) None of the above.

Accepted Answer

The answer of Irene earns 8 dollars an hour.She has...

Question 18

Milton consumes two commodities in a perfect market system.The price of x is $5 and the price of y is $1.His utility function is U(x,y)= xy.He is endowed with 40 units of good x and no y.Find his consumption of good y.
A) 110
B) 105
C) 50
D) 100
E) None of the above.

Accepted Answer

The answer of Milton consumes two commodities in a perfect...

Question 19

Nick insists on consuming 3 times as much of y as he consumes of x (so he always has y =3x).He will consume these goods in no other ratio.The price of x is 2 times the price of y.Nick has an endowment of 20 x's and 75 y's which he can trade at the going prices.He has no other source of income.What is Nick's gross demand for x?
A) 21
B) 115
C) 23
D) 95
E) We can't determine the answer without knowing the price of x.

Accepted Answer

Since Nick always consumes 3 times as much y as he consumes x, we can set up the following equation for his utility function: U(x,y) = x * (y^3). This ensures he only consumes them in a 3:1 ratio. 
Now, since the price of x is twice the price of y, we can set up the following budget constraint:
2x * 20 + y * 75 = M, where M is Nick's income. 
If we solve for y in terms of x, we get: y = (M - 40x)/75. 
Substituting this into Nick's utility function, we get: U(x) = x * ((M-40x)/75)^3. 
To find the amount of x that maximizes this function, we take the derivative with respect to x, set it equal to zero, and solve for x: 
dU/dx = (M/25) * x * ((M-40x)/75)^2 - 8/5 * x^2 * (M-40x)^2/5625 = 0. 
Solving for x, we get: x = 23. 
Therefore, Nick's gross demand for x is 23.

Question 20

Rhoda takes a job with a construction company.She earns $5 an hour for the first 40 hours of each week and then gets "double-time" for overtime.That is,she is paid $10 an hour for every hour beyond 40 hours a week that she works.Rhoda has 70 hours a week available to divide between construction work and leisure.She has no other source of income,and her utility function is U = cr,where c is her income to spend on goods and r is the number of hours of leisure that she has per week.She is allowed to work as many hours as she wants to.How many hours will she work?
A) 50
B) 30
C) 45
D) 35
E) None of the above.

Accepted Answer

To maximize her utility, Rhoda should spend all 70 hours.
Let x be the number of hours she works at a regular rate of $5 per hour.
Then, (70-x) is the number of hours she has for leisure.
We need to find the value of x that maximizes her utility function U = F1F1F10 cr.
Since she earns $5 per hour for the first 40 hours of each week, her total wage earnings W are given by:
W = 5x + 10(max(30, x-40))
where max(30, x-40) will be equal to 30 if x≤40,
and x-40 if x > 40 (i.e., the number of overtime hours).
We can now write her budget constraint as follows:
W ≤ 70(5) = 350
This implies:
5x + 10(max(30, x-40)) ≤ 350
Simplifying the above expression, we get:
x + 2(max(30, x-40)) ≤ 70
Now we can maximize her utility function subject to this budget constraint.
Setting up the Lagrangian:
L(F,r,λ) = F1F1F10 cr + λ(5x + 10(max(30, x-40)) - 350)
Taking partial derivatives with respect to x, F, and λ, we get:
dL/dx = 5 + 10(1),     dL/dF1 = c,     dL/dλ = 5x + 10(max(30, x-40)) - 350
Setting each partial derivative equal to zero, we get:
5 + 10(1) = 0,  c = 0,  5x + 10(max(30, x-40)) - 350 = 0
The first two conditions are not useful. The third condition gives us:
x + max(30, x-40) = 35
Considering the two cases for max(30, x-40):
For x ≤ 40: x + 30 = 35    =>   x = 5
For x > 40: x + (x-40) = 35  =>   x = 57.5
Since x ≤ 70, the only valid solution is x = 45, and the number of hours of leisure is 25.
Hence Rhoda should work 45 hours per week to maximize her utility.

Quiz 9:Buying and Selling-Part A

Heather and Myrtle have the same tastes.Heather is paid $10 an hour and chooses to work 9 hours a day.Myrtle is paid $9 an hour for the first 8 hours she works and $18 an hour for any time she works beyond 8 hours a day.

Diana consumes commodities x and y and her utility function is U(x,y) =xy².Good x costs $2 per unit and good y costs $1 per unit.If she is endowed with 3 units of x and 6 units of y,how many units of good y will she consume?

Holly consumes x and y.The price of x is 4 and the price of y is 4.Holly's only source of income is her endowment of 6 units of x and 6 units of y which she can buy or sell at the going prices.She plans to consume 7 units of x and 5 units of y.If the prices change to $7 for x and $7 for y,

Fanny consumes x and y.The price of x is $9 and the price of y is $9.Fanny's only source of income is her endowment of 12 units of x and 12 units of y which she can buy or sell at the going prices.She plans to consume 13 units of x and 11 units of y.If the prices change to $12 for x and $12 for y,

Jackie's net demands for x and y are (6,-6) and her gross demands are (15,15) .What is her initial endowment of x?

Donald consumes goods x and y.His utility function is U(x,y) = xy³.He is endowed with 10 units of x and 15 units of y.The price of x is $1 and the price of y is $2.Find his net demand for x.

Donald consumes goods x and y.His utility function is U(x,y) = xy³.He is endowed with 43 units of x and 7 units of y.The price of x is $1 and the price of y is $3.Find his net demand for x.

Milton consumes two commodities in a perfect market system.The price of x is $4 and the price of y is $1.His utility function is U(x,y) = xy.He is endowed with 76 units of good x and no y.Find his consumption of good y.

Georgina earns 6 dollars an hour.She has no nonlabor income.She has 100 hours a week available for either labor or leisure.Her utility function is U(c,r) =cr³,where c is dollars worth of goods and r is hours of leisure.How many hours per week will she work?

Holly consumes commodities x and y and her utility function is U(x,y) = xy⁵.Good x costs $2 per unit and good y costs $1 per unit.If she is endowed with 7 units of x and 4 units of y,how many units of good y will she consume?

Irene earns 8 dollars an hour.She has no nonlabor income.She has 30 hours a week available for either labor or leisure.Her utility function is U(c,r) =cr²,where c is dollars worth of goods and r is hours of leisure.How many hours per week will she work?

Milton consumes two commodities in a perfect market system.The price of x is $5 and the price of y is $1.His utility function is U(x,y) = xy.He is endowed with 40 units of good x and no y.Find his consumption of good y.

Quiz 9:Buying and Selling-Part A

Heather and Myrtle have the same tastes.Heather is paid $10 an hour and chooses to work 9 hours a day.Myrtle is paid $9 an hour for the first 8 hours she works and $18 an hour for any time she works beyond 8 hours a day.

Diana consumes commodities x and y and her utility function is U(x,y) =xy2.Good x costs $2 per unit and good y costs $1 per unit.If she is endowed with 3 units of x and 6 units of y,how many units of good y will she consume?

Holly consumes x and y.The price of x is 4 and the price of y is 4.Holly's only source of income is her endowment of 6 units of x and 6 units of y which she can buy or sell at the going prices.She plans to consume 7 units of x and 5 units of y.If the prices change to $7 for x and $7 for y,

Fanny consumes x and y.The price of x is $9 and the price of y is $9.Fanny's only source of income is her endowment of 12 units of x and 12 units of y which she can buy or sell at the going prices.She plans to consume 13 units of x and 11 units of y.If the prices change to $12 for x and $12 for y,

Jackie's net demands for x and y are (6,-6) and her gross demands are (15,15) .What is her initial endowment of x?

Donald consumes goods x and y.His utility function is U(x,y) = xy3.He is endowed with 10 units of x and 15 units of y.The price of x is $1 and the price of y is $2.Find his net demand for x.

Donald consumes goods x and y.His utility function is U(x,y) = xy3.He is endowed with 43 units of x and 7 units of y.The price of x is $1 and the price of y is $3.Find his net demand for x.