Question 1

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?

Accepted Answer

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

Question 2

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?

Accepted Answer

Jackie's net demand for x is 6, meaning she wants to consume 6 more units of x than she initially has. Her gross demand for x is 15, which is the total amount she wants to have. To find her initial endowment, subtract her net demand from her gross demand: 15 - 6 = 9.

Question 3

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

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 4

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?

Accepted Answer

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

Question 5

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?

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 6

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.

Accepted Answer

Milton will maximize his utility by spending all his income on good y, given the prices. He sells his 40 units of x for $200 (40 units * $5/unit) and uses this to buy 200 units of y ($200/$1 per unit).

Question 7

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?

Accepted Answer

Rhoda's goal is to maximize her utility, subject to the constraint that she has 70 hours per week to allocate between work and leisure. Let F1 be the number of hours she works and S1 be the number of hours she spends on leisure. Then, we have:
F1 + S1 = 70   (constraint)
Her income, I, is given by:
I = 5F1 + 10 max(0,F1-40)   (wage function)
We can simplify this as follows:
I = 5F1 + 10(F1-40)   (since max(0,F1-40) = F1-40 for F1 >= 40)
I = 15F1 - 400
Her utility function is:
U = F1 * S1^0.5
We want to choose F1 and S1 to maximize U subject to the constraint on time:
Maximize U = F1 * S1^0.5
Subject to F1 + S1 = 70
We can use Lagrange multipliers to solve this optimization problem:
L(F1,S1,lambda) = F1 * S1^0.5 + lambda(70 - F1 - S1)
Taking partial derivatives with respect to F1, S1, and lambda and setting them equal to zero, we get:
S1^0.5 = lambda
0.5 * F1 * S1^-0.5 - lambda = 0
70 - F1 - S1 = 0
From the first equation, we have S1 = lambda^2. Squaring the third equation gives:
F1^2 - 140F1 + 4900 = 0
Solving for F1 using the quadratic formula, we get:
F1 = 70 - S1 = 45 (rounded to the nearest integer)
So Rhoda should work 45 hours and spend 25 hours on leisure to maximize her utility.

Question 8

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?

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 9

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.

Accepted Answer

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

Question 10

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?

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 11

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

Accepted Answer

The answer of Wendy and Mac work in fast-food restaurants.Wendy...

Question 12

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?

Accepted Answer

Russ Tickman's budget constraint is 2x + y = 38 (since he can sell 19 units of milk at $2 each). To maximize utility U(x, y) = y(x + 1), set the marginal rate of substitution equal to the price ratio: (x + 1) = 2. Solving gives x = 9 gallons.

Question 13

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?

Accepted Answer

The answer of Georgina earns 6 dollars an hour.She has...

Question 14

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.

Accepted Answer

Since Milton has no initial endowment of good y, he can only consume y by purchasing it with the money he gets by selling some of his good x.

Let Milton consume x and y in quantities x1 and y1 respectively. Then his total expenditure would be:

4x1 + y1 = income or 4x1 = income - y1

As Milton wants to maximize his utility, he will choose the quantities of x and y such that their marginal utilities are equal to each other:

MUx/MUy = Px/Py

=> MUx/MUy = 4

=> (d/dx (xy))/ (d/dy (xy)) = 4

=> y/x = 4/1

=> y1/x1 = 4/1

=> y1 = 4x1

Substituting this value in the budget equation, we get:

4x1 + 4x1 = income

=> x1 = income/8

As Milton is endowed with 76 units of good x, his maximum income would be 4*76 = 304

Therefore, his consumption of good x would be:

x1 = 304/8 = 38

And his consumption of good y would be:

y1 = 4x1 = 4*38 = 152

Hence, the answer is C) 152.

Question 15

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?

Accepted Answer

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

Question 16

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,

Accepted Answer

Fanny's budget constraint remains the same because the relative prices and her endowment value do not change, so she is neither better off nor worse off.

Question 17

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?

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 18

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.

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 19

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.

Accepted Answer

The correct answer is A.The net demand for x is the amount of x that Donald wants to consume, given his budget constraint. To find the net demand for x, we need to solve the following equation:```MUx / Px = MUy / Py```where MUx and MUy are the marginal utilities of x and y, respectively, and Px and Py are the prices of x and y, respectively.The marginal utility of x is the change in utility that results from consuming one more unit of x, holding y constant. The marginal utility of y is the change in utility that results from consuming one more unit of y, holding x constant.The marginal utility of x is:```MUx = ∂U/∂x = y^3```The marginal utility of y is:```MUy = ∂U/∂y = 3xy^2```Substituting these values into the equation above, we get:```y^3 / 1 = 3xy^2 / 3```Simplifying, we get:```y^3 = xy^2```Dividing both sides by y^2, we get:```y = x```This means that Donald wants to consume the same amount of x and y.Given that Donald is endowed with 43 units of x and 7 units of y, and the price of x is $1 and the price of y is $3, his budget constraint is:```43x + 7y = 129```Substituting y = x into the budget constraint, we get:```43x + 7x = 129```Simplifying, we get:```50x = 129```Solving for x, we get:```x = 2.58```Therefore, Donald's net demand for x is 2.58 units.

Question 20

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,

Accepted Answer

Holly's budget constraint remains the same because both her endowment and consumption plans are affected equally by the price change.

Quiz 8: Buying and Selling-Part A

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?

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?

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?

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.

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.

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?

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.

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?

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,

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.

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,

Quiz 8: Buying and Selling-Part A

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?

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?

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?

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.

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.

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?

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.

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?

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,

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.

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,

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?

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?

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?

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?

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.