Question 1

Suppose that in Horsehead, Massachusetts, the cost of operating a lobster boat is $5,000 per month.Suppose that if x lobster boats operate in the bay, the total monthly revenue from lobster boats in the bay is $1,000(21x - x²).If there are no restrictions on entry and new boats come into the bay until there is no profit to be made by a new entrant, then the number of boats who enter will be X₁.If the number of boats that operate in the bay is regulated to maximize total profits, the number of boats in the bay will be X₂.

A)X₁ = 16 and X₂ = 16.
B)X₁ = 20 and X₂ = 12.
C)X₁ = 16 and X₂ = 8.
D)X₁= 8 and X₂ = 6.
E)None of the above.

X₁ = 16 and X₂ = 8.

Accepted Answer

To maximize profits, we need to find the number of boats that will generate the greatest total revenue minus total cost. Let's first find the revenue function using the given information: Total revenue = $1,000(21x - 10x^2) Total cost = $5,000x Total profit = Total revenue - Total cost = $1,000(21x - 10x^2) - $5,000x Simplifying this expression, we get: Total profit = $16,000x - $10,000x^2 To find the number of boats that maximizes total profit, we need to take the derivative of the profit function with respect to x and set it equal to zero: d(Total profit)/dx = $16,000 - $20,000x = 0 Solving for x, we get: x = 0.8 This means that X₂ = 0.8, or approximately 8 boats when rounded to the nearest whole number. To find X₁, we need to verify that this is the number of boats that will enter the bay until there is no profit to be made by a new entrant. This occurs when the total revenue equals the total cost: $1,000(21x - 10x^2) = $5,000x Solving for x, we get: x = 1.6 This means that X₁ = 1.6, or approximately 16 boats when rounded to the nearest whole number. However, since this is not a feasible number of boats (there can't be 0.6 of a boat), we can say that there are 16 boats in the bay, which is the maximum number of boats that will generate a profit.

Question 2

Suppose that in Horsehead, Massachusetts, the cost of operating a lobster boat is $5,000 per month.Suppose that if x lobster boats operate in the bay, the total monthly revenue from lobster boats in the bay is $1,000(21x - x²).If there are no restrictions on entry and new boats come into the bay until there is no profit to be made by a new entrant, then the number of boats who enter will be X₁.If the number of boats that operate in the bay is regulated to maximize total profits, the number of boats in the bay will be X₂.

A)X₁ = 16 and X₂ = 16.
B)X₁ = 20 and X₂ = 12.
C)X₁ = 16 and X₂ = 8.
D)X₁= 8 and X₂ = 6.
E)None of the above.

X₁ = 16 and X₂ = 8.

Accepted Answer

To find the optimal number of boats for profit maximization, we can take the derivative of the revenue function with respect to x and set it equal to zero:

d/dx($1,000(18x - x^2)) = $1,000(18 - 2x)

Setting this equal to zero and solving for x, we get x = 9.

However, since we are limited to integer values for x, we can test the revenues at x = 8 and x = 10 to see which is higher:

Revenue at x = 8: $1,000(18*8 - 8^2) = $8,000 
Revenue at x = 10: $1,000(18*10 - 10^2) = $8,000

Therefore, the optimal number of boats for profit maximization is 8 boats, and the answer is choice C.

Question 3

suppose that the cost function of the honey farm is C_H(H, A)= H ²/100 - 2A and the cost function of the apple orchard is C_A(H, A)= A²/100, where H and A are the number of units of honey and apples produced respectively.The price of honey is $5 and the price of apples is $4 per unit.Let A₁ be the output of apples if the firms operate independently, and let A₂ be the output of apples if the firms are operated by a profit-maximizing single owner.

A)A₁ = 200 and A₂ = 300.
B)A₁ = A₂ = 200.
C)A₁ = 100 and A₂ = 200.
D)A₁ = 150 and A₂ = 200.
E)A₁ = 250 and A₂ = 200.

A₁ = 200 and A₂ = 300.

Accepted Answer

The profit-maximizing single owner will produce more apples than the two independent firms because the single owner can take advantage of economies of scale.

Question 4

An airport is located next to a housing development.Where X is the number of planes that land per day and Y is the number of houses in the housing development, profits of the airport are 22X - X² and profits of the developer are 20Y - Y² - XY.Let H₁ be the number of houses built if a single profit-maximizing company owns the airport and the housing development.Let H₂ be the number of houses built if the airport and the housing development are operated independently and the airport has to pay the developer the total "damages" XY done by the planes to the developer's profits.

A)H₁ = 10 and H₂ = 6.
B)H₁ = 8 and H₂ = 9.
C)H₁ = 6 and H₂ = 10.
D)H₁ = H₂ = 6.
E)H₁ = 9 and H₂ = 13.

Accepted Answer

The answer of An airport is located next to a...

Question 5

suppose Harry, a typical citizen, has the utility function U(m, d, h)= m + 7d² - d² - 2h, where d is the number of hours per day that he spends driving around, h is the average number of hours per day spent driving around by other people in his home town, and m is the amount of money he has left to spend on other stuff besides gasoline and auto repairs.Gas and auto repairs cost $1 per hour of driving.If each citizen believes that their own driving will not affect the amount of driving done by others, they will all drive D₁ hours per day.If all citizens drive to maximize the utility of a typical citizen, they will all drive D₂ hours per day, where

A)D₁ = 6 and D₂ = 1.
B)D₁ = 5 and D₂ = 3.
C)D₁ = D₂ = 3.
D)D₁ = 3 and D₂ = 2.
E)D₁ = 3 and D₂ = 0.

Accepted Answer

To determine the optimal driving time for each citizen, we need to maximize the utility function U(m, d, h) with respect to d.

Taking the partial derivative of U with respect to d, we get:

∂U/∂d = 7S1/(P1 + 2P0) - P1S1/(P1 + P0)

Setting this equal to zero and solving for d, we get:

d* = (7S1P1 - P1P0S1)/(P1(P1 + 2P0))

Plugging in the values for S1, P1, and P0, we get:

d* = 3

Therefore, each citizen will drive 3 hours per day to maximize the utility of a typical citizen. This corresponds to choice D.

Question 6

suppose that the cost function of the honey farm is C_H(H, A)= H ²/100 - 2A and the cost function of the apple orchard is C_A(H, A)= A²/100, where H and A are the number of units of honey and apples produced respectively.The price of honey is $5 and the price of apples is $4 per unit.Let A₁ be the output of apples if the firms operate independently, and let A₂ be the output of apples if the firms are operated by a profit-maximizing single owner.

A)A₁ = 200 and A₂ = 300.
B)A₁ = A₂ = 200.
C)A₁ = 100 and A₂ = 200.
D)A₁ = 150 and A₂ = 200.
E)A₁ = 250 and A₂ = 200.

A₁ = 200 and A₂ = 300.

Accepted Answer

To find the output of apples for each scenario, we need to maximize the profit function of the honey farm and the apple orchard. For the honey farm: πH = revenue - cost πH = 7H - C_H(H, A)F1F1F1S1 Taking the derivative of πH with respect to H and setting it equal to 0 gives: 7 - ∂C_H(H, A)F1F1F1S1/∂H = 0 ∂C_H(H, A)F1F1F1S1/∂H = 7/3 Similarly, for the apple orchard: πA = 5A - C_A(H, A)F1F1F1S1 Taking the derivative of πA with respect to A and setting it equal to 0 gives: 5 - ∂C_A(H, A)F1F1F1S1/∂A = 0 ∂C_A(H, A)F1F1F1S1/∂A = 5/2 If the firms operate independently, then we have: ∂C_H(H, A₁)F1F1F1S1/∂H = 7/3 ∂C_A(A₁, H)F1F1F1S1/∂A = 5/2 Solving the above two equations simultaneously will give us A₁ = 250. If the firms are operated by a profit-maximizing single owner, then we have: Total profit = πH + πA Total profit = 7H + 5A - (C_H(H, A)F1F1F1S1 + C_A(H, A)F1F1F1S1) We need to maximize this function with respect to both H and A. By taking partial derivative with respect to H and A, we get: 7 - ∂C_H(H, A)F1F1F1S1/∂H = 0 5 - ∂C_A(H, A)F1F1F1S1/∂A = 0 Solving the above two equations simultaneously will give us A₂ = 400. Therefore, the answer is D) A₁ = 250 and A₂ = 400.

Question 7

suppose that the cost function of the honey farm is C_H(H, A)= H ²/100 - 2A and the cost function of the apple orchard is C_A(H, A)= A²/100, where H and A are the number of units of honey and apples produced respectively.The price of honey is $5 and the price of apples is $4 per unit.Let A₁ be the output of apples if the firms operate independently, and let A₂ be the output of apples if the firms are operated by a profit-maximizing single owner.

A)A₁ = 200 and A₂ = 300.
B)A₁ = A₂ = 200.
C)A₁ = 100 and A₂ = 200.
D)A₁ = 150 and A₂ = 200.
E)A₁ = 250 and A₂ = 200.

A₁ = 200 and A₂ = 300.

Accepted Answer

The answer of  suppose that the cost function of...

Question 8

suppose Albert, a typical citizen, has the utility function U(m, d, h)= m + 5d² - d² - 2h, where d is the number of hours per day that he spends driving around, h is the average number of hours per day spent driving around by other people in his home town, and m is the amount of money he has left to spend on other stuff besides gasoline and auto repairs.Gas and auto repairs cost $1 per hour of driving.If each citizen believes that their own driving will not affect the amount of driving done by others, they will all drive D₁ hours per day.If all citizens drive to maximize the utility of a typical citizen, they will all drive D₂ hours per day, where

A)D₁ = 5 and D₂ = 0.
B)D₁ = D₂ = 2.
C)D₁ = 2 and D₂ = 1.
D)D₁ = 4 and D₂ = 2.
E)D₁ = 2 and D₂ = 0.

Accepted Answer

The answer of suppose Albert, a typical citizen, has the...

Question 9

suppose Wilfred, a typical citizen, has the utility function U(m, d, h)= m + 13d² - d² - 4h, where d is the number of hours per day that he spends driving around, h is the average number of hours per day spent driving around by other people in his home town, and m is the amount of money he has left to spend on other stuff besides gasoline and auto repairs.Gas and auto repairs cost $1 per hour of driving.If each citizen believes that their own driving will not affect the amount of driving done by others, they will all drive D₁ hours per day.If all citizens drive to maximize the utility of a typical citizen, they will all drive D₂ hours per day, where

A)D₁ = 6 and D₂ = 4.
B)D₁ = D₂ = 6.
C)D₁ = 8 and D₂ = 5.
D)D₁ = 9 and D₂ = 0.
E)D₁ = 6 and D₂ = 2.

Accepted Answer

The correct answer is based on the assumption that individuals aim to maximize their utility given the utility function U(m, d, h). The utility function suggests a trade-off between driving (d), the average driving by others (h), and money left for other expenses (m). The choices given imply different scenarios of individual versus collective optimization. Choice A suggests a scenario where individuals drive more when not considering the collective impact (6 hours) but drive less when optimizing for the collective utility (4 hours), which aligns with the principle of externalities affecting optimal individual behavior.

Question 10

An airport is located next to a housing development.Where X is the number of planes that land per day and Y is the number of houses in the housing development, profits of the airport are 22X - X ² and profits of the developer are 26Y - Y ² - XY.Let H₁ be the number of houses built if a single profit-maximizing company owns the airport and the housing development.Let H₂ be the number of houses built if the airport and the housing development are operated independently and the airport has to pay the developer the total "damages" XY done by the planes to the developer's profits.

A)H₁ = H₂ = 10.
B)H₁ = 10 and H₂ = 13.
C)H₁ = 13 and H₂ = 10.
D)H₁ = 12 and H₂ = 12.
E)H₁ = 12 and H₂ = 16.

Accepted Answer

The profit-maximizing number of planes is X = 11. If the airport and housing development are owned by the same company, the number of houses is H₁ = 10. If they are operated independently, the airport has to pay the developer the total "damages" XY = 11 * H₂, so the developer's profit is 26H₂ - H₂² - 11H₂ = 15H₂ - H₂². The profit-maximizing number of houses is H₂ = 13.

Question 11

An airport is located next to a housing development.Where X is the number of planes that land per day and Y is the number of houses in the housing development, profits of the airport are 22X - X ² and profits of the developer are 26Y - Y ² - XY.Let H₁ be the number of houses built if a single profit-maximizing company owns the airport and the housing development.Let H₂ be the number of houses built if the airport and the housing development are operated independently and the airport has to pay the developer the total "damages" XY done by the planes to the developer's profits.

A)H₁ = H₂ = 10.
B)H₁ = 10 and H₂ = 13.
C)H₁ = 13 and H₂ = 10.
D)H₁ = 12 and H₂ = 12.
E)H₁ = 12 and H₂ = 16.

Accepted Answer

The answer of An airport is located next to a...

Question 12

Suppose that in Horsehead, Massachusetts, the cost of operating a lobster boat is $5,000 per month.Suppose that if x lobster boats operate in the bay, the total monthly revenue from lobster boats in the bay is $1,000(21x - x²).If there are no restrictions on entry and new boats come into the bay until there is no profit to be made by a new entrant, then the number of boats who enter will be X₁.If the number of boats that operate in the bay is regulated to maximize total profits, the number of boats in the bay will be X₂.

A)X₁ = 16 and X₂ = 16.
B)X₁ = 20 and X₂ = 12.
C)X₁ = 16 and X₂ = 8.
D)X₁= 8 and X₂ = 6.
E)None of the above.

X₁ = 16 and X₂ = 8.

Accepted Answer

The answer of Suppose that in Horsehead, Massachusetts, the cost...

Question 13

suppose Sam, a typical citizen, has the utility function U(m, d, h)= m + 13d² - d² - 6h, where d is the number of hours per day that he spends driving around, h is the average number of hours per day spent driving around by other people in his home town, and m is the amount of money he has left to spend on other stuff besides gasoline and auto repairs.Gas and auto repairs cost $1 per hour of driving.If each citizen believes that their own driving will not affect the amount of driving done by others, they will all drive D₁ hours per day.If all citizens drive to maximize the utility of a typical citizen, they will all drive D₂ hours per day, where

A)D₁ = 8 and D₂ = 4.
B)D₁ = 6 and D₂ = 3.
C)D₁ = D₂ = 6.
D)D₁ = 9 and D₂ = 0.
E)D₁ = 6 and D₂ = 1.

Accepted Answer

The answer of suppose Sam, a typical citizen, has the...

Question 14

suppose Lawrence, a typical citizen, has the utility function U(m, d, h)= m + 7d² - d² - 4h, where d is the number of hours per day that he spends driving around, h is the average number of hours per day spent driving around by other people in his home town, and m is the amount of money he has left to spend on other stuff besides gasoline and auto repairs.Gas and auto repairs cost $1 per hour of driving.If each citizen believes that their own driving will not affect the amount of driving done by others, they will all drive D₁ hours per day.If all citizens drive to maximize the utility of a typical citizen, they will all drive D₂ hours per day, where

A)D₁ = 5 and D₂ = 2.
B)D₁ = D₂ = 3.
C)D₁ = 3 and D₂ = 1.
D)D₁ = 6 and D₂ = 0.
E)D₁ = 3 and D₂ = 0.

Accepted Answer

The answer of suppose Lawrence, a typical citizen, has the...

Question 15

suppose that the cost function of the honey farm is C_H(H, A)= H ²/100 - 2A and the cost function of the apple orchard is C_A(H, A)= A²/100, where H and A are the number of units of honey and apples produced respectively.The price of honey is $5 and the price of apples is $4 per unit.Let A₁ be the output of apples if the firms operate independently, and let A₂ be the output of apples if the firms are operated by a profit-maximizing single owner.

A)A₁ = 200 and A₂ = 300.
B)A₁ = A₂ = 200.
C)A₁ = 100 and A₂ = 200.
D)A₁ = 150 and A₂ = 200.
E)A₁ = 250 and A₂ = 200.

A₁ = 200 and A₂ = 300.

Accepted Answer

The answer of suppose that the cost function of the...

Question 16

An airport is located next to a housing development.Where X is the number of planes that land per day and Y is the number of houses in the housing development, profits of the airport are 22X - X² and profits of the developer are 32Y - Y ² - XY.Let H₁ be the number of houses built if a single profit-maximizing company owns the airport and the housing development.Let H₂ be the number of houses built if the airport and the housing development are operated independently and the airport has to pay the developer the total "damages" XY done by the planes to the developer's profits.

A)H₁ = 16 and H₂ = 15.
B)H₁ = 14 and H₂ = 16.
C)H₁ = 16 and H₂ = 14.
D)H₁ =H₂ = 14.
E)H₁ = 15 and H₂ = 19.

Accepted Answer

The answer of An airport is located next to a...

Question 17

Suppose that in Horsehead, Massachusetts, the cost of operating a lobster boat is $5,000 per month.Suppose that if x lobster boats operate in the bay, the total monthly revenue from lobster boats in the bay is $1,000(21x - x²).If there are no restrictions on entry and new boats come into the bay until there is no profit to be made by a new entrant, then the number of boats who enter will be X₁.If the number of boats that operate in the bay is regulated to maximize total profits, the number of boats in the bay will be X₂.

A)X₁ = 16 and X₂ = 16.
B)X₁ = 20 and X₂ = 12.
C)X₁ = 16 and X₂ = 8.
D)X₁= 8 and X₂ = 6.
E)None of the above.

X₁ = 16 and X₂ = 8.

Accepted Answer

The answer of Suppose that in Horsehead, Massachusetts, the cost...

Question 18

suppose that the cost function of the honey farm is C_H(H, A)= H ²/100 - 2A and the cost function of the apple orchard is C_A(H, A)= A²/100, where H and A are the number of units of honey and apples produced respectively.The price of honey is $5 and the price of apples is $4 per unit.Let A₁ be the output of apples if the firms operate independently, and let A₂ be the output of apples if the firms are operated by a profit-maximizing single owner.

A)A₁ = 200 and A₂ = 300.
B)A₁ = A₂ = 200.
C)A₁ = 100 and A₂ = 200.
D)A₁ = 150 and A₂ = 200.
E)A₁ = 250 and A₂ = 200.

A₁ = 200 and A₂ = 300.

Accepted Answer

The answer of suppose that the cost function of the...

Question 19

An airport is located next to a housing development.Where X is the number of planes that land per day and Y is the number of houses in the housing development, profits of the airport are 38X - X ² and profits of the developer are 28Y - Y ² - XY.Let H₁ be the number of houses built if a single profit-maximizing company owns the airport and the housing development.Let H₂ be the number of houses built if the airport and the housing development are operated independently and the airport has to pay the developer the total "damages" XY done by the planes to the developer's profits.

A)H₁ = H₂ = 6.
B)H₁ = 14 and H₂ = 6.
C)H₁ = 6 and H₂ = 14.
D)H₁ = 8 and H₂ = 13.
E)H₁ = 13 and H₂ = 17.

Accepted Answer

The answer of An airport is located next to a...

Question 20

Suppose that in Horsehead, Massachusetts, the cost of operating a lobster boat is $5,000 per month.Suppose that if x lobster boats operate in the bay, the total monthly revenue from lobster boats in the bay is $1,000(21x - x²).If there are no restrictions on entry and new boats come into the bay until there is no profit to be made by a new entrant, then the number of boats who enter will be X₁.If the number of boats that operate in the bay is regulated to maximize total profits, the number of boats in the bay will be X₂.

A)X₁ = 16 and X₂ = 16.
B)X₁ = 20 and X₂ = 12.
C)X₁ = 16 and X₂ = 8.
D)X₁= 8 and X₂ = 6.
E)None of the above.

X₁ = 16 and X₂ = 8.

Accepted Answer

The answer of Suppose that in Horsehead, Massachusetts, the cost...

Question 21

A clothing store and a jeweler are located side by side in a shopping mall.If the clothing store spends C dollars on advertising and the jeweler spends J dollars on advertising, then the profits of the clothing store will be (18+ J)C - C² and the profits of the jeweler will be (36 + C)J - 2J ².The clothing store gets to choose its amount of advertising first, knowing that the jeweler will find out how much the clothing store advertised before deciding how much to spend.The amount spent by the clothing store will be

A)54.
B)9.
C)36.
D)18.
E)27.

Accepted Answer

The answer of A clothing store and a jeweler are...

Question 22

A clothing store and a jeweler are located side by side in a shopping mall.If the clothing store spends C dollars on advertising and the jeweler spends J dollars on advertising, then the profits of the clothing store will be (42 + J)C - C² and the profits of the jeweler will be (54 + C)J - 2J².The clothing store gets to choose its amount of advertising first, knowing that the jeweler will find out how much the clothing store advertised before deciding how much to spend.The amount spent by the clothing store will be

A)74.
B)111.
C)18.50.
D)37.
E)55.50.

Accepted Answer

The answer of A clothing store and a jeweler are...

Question 23

A clothing store and a jeweler are located side by side in a shopping mall.If the clothing store spends C dollars on advertising and the jeweler spends J dollars on advertising, then the profits of the clothing store will be (6 + J)C - C² and the profits of the jeweler will be (6 + C)J - 2J ².The clothing store gets to choose its amount of advertising first, knowing that the jeweler will find out how much the clothing store advertised before deciding how much to spend.The amount spent by the clothing store will be

A)5.
B)10.
C)15.
D)2.50.
E)7.50.

Accepted Answer

The answer of A clothing store and a jeweler are...

Question 24

A clothing store and a jeweler are located side by side in a shopping mall.If the clothing store spends C dollars on advertising and the jeweler spends J dollars on advertising, then the profits of the clothing store will be (18 + J)C - C² and the profits of the jeweler will be (24 + C)J - 2J ².The clothing store gets to choose its amount of advertising first, knowing that the jeweler will find out how much the clothing store advertised before deciding how much to spend.The amount spent by the clothing store will be

A)48.
B)16.
C)8.
D)32.
E)24.

Accepted Answer

The answer of A clothing store and a jeweler are...

Question 25

A clothing store and a jeweler are located side by side in a shopping mall.If the clothing store spends C dollars on advertising and the jeweler spends J dollars on advertising, then the profits of the clothing store will be (42 + J)C - C² and the profits of the jeweler will be (54 + C)J - 2J².The clothing store gets to choose its amount of advertising first, knowing that the jeweler will find out how much the clothing store advertised before deciding how much to spend.The amount spent by the clothing store will be

A)74.
B)111.
C)18.50.
D)37.
E)55.50.

Accepted Answer

The answer of A clothing store and a jeweler are...

Deck 35: Extension: A: Externalities