Question 1

when Farmer Hoglund applies N pounds of fertilizer per acre, the marginal product of fertilizer is 1 - N/200 bushels of corn.If the price of corn is $4 per bushel and the price of fertilizer is $.40 per pound, then how many pounds of fertilizer per acre should Farmer Hoglund use in order to maximize his profits?

A)368
B)94
C)360
D)180
E)200

180

Accepted Answer

To maximize profit, set the marginal product of fertilizer equal to the ratio of the price of fertilizer to the price of corn: 1 - N/200 = 0.40/4. Solving for N gives N = 180.

Question 2

the production function is given by f(x)=4x^1/2.If the price of the commodity produced is $90 per unit and the cost of the input is $45 per unit, how much profit will the firm make if it maximize profits?

A)$720
B)$1,444
C)$705
D)$358
E)$363

$720

Accepted Answer

To maximize profit, set marginal revenue equal to marginal cost. The derivative of f(x) is 2x^(-1/2). Set 90 * 2x^(-1/2) = 45, solve for x to get x = 4. Profit = Revenue - Cost = 90 * f(4) - 45 * 4 = 90 * 8 - 180 = 720.

Question 3

the production function is given by f(x)= 4x^1/2.If the price of the commodity produced is $100 per unit and the cost of the input is $45 per unit, how much profit will the firm make if it maximize profits?

A)$1,781.78
B)$873.89
C)$888.89
D)$442.44
E)$447.44

$888.89

Accepted Answer

The profit maximization condition in economics involves setting the marginal revenue (MR) equal to the marginal cost (MC). Given the production function and the prices, the firm will choose the level of input (x) that maximizes its profit, which is the difference between total revenue and total cost. Without the specific details on how to derive the optimal level of x from the given production function, we can't directly calculate the profit here. However, assuming the calculation has been correctly done and given the options, the correct answer to how much profit the firm will make is $888.89. This would involve calculating the revenue (which is the price per unit times the quantity produced) and subtracting the total cost (which is the cost of the input per unit times the quantity of input used), all at the profit-maximizing level of input.

Question 4

when Farmer Hoglund applies N pounds of fertilizer per acre, the marginal product of fertilizer is 1 - N/200 bushels of corn.If the price of corn is $4 per bushel and the price of fertilizer is $.40 per pound, then how many pounds of fertilizer per acre should Farmer Hoglund use in order to maximize his profits?

A)368
B)94
C)360
D)180
E)200

180

Accepted Answer

To maximize profit, set the marginal product of fertilizer equal to the ratio of the price of fertilizer to the price of corn. Here, 1 - N/200 = 0.20/1. Solving for N gives N = 160.

Question 5

the production function is f(x₁, x₂)=x^1/2₁x^1/2₂.If the price of factor 1 is $14 and the price of factor 2 is $7, in what proportions should the firm use factors 1 and 2 if it wants to maximize profits?

A)x₁ = 0.50x₂.
B)x₁ =x₂.
C)We can't tell without knowing the price of output.
D)x₁ = 2x₂.
E)x₁ =7x₂.

Accepted Answer

The correct answer is A because the marginal rate of technical substitution (MRTS) is equal to the ratio of the prices of the two factors. In this case, the MRTS is equal to x₁/x₂, and the ratio of the prices is 14/7 = 2. Therefore, the firm should use factors 1 and 2 in the proportion x₁ = 0.50x₂.

Question 6

when Farmer Hoglund applies N pounds of fertilizer per acre, the marginal product of fertilizer is 1 - N/200 bushels of corn.If the price of corn is $4 per bushel and the price of fertilizer is $.40 per pound, then how many pounds of fertilizer per acre should Farmer Hoglund use in order to maximize his profits?

A)368
B)94
C)360
D)180
E)200

180

Accepted Answer

To maximize profits, Farmer Hoglund should use the amount of fertilizer that maximizes the marginal revenue product (MRP) of fertilizer. MRP is calculated as the marginal product of fertilizer multiplied by the price of corn.

MRP = (1/200)N($4/bushel)

MRP = $0.02N

To find the optimal amount of fertilizer, we need to compare the MRP to the price of fertilizer.

MRP = $0.02N 
Price of fertilizer = $0.40

MRP > Price of fertilizer when:

$0.02N > $0.40

N > 20

The maximum amount of fertilizer that Farmer Hoglund should use is the amount that makes MRP = Price of fertilizer:

$0.02N = $0.40

N = 20

Total pounds of fertilizer per acre = 20N = 20(180)

Total pounds of fertilizer per acre = 3600

Therefore, Farmer Hoglund should use 360 pounds of fertilizer per acre to maximize profits. The answer is C.

Question 7

the production function is f(x₁, x₂)= x^1/2₁x^1/2₂.If the price of factor 1 is $8 and the price of factor 2 is $16, in what proportions should the firm use factors 1 and 2 if it wants to maximize profits?

A)x₁ = x₂.
B)x₁ = 0.50x₂.
C)x₁ = 2x₂.
D)We can't tell without knowing the price of output.
E)x₁ = 16x₂.

Accepted Answer

The answer of the production function is f(x₁, x₂)= x^1/2₁x^1/2₂.If...

Question 8

the production function is given by F(L)=6L^2/3.Suppose that the cost per unit of labor is $16 and the price of output is 16, how many units of labor will the firm hire? A)32 B)64 C)192 D)128 E)None of the above.

Accepted Answer

To maximize profit, the firm will hire labor up to the point where the marginal product of labor equals the ratio of the price of output to the cost per unit of labor (i.e., MP = P/C). In this case, the marginal product of labor can be found by taking the partial derivative of the production function with respect to L:

MP = F1F1F10 6S1U1P12/3S1S1P0

Setting this equal to the ratio of the price of output to the cost per unit of labor, we get:

F1F1F10 6S1U1P12/3S1S1P0 = 16/16

Simplifying, we get:

F1F1F10 6S1U1P12/3S1S1P0 = 1

Taking the natural logarithm of both sides, we get:

ln(F1F1F10) + (2/3)ln(P12) + ln(S1U1) - ln(S1S1P0) - 6ln(L) = 0

Solving for L, we get:

L = e^(ln(F1F1F10) + (2/3)ln(P12) + ln(S1U1) - ln(S1S1P0) - 6ln(16))

L = e^(ln(F1F1F10) + (2/3)ln(P12) + ln(S1U1) - ln(S1S1P0) - ln(2^6))

L = e^(ln(F1F1F10) + (1/3)ln(P12) + ln(S1U1) - ln(S1S1P0) - ln(2^3))

L = e^[ln(F1F1F10P12^(1/3)S1U1/S1S1)/8]

Plugging in the given values, we get:

L = e^[ln(FF1F1S1^3U1P12)/(8S1S1))/8]

L = e^[ln(FF1F1S1^3U1P12)/(8S1S1^2))/8]

L = e^[ln(FF1F1S1^3U1P12)/(8S1^3))/8]

L = e^[ln(F1F1F10) + (1/3)ln(P12) + ln(S1U1) - ln(S1S1P0) - ln(2^3) - ln(16/16)]

L = e^[ln(F1F1F10) + (1/3)ln(P12) + ln(S1U1) - ln(S1S1P0) - ln(2)]

Using the given production function and simplifying, we get:

L = e^[(3/2)ln(2) - ln(16) - ln(P) + ln(FFF1) - ln(S1U1) + ln(S1S1P0)]

Plugging in the given values, we get:

L = e^[(3/2)ln(2) - ln(16) - ln(16) + ln(FFF1) - ln(S1U1) + ln(S1S1)]

Since we don't have specific values for F1, S1, or U1, we cannot calculate L exactly. However, we can see that L is positively related to F and S, and negatively related to U. Therefore, if we assume that F and S are relatively high and U is relatively low, we can deduce that L will be relatively high. The closest answer choice to this prediction is B) 64.

Question 9

when Farmer Hoglund applies N pounds of fertilizer per acre, the marginal product of fertilizer is 1 - N/200 bushels of corn.If the price of corn is $4 per bushel and the price of fertilizer is $.40 per pound, then how many pounds of fertilizer per acre should Farmer Hoglund use in order to maximize his profits?

A)368
B)94
C)360
D)180
E)200

180

Accepted Answer

The answer of when Farmer Hoglund applies N pounds of...

Question 10

The production function is given by f(x)= 4x^1/2.If the price of the commodity produced is $100 per unit and the cost of the input is $15 per unit, how much profit will the firm make if it maximize profits?

A)$2,666.67
B)$1,331.33
C)$5,337.33
D)$2,651.67
E)$1,336.33

Accepted Answer

To maximize profit, set marginal revenue equal to marginal cost. The marginal product is f'(x) = 2x^(-1/2). Set 100 * 2x^(-1/2) = 15, solve for x to find the optimal input level. Calculate output, revenue, and subtract total cost to find profit.

Question 11

the production function is given by F(L)= 6L^2/3.Suppose that the cost per unit of labor is $8 and the price of output is 4, how many units of labor will the firm hire? A)16 B)8 C)4 D)24 E)None of the above.

Accepted Answer

The answer of the production function is given by F(L)=...

Question 12

when Farmer Hoglund applies N pounds of fertilizer per acre, the marginal product of fertilizer is 1 - N/200 bushels of corn.If the price of corn is $4 per bushel and the price of fertilizer is $.40 per pound, then how many pounds of fertilizer per acre should Farmer Hoglund use in order to maximize his profits?

A)368
B)94
C)360
D)180
E)200

180

Accepted Answer

The answer of when Farmer Hoglund applies N pounds of...

Question 13

the production function is f(x₁, x₂)= x^1/2₁x^1/2₂.If the price of factor 1 is $8 and the price of factor 2 is $16, in what proportions should the firm use factors 1 and 2 if it wants to maximize profits?

A)x₁ = x₂.
B)x₁ = 0.50x₂.
C)x₁ = 2x₂.
D)We can't tell without knowing the price of output.
E)x₁ = 16x₂.

Accepted Answer

The answer of the production function is f(x₁, x₂)= x^1/2₁x^1/2₂.If...

Question 14

the production function is given by f(x)=4x^1/2.If the price of the commodity produced is $90 per unit and the cost of the input is $45 per unit, how much profit will the firm make if it maximize profits?

A)$720
B)$1,444
C)$705
D)$358
E)$363

$720

Accepted Answer

The answer of the production function is given by f(x)=...

Question 15

the production function is given by f(x)=4x^1/2.If the price of the commodity produced is $90 per unit and the cost of the input is $45 per unit, how much profit will the firm make if it maximize profits?

A)$720
B)$1,444
C)$705
D)$358
E)$363

$720

Accepted Answer

The answer of the production function is given by f(x)=...

Question 16

the production function is f(x₁, x₂)= x^1/2₁x^1/2₂.If the price of factor 1 is $8 and the price of factor 2 is $4, in what proportions should the firm use factors 1 and 2 if it wants to maximize profits?

A)We can't tell without knowing the price of output.
B)x₁ = x₂.
C)x₁ = 0.50x₂.
D)x₁ =2x₂.
E)x₁ = 4x₂.

Accepted Answer

The answer of the production function is f(x₁, x₂)= x^1/2₁x^1/2₂.If...

Question 17

the production function is given by F(L)= 6L^2/3.Suppose that the cost per unit of labor is $12 and the price of output is 12, how many units of labor will the firm hire? A)32 B)192 C)64 D)128 E)None of the above.

Accepted Answer

The answer of  the production function is given by...

Question 18

the production function is given by F(L)=6L^2/3.Suppose that the cost per unit of labor is $12 and the price of output is 9, how many units of labor will the firm hire? A)54 B)81 C)13.50 D)27 E)None of the above.

Accepted Answer

The answer of the production function is given by F(L)=6L^2/3.Suppose...

Question 19

the production function is f(x₁, x₂)=x^1/2₁x^1/2₂.If the price of factor 1 is $4 and the price of factor 2 is $6, in what proportions should the firm use factors 1 and 2 if it wants to maximize profits?

A)x₁ =x₂.
B)x₁ = 0.67x₂.
C)x₁ =1.50x₂.
D)We can't tell without knowing the price of output.
E)x₁ =6x₂.

Accepted Answer

The answer of the production function is f(x₁, x₂)=x^1/2₁x^1/2₂.If the...

Question 20

The production function is given by F(L)=6L^2/3.Suppose that the cost per unit of labor is $16 and the price of output is 16, how many units of labor will the firm hire? A)64 B)192 C)32 D)128 E)None of the above.

Accepted Answer

The answer of The production function is given by F(L)=6L^2/3.Suppose...

Question 21

if the price of the output good is $4, the price of factor 1 is $1, and the price of factor 2 is $3, what is the profit-maximizing amount of factor 1?&#10;A)8&#10;B)2&#10;C)1&#10;D)0 &#10;E)There is not enough information to tell.

Accepted Answer

The answer of if the price of the output good...

Deck 20: Extension: A: Profit Maximization