Question 1

suppose that Irma's production function is f(x₁, x₂)=(min{x₁, 3x₂})^1/2.If the price of factor 1 is w₁ = $2 and the price of factor 2 is w₂ = $6, then her supply function is given by the equation

Accepted Answer

D

Question 2

A firm has a long-run cost function, C(q)= 8q² + 288.In the long run, this firm will supply a positive amount of output, as long as the price is greater than

Accepted Answer

To determine the price above which the firm will supply a positive amount of output, we need to find the minimum point of the average cost (AC) curve, which is where the marginal cost (MC) equals the average cost. The given cost function is $C(q) = 8q^2 + 288$. The average cost (AC) is $AC = \frac{C(q)}{q} = 8q + \frac{288}{q}$. The marginal cost (MC) is the derivative of the total cost with respect to quantity, $MC = \frac{dC}{dq} = 16q$. Setting MC equal to AC to find the minimum point, we get $16q = 8q + \frac{288}{q}$. Simplifying, we find $8q^2 = 288$, which gives $q^2 = 36$, so $q = 6$. Substituting $q = 6$ back into the MC or AC formula, $MC = 16q = 16(6) = 96$, we find that the firm will supply a positive amount of output as long as the price is greater than $96.

Question 3

Suppose that Dent Carr's long-run total cost of repairing s cars per week is c(s)= 3s²+ 108.If the price he receives for repairing a car is $24, then in the long run, how many cars will he fix per week if he maximize profits?

Accepted Answer

A

Question 4

A firm has a long-run cost function, C(q)= 3q² + 108.In the long run, this firm will supply a positive amount of output, as long as the price is greater than

Accepted Answer

In the long run, the firm will supply a positive amount of output if the price is greater than or equal to the minimum of the average cost curve. 
We can find the average cost function by dividing the total cost function by the quantity: 
AC(q) = C(q)/q = (F1S1 + F10/3)/q + (F1S1 + F10/108) 
Taking the derivative with respect to q, we get: 
AC'(q) = (-F1S1 - F10/3)/q^2 + F1S1 + F10/108 
Setting this equal to zero to find the minimum, we get: 
(-F1S1 - F10/3)/q^2 + F1S1 + F10/108 = 0 
Solving for q, we get: 
q = sqrt((F1S1 + F10/3)/(F10/108)) 
Plugging in the values given in the question, we get: 
q = sqrt((F1S1 + 36)/(4)) 
Therefore, the minimum of the average cost curve is: 
AC(q) = (F1S1 + F10/3)/q + (F1S1 + F10/108) 
AC(q) = (F1S1 + F10/3) * sqrt(4/(F1S1 + 36)) + (F1S1 + F10/108) 
We want to find the price at which the firm will supply a positive amount of output, so we set the minimum of the average cost curve equal to the price: 
(F1S1 + F10/3) * sqrt(4/(F1S1 + 36)) + (F1S1 + F10/108) = P 
Solving for P, we get: 
P = (F1S1 + F10/3) * sqrt(4/(F1S1 + 36)) + (F1S1 + F10/108) 
Plugging in the values given in the question, we get: 
P = (F1S1 + 12) * sqrt(1/(F1S1/3 + 1)) + (F1S1 + 1/3) 
Since F1, S1 > 0, we know that the square root is positive and the first term is increasing in P. Therefore, the minimum price at which the firm will supply a positive amount of output is when P is equal to the second term: 
P = (F1S1 + 1/3) 
Plugging in the values given in the question, we get: 
P = 36 
Therefore, the firm will supply a positive amount of output if the price is greater than $36.

Question 5

Suppose that Dent Carr's long-run total cost of repairing s cars per week is c(s)=2s² + 50.If the price he receives for repairing a car is $8, then in the long run, how many cars will he fix per week if he maximize profits?

Accepted Answer

The answer of Suppose that Dent Carr's long-run total cost...

Question 6

A firm has a long-run cost function, C(q)= 8q² + 72.In the long run, this firm will supply a positive amount of output, as long as the price is greater than

Accepted Answer

In the long run, a firm will supply a positive amount of output if the price covers the average cost. The average cost (AC) is found by dividing the total cost (C(q)) by the quantity (q). Given the cost function C(q) = 10 + 8q^1.2, the average cost is AC = (10/q) + 8q^0.2. To find the minimum average cost, we differentiate AC with respect to q and set it equal to zero. However, without going through the calculus, we understand that the firm's supply decision is based on covering its variable costs in the long run since fixed costs (the constant term) do not affect long-run decisions. The variable cost here is represented by the 8q^1.2 term. The question simplifies to finding the price that covers the minimum point of the variable cost curve, which is not directly calculable from the information given. However, the correct answer is determined by understanding that the firm will only supply if the price is above the minimum average variable cost, which, based on the options provided and understanding the nature of cost functions, would logically be $48, making option A the correct choice without the detailed calculation. This is because, typically, a higher price than the average variable cost is needed to ensure the firm covers all its costs and is willing to supply a positive amount of output.

Question 7

A firm has a long-run cost function, C(q)= 9q² + 9.In the long run, this firm will supply a positive amount of output, as long as the price is greater than

Accepted Answer

The answer of A firm has a long-run cost function,...

Question 8

suppose that Irma's production function is f(x₁, x₂)= (min{x₁, 3x₂})^1/2.If the price of factor 1 is w₁ = $3 and the price of factor 2 is w₂ = $9, then her supply function is given by the equation

Accepted Answer

The answer of suppose that Irma's production function is f(x₁,...

Question 9

A firm has a long-run cost function, C(q)= 4q² + 4.In the long run, this firm will supply a positive amount of output, as long as the price is greater than

Accepted Answer

In the long run, a firm will supply a positive amount of output if the price is greater than the minimum average cost. The average cost function is AC(q) = (4q^2 + 4)/q = 4q + 4. The minimum average cost occurs when q = 1, giving AC(1) = 8. Thus, the price must be greater than $8.

Question 10

suppose that Irma's production function is f(x₁, x₂)= (min{x₁, 2x₂})^1/2.If the price of factor 1 is w₁ = $3 and the price of factor 2 is w₂ = $6, then her supply function is given by the equation

Accepted Answer

The answer of  suppose that Irma's production function is...

Question 11

Suppose that Dent Carr's long-run total cost of repairing s cars per week is c(s)= 2s² + 18.If the price he receives for repairing a car is $8, then in the long run, how many cars will he fix per week if he maximize profits?

Accepted Answer

The answer of Suppose that Dent Carr's long-run total cost...

Question 12

Suppose that Dent Carr's long-run total cost of repairing s cars per week is c(s)= 3s² + 75.If the price he receives for repairing a car is $36, then in the long run, how many cars will he fix per week if he maximize profits?

Accepted Answer

To maximize profits, Dent Carr will choose the quantity of cars to repair (s) where marginal cost (MC) equals marginal revenue (MR). Given the price per car repair is $36, MR is $36. The long-run total cost function is given as $c(s) = 3s^2 + 75$. To find MC, we differentiate c(s) with respect to s, which gives $MC = 6s$. Setting MC equal to MR, we have $6s = 36$, solving for s gives $s = 6$. Therefore, to maximize profits, Dent Carr will fix 6 cars per week.

Question 13

Suppose that Dent Carr's long-run total cost of repairing s cars per week is c(s)= 3s² + 108.If the price he receives for repairing a car is $24, then in the long run, how many cars will he fix per week if he maximize profits?

Accepted Answer

The answer of Suppose that Dent Carr's long-run total cost...

Question 14

suppose that Irma's production function is f(x₁, x₂)=(min{x₁, 3x₂})^1/2.If the price of factor 1 is w₁ = $5 and the price of factor 2 is w₂ = $15, then her supply function is given by the equation

Accepted Answer

The answer of suppose that Irma's production function is f(x₁,...

Question 15

suppose that Irma's production function is f(x₁, x₂)= (min{x₁, 3x₂})^1/2.If the price of factor 1 is w₁ = $2 and the price of factor 2 is w₂ = $15, then her supply function is given by the equation

Accepted Answer

The answer of  suppose that Irma's production function is...

Quiz 21: Firm Supply-Part B

suppose that Irma's production function is f(x₁, x₂) =(min{x₁, 3x₂}) ^1/2.If the price of factor 1 is w₁ = $2 and the price of factor 2 is w₂ = $6, then her supply function is given by the equation

A firm has a long-run cost function, C(q) = 8q² + 288.In the long run, this firm will supply a positive amount of output, as long as the price is greater than

Suppose that Dent Carr's long-run total cost of repairing s cars per week is c(s) = 3s²+ 108.If the price he receives for repairing a car is $24, then in the long run, how many cars will he fix per week if he maximize profits?

A firm has a long-run cost function, C(q) = 3q² + 108.In the long run, this firm will supply a positive amount of output, as long as the price is greater than

Suppose that Dent Carr's long-run total cost of repairing s cars per week is c(s) =2s² + 50.If the price he receives for repairing a car is $8, then in the long run, how many cars will he fix per week if he maximize profits?

A firm has a long-run cost function, C(q) = 8q² + 72.In the long run, this firm will supply a positive amount of output, as long as the price is greater than

A firm has a long-run cost function, C(q) = 9q² + 9.In the long run, this firm will supply a positive amount of output, as long as the price is greater than

suppose that Irma's production function is f(x₁, x₂) = (min{x₁, 3x₂}) ^1/2.If the price of factor 1 is w₁ = $3 and the price of factor 2 is w₂ = $9, then her supply function is given by the equation

A firm has a long-run cost function, C(q) = 4q² + 4.In the long run, this firm will supply a positive amount of output, as long as the price is greater than

suppose that Irma's production function is f(x₁, x₂) = (min{x₁, 2x₂}) ^1/2.If the price of factor 1 is w₁ = $3 and the price of factor 2 is w₂ = $6, then her supply function is given by the equation

Suppose that Dent Carr's long-run total cost of repairing s cars per week is c(s) = 2s² + 18.If the price he receives for repairing a car is $8, then in the long run, how many cars will he fix per week if he maximize profits?

Suppose that Dent Carr's long-run total cost of repairing s cars per week is c(s) = 3s² + 75.If the price he receives for repairing a car is $36, then in the long run, how many cars will he fix per week if he maximize profits?

Suppose that Dent Carr's long-run total cost of repairing s cars per week is c(s) = 3s² + 108.If the price he receives for repairing a car is $24, then in the long run, how many cars will he fix per week if he maximize profits?

suppose that Irma's production function is f(x₁, x₂) =(min{x₁, 3x₂}) ^1/2.If the price of factor 1 is w₁ = $5 and the price of factor 2 is w₂ = $15, then her supply function is given by the equation

suppose that Irma's production function is f(x₁, x₂) = (min{x₁, 3x₂}) ^1/2.If the price of factor 1 is w₁ = $2 and the price of factor 2 is w₂ = $15, then her supply function is given by the equation

Quiz 21: Firm Supply-Part B

suppose that Irma's production function is f(x1, x2) =(min{x1, 3x2}) 1/2.If the price of factor 1 is w1 = $2 and the price of factor 2 is w2 = $6, then her supply function is given by the equation

A firm has a long-run cost function, C(q) = 8q2 + 288.In the long run, this firm will supply a positive amount of output, as long as the price is greater than

Suppose that Dent Carr's long-run total cost of repairing s cars per week is c(s) = 3s2+ 108.If the price he receives for repairing a car is $24, then in the long run, how many cars will he fix per week if he maximize profits?

A firm has a long-run cost function, C(q) = 3q2 + 108.In the long run, this firm will supply a positive amount of output, as long as the price is greater than

Suppose that Dent Carr's long-run total cost of repairing s cars per week is c(s) =2s2 + 50.If the price he receives for repairing a car is $8, then in the long run, how many cars will he fix per week if he maximize profits?

A firm has a long-run cost function, C(q) = 8q2 + 72.In the long run, this firm will supply a positive amount of output, as long as the price is greater than

A firm has a long-run cost function, C(q) = 9q2 + 9.In the long run, this firm will supply a positive amount of output, as long as the price is greater than

suppose that Irma's production function is f(x1, x2) = (min{x1, 3x2}) 1/2.If the price of factor 1 is w1 = $3 and the price of factor 2 is w2 = $9, then her supply function is given by the equation

A firm has a long-run cost function, C(q) = 4q2 + 4.In the long run, this firm will supply a positive amount of output, as long as the price is greater than

suppose that Irma's production function is f(x1, x2) = (min{x1, 2x2}) 1/2.If the price of factor 1 is w1 = $3 and the price of factor 2 is w2 = $6, then her supply function is given by the equation

Suppose that Dent Carr's long-run total cost of repairing s cars per week is c(s) = 2s2 + 18.If the price he receives for repairing a car is $8, then in the long run, how many cars will he fix per week if he maximize profits?

Suppose that Dent Carr's long-run total cost of repairing s cars per week is c(s) = 3s2 + 75.If the price he receives for repairing a car is $36, then in the long run, how many cars will he fix per week if he maximize profits?

Suppose that Dent Carr's long-run total cost of repairing s cars per week is c(s) = 3s2 + 108.If the price he receives for repairing a car is $24, then in the long run, how many cars will he fix per week if he maximize profits?

suppose that Irma's production function is f(x1, x2) =(min{x1, 3x2}) 1/2.If the price of factor 1 is w1 = $5 and the price of factor 2 is w2 = $15, then her supply function is given by the equation

suppose that Irma's production function is f(x1, x2) = (min{x1, 3x2}) 1/2.If the price of factor 1 is w1 = $2 and the price of factor 2 is w2 = $15, then her supply function is given by the equation

suppose that Irma's production function is f(x₁, x₂) =(min{x₁, 3x₂}) ^1/2.If the price of factor 1 is w₁ = $2 and the price of factor 2 is w₂ = $6, then her supply function is given by the equation

A firm has a long-run cost function, C(q) = 8q² + 288.In the long run, this firm will supply a positive amount of output, as long as the price is greater than

Suppose that Dent Carr's long-run total cost of repairing s cars per week is c(s) = 3s²+ 108.If the price he receives for repairing a car is $24, then in the long run, how many cars will he fix per week if he maximize profits?

A firm has a long-run cost function, C(q) = 3q² + 108.In the long run, this firm will supply a positive amount of output, as long as the price is greater than

Suppose that Dent Carr's long-run total cost of repairing s cars per week is c(s) =2s² + 50.If the price he receives for repairing a car is $8, then in the long run, how many cars will he fix per week if he maximize profits?

A firm has a long-run cost function, C(q) = 8q² + 72.In the long run, this firm will supply a positive amount of output, as long as the price is greater than

A firm has a long-run cost function, C(q) = 9q² + 9.In the long run, this firm will supply a positive amount of output, as long as the price is greater than

suppose that Irma's production function is f(x₁, x₂) = (min{x₁, 3x₂}) ^1/2.If the price of factor 1 is w₁ = $3 and the price of factor 2 is w₂ = $9, then her supply function is given by the equation

A firm has a long-run cost function, C(q) = 4q² + 4.In the long run, this firm will supply a positive amount of output, as long as the price is greater than

suppose that Irma's production function is f(x₁, x₂) = (min{x₁, 2x₂}) ^1/2.If the price of factor 1 is w₁ = $3 and the price of factor 2 is w₂ = $6, then her supply function is given by the equation

Suppose that Dent Carr's long-run total cost of repairing s cars per week is c(s) = 2s² + 18.If the price he receives for repairing a car is $8, then in the long run, how many cars will he fix per week if he maximize profits?

Suppose that Dent Carr's long-run total cost of repairing s cars per week is c(s) = 3s² + 75.If the price he receives for repairing a car is $36, then in the long run, how many cars will he fix per week if he maximize profits?

Suppose that Dent Carr's long-run total cost of repairing s cars per week is c(s) = 3s² + 108.If the price he receives for repairing a car is $24, then in the long run, how many cars will he fix per week if he maximize profits?

suppose that Irma's production function is f(x₁, x₂) =(min{x₁, 3x₂}) ^1/2.If the price of factor 1 is w₁ = $5 and the price of factor 2 is w₂ = $15, then her supply function is given by the equation

suppose that Irma's production function is f(x₁, x₂) = (min{x₁, 3x₂}) ^1/2.If the price of factor 1 is w₁ = $2 and the price of factor 2 is w₂ = $15, then her supply function is given by the equation