Question 1

In Problem 9,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) S(p)=p(min{w₁,3w₂})².
B) S(p)=6p.
C) S(p)= p/12.
D) S(p)=p(max{w₁,3w₂})².
E) S(p)= min{3p,27p}.

S(p)= p/12.

Accepted Answer

S(p)= p/12.&#10;

Question 2

In Problem 9,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) S(p)=p(min{w₁,3w₂})².
B) S(p)=6p.
C) S(p)= p/12.
D) S(p)=p(max{w₁,3w₂})².
E) S(p)= min{3p,27p}.

S(p)= p/12.

Accepted Answer

S(p)= p/14.&#10;

Question 3

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 A) $72. B) $80. C) $36. D) $18. E) $41.

Accepted Answer

For the firm to supply a positive amount of output in the long run, its price (P) must be greater than or equal to its minimum average total cost (MATC).

MATC can be found by taking the derivative of the cost function with respect to q and setting it equal to 0:

MC(q) = C'(q) = 3F1S1U1P1 - 108S1 = 0

Solving for Q, we get Q = 36P1F1S1U1

Plugging this expression back into the cost function:

C(q) = F1S1P10Q3 + F10S1Q

C(P) = F1S1P10(36P1F1S1U1)3 + F10S1(36P1F1S1U1)

C(P) = 46656P4F13S13U1 + 6P1F10S1S1

MATC = C(Q)/Q = 46656P4F13S13U1/Q + 6P1F10S1S1/Q

MATC = 46656P3F13S13U1 + 6P0F10S1S1/Q

As Q approaches infinity in the long run, the second term (6P0F10S1S1/Q) becomes negligible, so:

MATC ≈ 46656P3F13S13U1

Therefore, the firm will supply a positive amount of output if:

P ≥ MATC

P ≥ 46656P3F13S13U1

P ≥ 36

Hence, the answer is C.

Question 4

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) 0
B) 4
C) 6
D) 8
E) 12

Accepted Answer

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

Question 5

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) $48. B) $104. C) $96. D) $24. E) $53.

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 6

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) 0
B) 4
C) 6
D) 8
E) 12

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 7

In Problem 9,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) S(p)=p(min{w₁,3w₂})².
B) S(p)=6p.
C) S(p)= p/12.
D) S(p)=p(max{w₁,3w₂})².
E) S(p)= min{3p,27p}.

S(p)= p/12.

Accepted Answer

The answer of In Problem 9,suppose that Irma's production function...

Question 8

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) 2
B) 0
C) 4
D) 3
E) 6

Accepted Answer

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

Question 9

In Problem 9,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) S(p)=p(min{w₁,3w₂})².
B) S(p)=6p.
C) S(p)= p/12.
D) S(p)=p(max{w₁,3w₂})².
E) S(p)= min{3p,27p}.

S(p)= p/12.

Accepted Answer

The answer of In Problem 9,suppose that Irma's production function...

Question 10

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 A) $200. B) $192. C) $96. D) $48. E) $101.

Accepted Answer

In the long run, the firm will supply a positive amount of output as long as the price is greater than or equal to the minimum of the average variable cost (AVC) curve. AVC is found by taking the variable cost (VC) and dividing it by the quantity (q) produced. VC = ² AVC = VC/q = (²)/q To find the minimum value of AVC, we take the derivative with respect to q and set it equal to zero: dAVC/dq = (-²)/q^2 + ²/q^3 = 0 Solving for q, we get q = 3U1P1. Plugging this value of q back into the AVC equation, we get: AVC = (²)/(3U1P1) = (1/3)(²)/(U1P1) So the firm will supply a positive amount of output as long as the price is greater than or equal to the minimum value of AVC: Price >= AVC = (1/3)(²)/(U1P1) Plugging in the values given in the question, we get: Price >= (1/3)(288)/(8) = $12 To find the corresponding quantity of output, we plug in the price into the long-run cost function: C(q) = F1F1F1(S1F1F10)8q + F1F1F1(S1F1F10)288 C(q) = (1/8)(S1F1F10)q + 36(S1F1F10) At a price of $12, the firm will supply a positive amount of output if it can produce at a cost lower than $12. Plugging in $12 for the cost, we get: $12 = (1/8)(S1F1F10)q + 36(S1F1F10) Solving for q, we get: q = 96 Therefore, the firm will supply a positive amount of output if the price is greater than or equal to $12, which corresponds to a quantity of output of 96 units. Thus, the answer is C) $96.

Question 11

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 A) $8. B) $4. C) $24. D) $16. E) $13.

Accepted Answer

The answer of A firm has a long-run cost function,C(q)=4q²...

Question 12

In Problem 9,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) S(p)=p(min{w₁,3w₂})².
B) S(p)=6p.
C) S(p)= p/12.
D) S(p)=p(max{w₁,3w₂})².
E) S(p)= min{3p,27p}.

S(p)= p/12.

Accepted Answer

The answer of In Problem 9,suppose that Irma's production function...

Question 13

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?

A) 4
B) 0
C) 3
D) 2
E) 6

Accepted Answer

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

Question 14

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) 0
B) 8
C) 4
D) 6
E) 12

Accepted Answer

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

Question 15

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 A) $36. B) $44. C) $9. D) $18. E) $23.

Accepted Answer

The answer of A firm has a long-run cost function,C(q)=9q²...

Deck 23: B: Firm Supply