Question 1

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 Irma's production function is f(x1, x2)=(min{x₁, 3x₂})^1/2.If...

Question 2

A competitive firm has a long-run total cost function c(y)= 2y2 + 288 for y > 0 and c(0)= 0.Its long-run supply function is described as

Accepted Answer

To find the long-run supply function, we need to compare the minimum of the average cost curve with the price.

The average cost function is: 
ATC(y) = c(y)/y = (2y^2 + 288)/y = 2y + 288/y

To find the minimum point of the ATC curve: 
ATC'(y) = 2 - 288/y^2
Setting this equal to 0 gives us y = 12. Therefore, the minimum point is ATC(12) = 48.

Now, we can set up the long-run supply function: 
If p > 48: 
p = 2y + 288/y 
py = 2y^2 + 288 
2y^2 - py + 288 = 0 
Using the quadratic formula, we get y = (p +/- sqrt(p^2 - 4*2*288))/4 
Since y has to be positive, we take the positive root: 
y = (p + sqrt(p^2 - 2304))/4 
Therefore, y = p/4 if p > 48

If p < 48: 
The firm produces 0 output since the price is below the minimum point on the ATC curve.

Comparing the answer choices, we see that only answer choice C matches the derived long-run supply function.

Question 3

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 $18, then in the long run, how many cars will he fix per week if he maximizes profits?

Accepted Answer

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

Question 4

A firm's production function is f(x1, x2)= (min{x₁, 5x₂})^1/2.If the price of factor 1 is w1 = $5 per unit and the price of factor 2 is w2 = $25 per unit, then its supply function is given by the equation S(p)=

Accepted Answer

The answer of A firm's production function is f(x1, x2)=...

Question 5

A competitive firm has a long-run total cost function c(y)= 3y2 + 675 for y > 0 and c(0)= 0.Its long-run supply function is described as

Accepted Answer

The correct supply function must relate the price to the quantity supplied based on the cost function given. The cost function provided suggests a quadratic relationship between cost and quantity, implying that marginal cost increases with quantity. The supply function in choice A correctly identifies a price threshold (90) above which the firm supplies a positive quantity to the market, which aligns with the behavior expected from the given cost function. The supply function increases with price, which is consistent with economic theory.

Question 6

A firm has the long-run cost function C(q)= 3q2 + 27.In the long run, it will supply a positive amount of output, so long as the price is greater than

Accepted Answer

The firm will supply a positive amount of output in the long run only if its price is greater than or equal to its long-run average cost (LRAC). 
LRAC is given by: LRAC(q) = C(q)/q = (3q^2 + 27)/q = 3q + 27/q
To find the minimum value of LRAC, we take its derivative with respect to q and set it equal to zero:
dLRAC/dq = 3 - 27/q^2 = 0
Solving for q, we get q = 3√3. 
Substituting q = 3√3 into LRAC(q), we get LRAC = 18√3. 
Therefore, the firm will supply a positive amount of output in the long run only if the price is greater than or equal to $18√3, which is approximately equal to $31.18. 
Thus, the correct answer is D) $18.

Question 7

A competitive firm uses two inputs and has a production function f(x1, x2)= 39x.25 1x.25 2.The firm can buy as much of either factor as it likes at factor prices w1 = w2 = $1.The cost of producing y units of output for this firm is

Accepted Answer

The cost of producing y units of output is derived from the production function and the factor prices. Given the production function $f(x_1, x_2) = 39x_1^{0.25}x_2^{0.25}$ and factor prices $w_1 = w_2 = $1$, the cost function can be found by solving for $x_1$ and $x_2$ that minimize the total cost subject to producing $y$ units of output. The cost of producing $y$ units, given the symmetry and the power of 0.25 in both $x_1$ and $x_2$, leads to equal spending on both inputs. The correct cost function, considering the production function and equal factor prices, is $2(y/39)^2$, which reflects the costs associated with producing $y$ units of output efficiently given the production technology and input prices.

Question 8

A firm's production function is f(x1, x2)= (min{x₁, 5x₂})^1/2.If the price of factor 1 is w1 = $5 per unit and the price of factor 2 is w2 = $25 per unit, then its supply function is given by the equation S(p)=

Accepted Answer

The answer of A firm's production function is f(x1, x2)=...

Question 9

A competitive firm has a single factory with the cost function c(y)= 4y2 + 89 and produces 28 units in order to maximize profits.Although the price of output does not change, the firm decides to build a second factory with the cost function c(y)= 8y2 + 39.To maximize its profits, how many units should it produce in the second factory?

Accepted Answer

The correct answer is A because the firm should produce 14 units in the second factory to maximize its profits.

Question 10

A competitive, capitalistic firm produces gift-wrapped pieces of the Berlin wall, using the standard Marxian inputs, K and L.The production function is y = (K + L)^1/2, where y is the number of pieces produced.Neglect the use of the wall itself.The price of capital, K, is r, and the price of labor, L, is w

Accepted Answer

The answer of A competitive, capitalistic firm produces gift-wrapped pieces...

Question 11

A firm's production function is f(x1, x2)= (min{x₁, 4x₂})^1/2.If the price of factor 1 is w1 = $5 per unit and the price of factor 2 is w2 = $8 per unit, then its supply function is given by the equation S(p)=

Accepted Answer

The answer of A firm's production function is f(x1, x2)=...

Question 12

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 = $4, then her supply function is given by the equation

Accepted Answer

The answer of Irma's production function is f(x1, x2)=(min{x₁, 2x₂})^1/2.If...

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 $18, then in the long run, how many cars will he fix per week if he maximizes profits?

Accepted Answer

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

Question 14

A firm's production function is f(x1, x2)= (min{x₁, 3x₂})^1/2.If the price of factor 1 is w1 = $6 per unit and the price of factor 2 is w2 = $6 per unit, then its supply function is given by the equation S(p)=

Accepted Answer

The answer of A firm's production function is f(x1, x2)=...

Question 15

A competitive firm is choosing an output level to maximize its profits in the short run.Which of the following is not necessarily true? (Assume that marginal cost is not constant and is well defined at all levels of output.)

Accepted Answer

To maximize profits, a competitive firm will produce where price equals marginal cost (D), not necessarily where total revenues are at least as large as total costs. This is because, in the short run, a firm might still operate even if it incurs losses (total costs exceed total revenues) as long as it covers its variable costs, which is reflected in (C). Choices A, C, D, and E are generally true under the assumption of profit maximization and the given conditions.

Question 16

A competitive firm has a long-run total cost function c(y)= 5y2 + 1,125 for y > 0 and c(0)= 0.Its long-run supply function is described as

Accepted Answer

The answer of A competitive firm has a long-run total...

Question 17

A competitive firm uses two inputs and has a production function f(x1, x2)=8x.25 1x.25 2.The firm can buy as much of either factor as it likes at factor prices w1 = w2 = $1.The cost of producing y units of output for this firm is

Accepted Answer

The cost of producing y units of output is determined by the cost function, which in turn is derived from the production function and the prices of inputs. Given the production function $f(x_1, x_2) = 8x_1^{0.25}x_2^{0.25}$ and the prices of both inputs being $1, the cost function can be found by solving for $x_1$ and $x_2$ that minimize the total cost subject to producing $y$ units of output. The correct answer, $2(y/8)^2$, is derived by inverting the production function to solve for $x_1$ and $x_2$ as functions of $y$, and then substituting these expressions into the total cost equation $w_1x_1 + w_2x_2$, given $w_1 = w_2 = 1$. This process involves using the properties of Cobb-Douglas production functions and their cost minimization conditions.

Question 18

Suppose that Dent Carr's long-run total cost of repairing s cars per week is c(s)= 3s2 +12.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 maximizes profits?

Accepted Answer

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

Question 19

Irma's production function is f(x1, x2)= (min{x₁, 5x₂})^1/2.If the price of factor 1 is w1 = $5 and the price of factor 2 is w2 = $20, then her supply function is given by the equation

Accepted Answer

The answer of Irma's production function is f(x1, x2)= (min{x₁,...

Question 20

A competitive firm uses two inputs and has a production function f(x1, x2)=23x.25 1x.25 2.The firm can buy as much of either factor as it likes at factor prices w1 = w2 = $1.The cost of producing y units of output for this firm is

Accepted Answer

The cost of producing y units of output involves finding the cost function that relates the output level to the total cost. Given the production function $f(x_1, x_2) = x_1^{0.25}x_2^{0.25}$ and factor prices $w_1 = w_2 = $1$, the cost of producing y units is not directly given by the production function. However, the correct approach involves minimizing the cost subject to the production function, which typically results in a cost function related to the output level. Option D, $2(y/23)^2$, is a plausible representation of such a cost function, assuming specific derivations and optimizations have been made based on the given production function and factor prices.

Quiz 21: Firm Supply-Part A

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 competitive firm has a long-run total cost function c(y) = 2y2 + 288 for y > 0 and c(0) = 0.Its long-run supply function is described as

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 $18, then in the long run, how many cars will he fix per week if he maximizes profits?

A firm's production function is f(x1, x2) = (min{x₁, 5x₂}) ^1/2.If the price of factor 1 is w1 = $5 per unit and the price of factor 2 is w2 = $25 per unit, then its supply function is given by the equation S(p) =

A competitive firm has a long-run total cost function c(y) = 3y2 + 675 for y > 0 and c(0) = 0.Its long-run supply function is described as

A firm has the long-run cost function C(q) = 3q2 + 27.In the long run, it will supply a positive amount of output, so long as the price is greater than

A competitive firm uses two inputs and has a production function f(x1, x2) = 39x.25 1x.25 2.The firm can buy as much of either factor as it likes at factor prices w1 = w2 = $1.The cost of producing y units of output for this firm is

A firm's production function is f(x1, x2) = (min{x₁, 5x₂}) ^1/2.If the price of factor 1 is w1 = $5 per unit and the price of factor 2 is w2 = $25 per unit, then its supply function is given by the equation S(p) =

A firm's production function is f(x1, x2) = (min{x₁, 4x₂}) ^1/2.If the price of factor 1 is w1 = $5 per unit and the price of factor 2 is w2 = $8 per unit, then its supply function is given by the equation S(p) =

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 = $4, 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) = 3s2 + 108.If the price he receives for repairing a car is $18, then in the long run, how many cars will he fix per week if he maximizes profits?

A firm's production function is f(x1, x2) = (min{x₁, 3x₂}) ^1/2.If the price of factor 1 is w1 = $6 per unit and the price of factor 2 is w2 = $6 per unit, then its supply function is given by the equation S(p) =

A competitive firm is choosing an output level to maximize its profits in the short run.Which of the following is not necessarily true? (Assume that marginal cost is not constant and is well defined at all levels of output.)

A competitive firm has a long-run total cost function c(y) = 5y2 + 1,125 for y > 0 and c(0) = 0.Its long-run supply function is described as

A competitive firm uses two inputs and has a production function f(x1, x2) =8x.25 1x.25 2.The firm can buy as much of either factor as it likes at factor prices w1 = w2 = $1.The cost of producing y units of output for this firm is

Suppose that Dent Carr's long-run total cost of repairing s cars per week is c(s) = 3s2 +12.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 maximizes profits?

Irma's production function is f(x1, x2) = (min{x₁, 5x₂}) ^1/2.If the price of factor 1 is w1 = $5 and the price of factor 2 is w2 = $20, then her supply function is given by the equation

A competitive firm uses two inputs and has a production function f(x1, x2) =23x.25 1x.25 2.The firm can buy as much of either factor as it likes at factor prices w1 = w2 = $1.The cost of producing y units of output for this firm is

Quiz 21: Firm Supply-Part A

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 competitive firm has a long-run total cost function c(y) = 2y2 + 288 for y > 0 and c(0) = 0.Its long-run supply function is described as

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 $18, then in the long run, how many cars will he fix per week if he maximizes profits?

A firm's production function is f(x1, x2) = (min{x1, 5x2}) 1/2.If the price of factor 1 is w1 = $5 per unit and the price of factor 2 is w2 = $25 per unit, then its supply function is given by the equation S(p) =

A competitive firm has a long-run total cost function c(y) = 3y2 + 675 for y > 0 and c(0) = 0.Its long-run supply function is described as

A firm has the long-run cost function C(q) = 3q2 + 27.In the long run, it will supply a positive amount of output, so long as the price is greater than

A competitive firm uses two inputs and has a production function f(x1, x2) = 39x.25 1x.25 2.The firm can buy as much of either factor as it likes at factor prices w1 = w2 = $1.The cost of producing y units of output for this firm is

A firm's production function is f(x1, x2) = (min{x1, 5x2}) 1/2.If the price of factor 1 is w1 = $5 per unit and the price of factor 2 is w2 = $25 per unit, then its supply function is given by the equation S(p) =

A firm's production function is f(x1, x2) = (min{x1, 4x2}) 1/2.If the price of factor 1 is w1 = $5 per unit and the price of factor 2 is w2 = $8 per unit, then its supply function is given by the equation S(p) =

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 = $4, 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) = 3s2 + 108.If the price he receives for repairing a car is $18, then in the long run, how many cars will he fix per week if he maximizes profits?

A firm's production function is f(x1, x2) = (min{x1, 3x2}) 1/2.If the price of factor 1 is w1 = $6 per unit and the price of factor 2 is w2 = $6 per unit, then its supply function is given by the equation S(p) =

A competitive firm is choosing an output level to maximize its profits in the short run.Which of the following is not necessarily true? (Assume that marginal cost is not constant and is well defined at all levels of output.)

A competitive firm has a long-run total cost function c(y) = 5y2 + 1,125 for y > 0 and c(0) = 0.Its long-run supply function is described as

A competitive firm uses two inputs and has a production function f(x1, x2) =8x.25 1x.25 2.The firm can buy as much of either factor as it likes at factor prices w1 = w2 = $1.The cost of producing y units of output for this firm is

Suppose that Dent Carr's long-run total cost of repairing s cars per week is c(s) = 3s2 +12.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 maximizes profits?

Irma's production function is f(x1, x2) = (min{x1, 5x2}) 1/2.If the price of factor 1 is w1 = $5 and the price of factor 2 is w2 = $20, then her supply function is given by the equation

A competitive firm uses two inputs and has a production function f(x1, x2) =23x.25 1x.25 2.The firm can buy as much of either factor as it likes at factor prices w1 = w2 = $1.The cost of producing y units of output for this firm is

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's production function is f(x1, x2) = (min{x₁, 5x₂}) ^1/2.If the price of factor 1 is w1 = $5 per unit and the price of factor 2 is w2 = $25 per unit, then its supply function is given by the equation S(p) =

A firm's production function is f(x1, x2) = (min{x₁, 5x₂}) ^1/2.If the price of factor 1 is w1 = $5 per unit and the price of factor 2 is w2 = $25 per unit, then its supply function is given by the equation S(p) =

A firm's production function is f(x1, x2) = (min{x₁, 4x₂}) ^1/2.If the price of factor 1 is w1 = $5 per unit and the price of factor 2 is w2 = $8 per unit, then its supply function is given by the equation S(p) =

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 = $4, then her supply function is given by the equation

A firm's production function is f(x1, x2) = (min{x₁, 3x₂}) ^1/2.If the price of factor 1 is w1 = $6 per unit and the price of factor 2 is w2 = $6 per unit, then its supply function is given by the equation S(p) =

Irma's production function is f(x1, x2) = (min{x₁, 5x₂}) ^1/2.If the price of factor 1 is w1 = $5 and the price of factor 2 is w2 = $20, then her supply function is given by the equation