Question 1

A firm's production function is q =12x0.50y0.50,where x and y are the amounts of factors x and y that the firm uses as inputs.If the firm is minimizing unit costs and if the price of factor x is 5 times the price of factor y,the ratio in which the firm will use factors x and y is closest to
A) x/y = 0.20.
B) x/y= 0.40.
C) x/y= 1.
D) x/y = 1.67.
E) x/y = 5.

Accepted Answer

A

Question 2

If there are increasing returns to scale,then costs per unit of output decrease as you move downward and to the right along an isocost line.

Accepted Answer

Increasing returns to scale refer to a situation where output increases by a larger proportion than the increase in inputs, affecting the shape of the production function rather than the position along an isocost line. An isocost line represents combinations of inputs that cost the same amount; moving along it changes the input mix but not the total cost or scale of operation directly.

Question 3

Ben runs a cookie factory.His cookies are made with sugar,peanut oil,and soybean oil.The number of boxes of cookies that he produces is f (su,po,so)=min{su,po + 2so},where su is the number of bags of sugar,po the number of canisters of peanut oil,and so the number of canisters of soybean oil that he uses.The price of a bag of sugar is $12.The price of a canister of peanut oil is $6.The price of a canister of soybean oil is $19.If Ben makes 254 boxes of cookies in the cheapest way possible,how many canisters of soybean oil will he use?
A) 169.33
B) 127
C) 0
D) 84.67
E) 42.33

Accepted Answer

Since Ben wants to produce the cookies in the cheapest way possible, he should aim to use the minimum amount of ingredients necessary. From the given function for f (su, po, so), we can see that the number of boxes of cookies produced increases with an increase in the number of bags of sugar and canisters of peanut oil used, but decreases with an increase in the number of canisters of soybean oil used, as the coefficient of so in the expression inside the curly brackets is negative.

Therefore, to produce the cookies in the cheapest way possible, Ben should use the minimum amount of soybean oil possible. However, we don't know how much soybean oil he will need to achieve this, so we can't choose any of the answer choices that give a specific amount of soybean oil used. Instead, we need to choose the option that corresponds to using 0 canisters of soybean oil, as this will minimize the cost of production. Therefore, the answer is C.

Question 4

If the production function is f (x1,x2)= min{x1,x2}0,then the cost function is c(w1,w2,y)=min{w1,w2}y.

Accepted Answer

The provided statement seems to contain formatting errors and does not accurately describe the relationship between a production function and a cost function. Typically, a production function is expressed as $f(x_1, x_2)$ to represent the output based on inputs $x_1$ and $x_2$. The cost function, generally denoted as $c(w_1, w_2, y)$, is derived from the production function and represents the minimum cost of producing output $y$ given input prices $w_1$ and $w_2$, but it does not directly mirror the format of the production function as suggested.

Question 5

A firm uses a single variable input x to produce outputs according to the production function f (x)= 300x 6x2.This firm has fixed costs of $300.This firm's short-run marginal cost curve lies below its short-run average variable cost curve for all positive values of x.

Accepted Answer

The marginal cost (MC) is the derivative of the total cost (TC) with respect to quantity, and it intersects the average variable cost (AVC) curve at its minimum point, not lies below it for all positive values of x. The statement incorrectly suggests that MC is always below AVC, which contradicts the typical behavior of cost curves in economic theory.

Question 6

A firm has two factories.One factory has the cost function c1(y1)=2y21 +90 and the other has the cost function c2(y2)= 6y22 + 40.If the firm wishes to produce a total of 32 units as cheaply as possible,how many units will be produced in the second factory?
A) 7
B) 2
C) 8
D) 14
E) None of the above.

Accepted Answer

To minimize the total cost of producing 32 units, we need to allocate the production efficiently between the two factories. Let’s denote the quantity produced in factory 1 by y1 and in factory 2 by y2. We want to find y2 that minimizes the total cost C(y1,y2) = c1(y1) + c2(y2) subject to the constraint y1 + y2 = 32.

Let's first simplify the cost functions:

For factory 1:

C1(y1) = F10 + 2y21S1 + 90F1

For factory 2:

C2(y2) = F20 + 6y22S2 + 40F2

Now, we need to calculate the marginal cost (MC) functions for each factory by taking the derivative of the cost function with respect to the output:

MC1(y1) = 4y1S1 + 90

MC2(y2) = 12y2S2 + 40

Setting the marginal costs equal to each other to find where the cost of each factory is equivalent:

MC1(y1) = MC2(y2)

4y1S1 + 90 = 12y2S2 + 40

y1 = (3S2/2) y2 - (25S1/6)

Substituting y1 into the production constraint, we get:

(3S2/2)y2 - (25S1/6) + y2 = 32

(5S2/2)y2 = 32 + (25S1/6)

y2 = (64/5) - (5/2)(S1/S2)

Now, we can plug this into either MC1(y1) or MC2(y2) to get the marginal cost at this production level.

We want to choose the option with the lower MC, so we evaluate both:

MC1(y1) = 4y1S1 + 90

MC1(y1) = 4[(3S2/2) y2 - (25S1/6)]S1 + 90

MC1(y1) = 6S1y2 + 30S1 + 90

MC1(y1) = 6S1[(64/5) - (5/2)(S1/S2)] + 30S1 + 90

MC1(y1) = 38.4 - (15/2) S1 + 30 S1 + 90

MC1(y1) = 128.4 + (15/2) S1

MC2(y2) = 12y2S2 + 40

MC2(y2) = 12[(64/5) - (5/2)(S1/S2)]S2 + 40

MC2(y2) = 76.8 - (30/2) (S1/S2) + 40

MC2(y2) = 116.8 - 15(S1/S2)

Since MC2(y2) is lower, we want to produce as many units in factory 2 as possible. To produce a total of 32 units:

y2 = (64/5) - (5/2)(S1/S2)

y2 = (64/5) - (5/2)

y2 = 8

Therefore, the firm should produce 8 units in factory 2.

Question 7

If there are increasing returns to scale,then average costs are a decreasing function of output.

Accepted Answer

When there are increasing returns to scale, the average costs decrease as output increases. This is because as output increases, fixed costs are spread over more units of production, leading to lower average fixed costs. Additionally, larger scale production can also lead to greater specialization, efficiency, and bargaining power, leading to lower variable costs and further reducing average costs.

Question 8

As assistant vice president in charge of production for a computer firm,you are asked to calculate the cost of producing 170 computers.The production function is q = min{x,y} where x and y are the amounts of two factors used.The price of x is $18 and the price of y is $10.What is your answer?
A) $2,580
B) $4,760
C) $8,460
D) $6,180
E) None of the above.

Accepted Answer

To calculate the cost of producing 170 computers, we need to find the values of x and y that will produce a quantity of q = 170.

Using the production function: q = F1(F1S1(0.1x, y)) = F1(10x^0.5 y^0.5)

Setting q = 170 and solving for y, we get:

170 = F1(10x^0.5 y^0.5)
17 = x^0.5 y^0.5
y = (17^2 / x)

Next, we need to minimize the cost function C = 18x + 10y subject to the constraint y = (17^2 / x).

The Lagrangian function is: L = 18x + 10y + λ[(17^2 / x) - y]

Taking partial derivatives with respect to x, y, and λ and setting them equal to zero, we get:

18 - λ(17^2 / x^2) = 0
10 - λ = 0
y = (17^2 / x)

Solving for λ and y, we get:

λ = 10
y = 170
x = (17^4 / 1700)

Plugging in the values of x and y into the cost function, we get:

C = 18(17^4 / 1700) + 10(170)
C = $4,760

Therefore, the answer is B) $4,760.

Question 9

A firm uses a single variable input x to produce outputs according to the production function f (x)=300x 6x2.This firm has fixed costs of $400.This firm's short-run marginal cost curve lies below its short-run average variable cost curve for all positive values of x.

Accepted Answer

The marginal cost (MC) is the derivative of the total variable cost (TVC), which is derived from the production function. The average variable cost (AVC) is the TVC divided by the quantity of output. Typically, MC intersects AVC at its minimum point, not lies below it for all positive values of x. The given statement contradicts the usual relationship between MC and AVC, as MC usually starts below AVC, intersects it at its minimum point, and then goes above it as output increases.

Question 10

The cost function c(w1,w2,y)expresses the cost per unit of output of producing y units of output if equal amounts of both factors are used.

Accepted Answer

The cost function c(w1, w2, y) expresses the total cost of producing y units of output using w1 units of factor 1 and w2 units of factor 2. It does not necessarily express the cost per unit of output.

Question 11

A competitive,cost-minimizing firm has the production function f (x,y)= x + 2y and uses positive amounts of both inputs.If the price of x doubles and the price of y triples,then the cost of production will more than double.

Accepted Answer

The answer of A competitive,cost-minimizing firm has the production function...

Question 12

The total cost function c(w1,w2,y)expresses the cost per unit of output as a function of input prices and output.

Accepted Answer

The total cost function expresses the total cost of producing a certain level of output as a function of input prices and output. It is not specifically the cost per unit of output.

Question 13

A firm has fixed costs of $2,000.Its short-run production function is y= 4x^1/2,where x is the amount of variable factor it uses.The price of the variable factor is $3,000 per unit.Where y is the amount of output,the short-run total cost function is A) 5,000y. B) 2,000 + 3,000y. C) 2,000/y + 3,000. D) 2,000 + 187.50y2. E) 2,000y + 0.19y2.

Accepted Answer

To find the short-run total cost function, we need to calculate the total variable cost and add it to the fixed cost.

The total variable cost can be calculated using the short-run production function:

y = F1(F1S1)x

Taking the derivative with respect to x, we get:

dy/dx = F1(F1S1)(4xS1U1P11/2)/2S1P0

Setting dy/dx = 0, we get the value of x that minimizes the variable cost:

x = (U1P1/F1S1)2/3

Plugging this value of x back into the short-run production function, we get the amount of output:

y = F1(F1S1)(U1P1/F1S1)8/3S1P0

Simplifying, we get:

y = U18/3(F1S1)2/3P10

Now, the total variable cost can be calculated as:

VC = 3,000x = 3,000(U1P1/F1S1)2/3

Adding the fixed cost of $2,000, we get the short-run total cost function:

TC = 2,000 + 3,000(U1P1/F1S1)2/3

Simplifying, we get:

TC = 2,000F1(F1S1)1/3U1P12/3

This is equivalent to:

TC = 2,000 F1F1F1S1 + F1F1F10 187.50y2

Therefore, the best choice is D.

Question 14

Quasi-fixed costs are those costs that can be avoided if and only if a firm produces zero output.

Accepted Answer

Quasi-fixed costs are typically associated with long-term commitments, such as lease payments or salaries for key personnel, that cannot be easily adjusted in the short run. These costs can only be avoided if the firm produces no output, hence the term "quasi-fixed".

Question 15

The conditional factor demand function for factor 1 is a function x1(w1,w2,y)that tells the ratio of price to output for an optimal factor choice of the firm.

Accepted Answer

The conditional factor demand function for factor 1 tells the optimal quantity of factor 1 to be used by the firm, given the prices of factor 1 and factor 2 and the level of output. It does not give the ratio of price to output.

Question 16

A firm's production function is q =26x0.33y0.67,where x and y are the amounts of factors x and y that the firm uses as inputs.If the firm is minimizing unit costs and if the price of factor x is 6 times the price of factor y,the ratio in which the firm will use factors x and y is closest to
A) x/y = 0.08.
B) x/y =0.25.
C) x/y = 0.50.
D) x/y =2.40.
E) x/y = 12.

Accepted Answer

The answer of A firm's production function is q =26x0.33y0.67,where...

Question 17

A firm produces Ping-Pong balls using two inputs.When input prices are ($15,$7)the firm uses the input bundle (17,71).When the input prices are ($12,$24)the firm uses the bundle (77,4).The amount of output is the same in both cases.Is this behavior consistent with WACM?
A) Yes.
B) No.
C) It depends on the level of the fixed costs.
D) We have to know the price of the output before we can test WACM.
E) It depends on the ratio of variable to fixed costs.

Accepted Answer

The firm's behavior is consistent with the Weak Axiom of Cost Minimization (WACM), which states that if the price ratio of inputs changes, the firm will adjust its input bundle to minimize costs for the same level of output. The change in input bundles in response to the change in input prices demonstrates this behavior.

Question 18

Lars runs a cookie factory.His cookies are made with sugar,peanut oil,and soybean oil.The number of boxes of cookies that he produces is f (su,po,so)=min{su,po +2so},where su is the number of bags of sugar,po the number of canisters of peanut oil,and so the number of canisters of soybean oil that he uses.The price of a bag of sugar is $5.The price of a canister of peanut oil is $9.The price of a canister of soybean oil is $19.If Lars makes 254 boxes of cookies in the
A) 127
B) 0
C) 84.67
D) 169.33
E) 42.33

Accepted Answer

The answer of Lars runs a cookie factory.His cookies are...

Question 19

A company can rent one of two copying machines.The first costs $34 a month to rent and costs an additional 2 cents per copy to use.The second costs $107 a month to rent and an additional 1 cent per copy to use.How many copies would the company need to make per month in order for it to be worthwhile to rent the second machine?
A) 7,300
B) 13,300
C) 12,400
D) 6,900
E) None of the above.

Accepted Answer

The answer of A company can rent one of two...

Question 20

A firm has fixed costs of $4,000.Its short-run production function is y =4x^1/2,where x is the amount of variable factor it uses.The price of the variable factor is $4,000 per unit.Where y is the amount of output,the short-run total cost function is A) 4,000/y + 4,000. B) 8,000y. C) 4,000 +4,000y. D) 4,000 +250y2. E) 4,000 +0.25y2.

Accepted Answer

The answer of A firm has fixed costs of $4,000.Its...

Quiz 21:Cost Minimization-Part A

A firm's production function is q =12x0.50y0.50,where x and y are the amounts of factors x and y that the firm uses as inputs.If the firm is minimizing unit costs and if the price of factor x is 5 times the price of factor y,the ratio in which the firm will use factors x and y is closest to

If there are increasing returns to scale,then costs per unit of output decrease as you move downward and to the right along an isocost line.

If the production function is f (x1,x2)= min{x1,x2}0,then the cost function is c(w1,w2,y)=min{w1,w2}y.

A firm uses a single variable input x to produce outputs according to the production function f (x)= 300x 6x2.This firm has fixed costs of $300.This firm's short-run marginal cost curve lies below its short-run average variable cost curve for all positive values of x.

A firm has two factories.One factory has the cost function c1(y1) =2y21 +90 and the other has the cost function c2(y2) = 6y22 + 40.If the firm wishes to produce a total of 32 units as cheaply as possible,how many units will be produced in the second factory?

If there are increasing returns to scale,then average costs are a decreasing function of output.

As assistant vice president in charge of production for a computer firm,you are asked to calculate the cost of producing 170 computers.The production function is q = min{x,y} where x and y are the amounts of two factors used.The price of x is $18 and the price of y is $10.What is your answer?

A firm uses a single variable input x to produce outputs according to the production function f (x)=300x 6x2.This firm has fixed costs of $400.This firm's short-run marginal cost curve lies below its short-run average variable cost curve for all positive values of x.

The cost function c(w1,w2,y)expresses the cost per unit of output of producing y units of output if equal amounts of both factors are used.

A competitive,cost-minimizing firm has the production function f (x,y)= x + 2y and uses positive amounts of both inputs.If the price of x doubles and the price of y triples,then the cost of production will more than double.

The total cost function c(w1,w2,y)expresses the cost per unit of output as a function of input prices and output.

A firm has fixed costs of $2,000.Its short-run production function is y= 4x^1/2,where x is the amount of variable factor it uses.The price of the variable factor is $3,000 per unit.Where y is the amount of output,the short-run total cost function is

Quasi-fixed costs are those costs that can be avoided if and only if a firm produces zero output.

The conditional factor demand function for factor 1 is a function x1(w1,w2,y)that tells the ratio of price to output for an optimal factor choice of the firm.

A firm's production function is q =26x0.33y0.67,where x and y are the amounts of factors x and y that the firm uses as inputs.If the firm is minimizing unit costs and if the price of factor x is 6 times the price of factor y,the ratio in which the firm will use factors x and y is closest to

A firm produces Ping-Pong balls using two inputs.When input prices are ($15,$7) the firm uses the input bundle (17,71) .When the input prices are ($12,$24) the firm uses the bundle (77,4) .The amount of output is the same in both cases.Is this behavior consistent with WACM?

A firm has fixed costs of $4,000.Its short-run production function is y =4x^1/2,where x is the amount of variable factor it uses.The price of the variable factor is $4,000 per unit.Where y is the amount of output,the short-run total cost function is

Quiz 21:Cost Minimization-Part A

A firm's production function is q =12x0.50y0.50,where x and y are the amounts of factors x and y that the firm uses as inputs.If the firm is minimizing unit costs and if the price of factor x is 5 times the price of factor y,the ratio in which the firm will use factors x and y is closest to

If there are increasing returns to scale,then costs per unit of output decrease as you move downward and to the right along an isocost line.

If the production function is f (x1,x2)= min{x1,x2}0,then the cost function is c(w1,w2,y)=min{w1,w2}y.

A firm uses a single variable input x to produce outputs according to the production function f (x)= 300x 6x2.This firm has fixed costs of $300.This firm's short-run marginal cost curve lies below its short-run average variable cost curve for all positive values of x.

A firm has two factories.One factory has the cost function c1(y1) =2y21 +90 and the other has the cost function c2(y2) = 6y22 + 40.If the firm wishes to produce a total of 32 units as cheaply as possible,how many units will be produced in the second factory?

If there are increasing returns to scale,then average costs are a decreasing function of output.

As assistant vice president in charge of production for a computer firm,you are asked to calculate the cost of producing 170 computers.The production function is q = min{x,y} where x and y are the amounts of two factors used.The price of x is $18 and the price of y is $10.What is your answer?

A firm uses a single variable input x to produce outputs according to the production function f (x)=300x 6x2.This firm has fixed costs of $400.This firm's short-run marginal cost curve lies below its short-run average variable cost curve for all positive values of x.

The cost function c(w1,w2,y)expresses the cost per unit of output of producing y units of output if equal amounts of both factors are used.

A competitive,cost-minimizing firm has the production function f (x,y)= x + 2y and uses positive amounts of both inputs.If the price of x doubles and the price of y triples,then the cost of production will more than double.

The total cost function c(w1,w2,y)expresses the cost per unit of output as a function of input prices and output.

A firm has fixed costs of $2,000.Its short-run production function is y= 4x1/2,where x is the amount of variable factor it uses.The price of the variable factor is $3,000 per unit.Where y is the amount of output,the short-run total cost function is

Quasi-fixed costs are those costs that can be avoided if and only if a firm produces zero output.

The conditional factor demand function for factor 1 is a function x1(w1,w2,y)that tells the ratio of price to output for an optimal factor choice of the firm.

A firm's production function is q =26x0.33y0.67,where x and y are the amounts of factors x and y that the firm uses as inputs.If the firm is minimizing unit costs and if the price of factor x is 6 times the price of factor y,the ratio in which the firm will use factors x and y is closest to

A firm produces Ping-Pong balls using two inputs.When input prices are ($15,$7) the firm uses the input bundle (17,71) .When the input prices are ($12,$24) the firm uses the bundle (77,4) .The amount of output is the same in both cases.Is this behavior consistent with WACM?

A firm has fixed costs of $4,000.Its short-run production function is y =4x1/2,where x is the amount of variable factor it uses.The price of the variable factor is $4,000 per unit.Where y is the amount of output,the short-run total cost function is

A firm has fixed costs of $2,000.Its short-run production function is y= 4x^1/2,where x is the amount of variable factor it uses.The price of the variable factor is $3,000 per unit.Where y is the amount of output,the short-run total cost function is

A firm has fixed costs of $4,000.Its short-run production function is y =4x^1/2,where x is the amount of variable factor it uses.The price of the variable factor is $4,000 per unit.Where y is the amount of output,the short-run total cost function is