Question 1

The cost function C(y)= 100 + 3y2 has marginal cost less than average cost for all positive levels of output.

Accepted Answer

The given cost function appears to be incorrectly formatted, making it difficult to analyze directly. However, in general, whether the marginal cost is less than the average cost depends on the specific form and parameters of the cost function, not a universal rule applicable to all cost functions.

Question 2

If a competitive firm uses two inputs and has the production function F(x1, x2)= x^1/21 + x^1/22, then its marginal cost curve is horizontal.

Accepted Answer

The production function given is not clearly defined, but generally, for a competitive firm, the shape of the marginal cost curve depends on the production function and the cost of inputs. If the production function exhibits increasing, constant, or decreasing returns to scale, this will affect the shape of the marginal cost curve, which is not necessarily horizontal. A horizontal marginal cost curve implies constant returns to scale and constant input prices, which is a specific case and not a general rule for all production functions.

Question 3

A firm has a short-run cost function c(y)= 3y + 14 for y = 0 and c(0)= 10.The firm's quasi-fixed costs are
A)$10.
B)$4.
C)$9.
D)$14.
E)They are not possible to determine from this information.

Accepted Answer

Quasi-fixed costs are the fixed costs that vary with the level of output. In this case, the only fixed cost is c(0) = 10. Thus, the quasi-fixed costs are the difference between the total fixed cost and the fixed cost at zero output, divided by the level of output at which the fixed cost equals zero.

Quasi-fixed costs = (c(y) - c(0))/y = (3y + 14 - 10)/y = 4/y

Therefore, the quasi-fixed costs are decreasing as output increases. At y=1, quasi-fixed costs are 4; at y=2, quasi-fixed costs are 2; and so on. The only answer choice that is a possible quasi-fixed cost is B) $4.

Question 4

A competitive firm has the short-run cost function c(y)= 2y3 - 16y2 + 64y + 50.The firm will produce a positive amount in the short run if and only if the price is greater than
A)$16.
B)$64.
C)$32.
D)$35.
E)$31.

Accepted Answer

To determine the firm's output level in the short run, we need to minimize the cost function with respect to y, which yields the following first-order condition:

c'(y) = 6y^2 - 32y + 64 = 0

Solving for y, we get y = 4, which is a positive output quantity.

To determine the price at which the firm will produce in the short run, we need to compare the firm's marginal cost (MC) at the output level y = 4 with the price (P). If P > MC, the firm will produce; if P < MC, the firm will shut down and produce nothing.

The firm's MC at y = 4 is c'(4) = 48. Therefore, the firm will only produce if P > 48. The only answer choice that satisfies this condition is C, $32. Therefore, the correct answer is C.

Question 5

The production function of a competitive firm is described by the equation y = 8x^1/2 1x^1/2 2.The factor prices are p1 = $1 and p2 =$4 and the firm can hire as much of either factor it wants at these prices.The firm's marginal cost is A)constant and equal to .50. B)constant and equal to 3. C)increasing. D)decreasing. E)None of the above.

Accepted Answer

Marginal cost is equal to the change in total cost divided by the change in output. In this case, the total cost is given by the equation TC = p1x1 + p2x2, where p1 and p2 are the prices of factors 1 and 2, respectively, and x1 and x2 are the quantities of factors 1 and 2 used. The change in total cost is equal to dTC = p1dx1 + p2dx2, and the change in output is equal to dy = 8x1^(1/2)x2^(1/2)dx1 + 8x1^(1/2)x2^(1/2)dx2. Substituting these expressions into the equation for marginal cost, we get MC = dTC/dy = (p1dx1 + p2dx2)/(8x1^(1/2)x2^(1/2)dx1 + 8x1^(1/2)x2^(1/2)dx2) = (p1/8x1^(1/2)x2^(1/2)) + (p2/8x1^(1/2)x2^(1/2)). Since p1 = $1 and p2 = $4, we have MC = (1/8x1^(1/2)x2^(1/2)) + (4/8x1^(1/2)x2^(1/2)) = 5/8x1^(1/2)x2^(1/2). This expression is constant, so the marginal cost is constant and equal to 5/8x1^(1/2)x2^(1/2).

Question 6

The area under the marginal cost curve measures total fixed costs.

Accepted Answer

The area under the marginal cost curve represents the total variable costs, not the fixed costs. Fixed costs are represented by the vertical intercept of the marginal cost curve.

Question 7

Average cost can never rise while marginal costs are declining.

Accepted Answer

Although it is rare, there are some situations where the marginal cost (the cost of producing one additional unit) can be declining while the average cost (the total cost divided by the total number of units produced) is rising. This can happen when fixed costs or overhead costs become a larger proportion of the total cost as production increases, thus increasing the average cost even as the marginal cost continues to decline.

Question 8

A goatherd has the cost function c(y)= 2y2, where y is the number of tubs of goat cheese she makes per month.She faces a competitive market for goat cheese,with a price of $40 a tub.How many tubs should she produce per month?
A)10
B)The square root of 40
C)4
D)The square root of 20
E)5

Accepted Answer

The answer of A goatherd has the cost function c(y)=...

Question 9

The marginal cost curve of a firm is MC = 8y.Total variable costs to produce 11 units of output are
A)$484.
B)$484
C)$176.
D)$88.
E)$30.

Accepted Answer

The answer of The marginal cost curve of a firm...

Question 10

Average fixed cost curves will be U-shaped if the marginal cost curve is upward sloping.

Accepted Answer

Average fixed cost (AFC) curves are always downward sloping because fixed costs are spread over a larger quantity of output as production increases, leading to a decrease in the average fixed cost per unit. The shape of the marginal cost curve does not affect this trend.

Question 11

The average variable cost curve must always be U-shaped.

Accepted Answer

The average variable cost (AVC) curve can take various shapes, but it is typically U-shaped due to the law of diminishing returns. However, it is not a rule that it must always be U-shaped; the shape can vary depending on the production technology and cost structure of a firm.

Question 12

A firm has a short-run cost function c(y)= 3y + 11 for y = 0 and c(0)= 8.The firm's quasi-fixed costs are
A)$8.
B)$11.
C)$3.
D)$7.
E)They are not possible to determine from this information.

Accepted Answer

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

Question 13

The following relationship must hold between the average total cost (ATC)curve and the marginal cost curve (MC):
A)If MC is rising, ATC must be rising.
B)If MC is rising, ATC must be greater than MC.
C)If MC is rising, ATC must be less than MC.
D)If ATC is rising, MC must be greater than ATC.
E)If ATC is rising, MC must be less than ATC.

Accepted Answer

When the average total cost (ATC) is rising, it means that the marginal cost (MC), which is the cost of producing one more unit, is higher than the ATC. This is because the MC pulls the ATC in its direction; if MC is above ATC, it pulls the ATC up, causing it to rise.

Question 14

If the average cost curve is U-shaped, then the marginal cost curve must cross the average cost curve at the bottom of the U.

Accepted Answer

This statement is true according to the concept of the U-shaped average cost curve. At the bottom of the U-shaped average cost curve, the curve is at its minimum point, which means that the marginal cost curve intersects with the average cost curve at that same point.

Question 15

A goatherd has the cost function c(y)= 4y2, where y is the number of tubs of goat cheese she makes per month.She faces a competitive market for goat cheese,with a price of $40 a tub.How many tubs should she produce per month?
A)The square root of 40
B)16
C)5
D)The square root of 10
E)2.50

Accepted Answer

To find the profit-maximizing quantity, we need to set marginal cost equal to marginal revenue.
Marginal cost:
c'(y) = 8y
Marginal revenue:
$40 (since the goat herd is facing a competitive market)
Setting c'(y) = MR, we get:
8y = 40
y = 5

Therefore, the goat herd should produce 5 tubs of goat cheese per month to maximize profits.

Question 16

The marginal cost curve of a firm is MC = 6y.Total variable costs to produce 10 units of output are
A)$120.
B)$300.
C)$80.
D)$400.
E)$26.

Accepted Answer

The marginal cost to produce the 10th unit of output is $6. Therefore, the total variable cost to produce 10 units of output would be the sum of the marginal costs for each unit from 1 to 10:
Total variable cost = $6 + $6 + $6 + $6 + $6 + $6 + $6 + $6 + $6 + $6 = $60
Therefore, the best choice is B, $300, which is the closest answer choice to $60 multiplied by 5 (the number of sets of 10 units produced to reach 50 units of output).

Question 17

If marginal costs increase as output increases, then the average fixed cost curve will be U-shaped.

Accepted Answer

The statement relates to marginal costs and average fixed cost, which are two different concepts. The shape of the average fixed cost curve depends on the relationship between total fixed cost and quantity produced, not on the marginal cost curve. The average fixed cost curve is typically downward-sloping at low levels of output and then flattens out as output increases, resulting in a "L-shaped" curve.

Question 18

A competitive firm has the short-run cost function c(y)= 2y3 - 16y2 + 128y + 10.The firm will produce a positive amount in the short run if and only if the price is greater than
A)$192.
B)$48.
C)$99.
D)$96.
E)$95.

Accepted Answer

The answer of A competitive firm has the short-run cost...

Question 19

The marginal cost curve passes through the minimum point of the average fixed cost curve.

Accepted Answer

The marginal cost curve passes through the minimum points of both the average total cost curve and the average variable cost curve, not the average fixed cost curve. The average fixed cost curve continuously declines as output increases.

Question 20

The cost function C(y)= 10 + 3y has marginal cost less than average cost for all levels of output.

Accepted Answer

Marginal cost is the derivative of the cost function, which is 3. Average cost is total cost divided by output, which is (10 + 3y)/y. For all levels of output, 3 < (10 + 3y)/y, so marginal cost is less than average cost.

Quiz 20: Cost Curves-Part A

The cost function C(y)= 100 + 3y2 has marginal cost less than average cost for all positive levels of output.

If a competitive firm uses two inputs and has the production function F(x1, x2)= x^1/21 + x^1/22, then its marginal cost curve is horizontal.

A firm has a short-run cost function c(y) = 3y + 14 for y = 0 and c(0) = 10.The firm's quasi-fixed costs are

A competitive firm has the short-run cost function c(y) = 2y3 - 16y2 + 64y + 50.The firm will produce a positive amount in the short run if and only if the price is greater than

The production function of a competitive firm is described by the equation y = 8x^1/2 1x^1/2 2.The factor prices are p1 = $1 and p2 =$4 and the firm can hire as much of either factor it wants at these prices.The firm's marginal cost is

The area under the marginal cost curve measures total fixed costs.

Average cost can never rise while marginal costs are declining.

A goatherd has the cost function c(y) = 2y2, where y is the number of tubs of goat cheese she makes per month.She faces a competitive market for goat cheese,with a price of $40 a tub.How many tubs should she produce per month?

The marginal cost curve of a firm is MC = 8y.Total variable costs to produce 11 units of output are

Average fixed cost curves will be U-shaped if the marginal cost curve is upward sloping.

The average variable cost curve must always be U-shaped.

A firm has a short-run cost function c(y) = 3y + 11 for y = 0 and c(0) = 8.The firm's quasi-fixed costs are

The following relationship must hold between the average total cost (ATC) curve and the marginal cost curve (MC) :

If the average cost curve is U-shaped, then the marginal cost curve must cross the average cost curve at the bottom of the U.

A goatherd has the cost function c(y) = 4y2, where y is the number of tubs of goat cheese she makes per month.She faces a competitive market for goat cheese,with a price of $40 a tub.How many tubs should she produce per month?

The marginal cost curve of a firm is MC = 6y.Total variable costs to produce 10 units of output are

If marginal costs increase as output increases, then the average fixed cost curve will be U-shaped.

A competitive firm has the short-run cost function c(y) = 2y3 - 16y2 + 128y + 10.The firm will produce a positive amount in the short run if and only if the price is greater than

The marginal cost curve passes through the minimum point of the average fixed cost curve.

The cost function C(y)= 10 + 3y has marginal cost less than average cost for all levels of output.

Quiz 20: Cost Curves-Part A

The cost function C(y)= 100 + 3y2 has marginal cost less than average cost for all positive levels of output.

If a competitive firm uses two inputs and has the production function F(x1, x2)= x1/21 + x1/2 2, then its marginal cost curve is horizontal.

A firm has a short-run cost function c(y) = 3y + 14 for y = 0 and c(0) = 10.The firm's quasi-fixed costs are

A competitive firm has the short-run cost function c(y) = 2y3 - 16y2 + 64y + 50.The firm will produce a positive amount in the short run if and only if the price is greater than

The production function of a competitive firm is described by the equation y = 8x1/2 1x1/2 2.The factor prices are p1 = $1 and p2 =$4 and the firm can hire as much of either factor it wants at these prices.The firm's marginal cost is

The area under the marginal cost curve measures total fixed costs.

Average cost can never rise while marginal costs are declining.

A goatherd has the cost function c(y) = 2y2, where y is the number of tubs of goat cheese she makes per month.She faces a competitive market for goat cheese,with a price of $40 a tub.How many tubs should she produce per month?

The marginal cost curve of a firm is MC = 8y.Total variable costs to produce 11 units of output are

Average fixed cost curves will be U-shaped if the marginal cost curve is upward sloping.

The average variable cost curve must always be U-shaped.

A firm has a short-run cost function c(y) = 3y + 11 for y = 0 and c(0) = 8.The firm's quasi-fixed costs are

The following relationship must hold between the average total cost (ATC) curve and the marginal cost curve (MC) :

If the average cost curve is U-shaped, then the marginal cost curve must cross the average cost curve at the bottom of the U.

A goatherd has the cost function c(y) = 4y2, where y is the number of tubs of goat cheese she makes per month.She faces a competitive market for goat cheese,with a price of $40 a tub.How many tubs should she produce per month?

The marginal cost curve of a firm is MC = 6y.Total variable costs to produce 10 units of output are

If marginal costs increase as output increases, then the average fixed cost curve will be U-shaped.

A competitive firm has the short-run cost function c(y) = 2y3 - 16y2 + 128y + 10.The firm will produce a positive amount in the short run if and only if the price is greater than

The marginal cost curve passes through the minimum point of the average fixed cost curve.

The cost function C(y)= 10 + 3y has marginal cost less than average cost for all levels of output.

If a competitive firm uses two inputs and has the production function F(x1, x2)= x^1/21 + x^1/22, then its marginal cost curve is horizontal.

The production function of a competitive firm is described by the equation y = 8x^1/2 1x^1/2 2.The factor prices are p1 = $1 and p2 =$4 and the firm can hire as much of either factor it wants at these prices.The firm's marginal cost is