CHAPTER 22: Cost Curves
TRUE/FALSE
1. The average variable cost curve must always be U-shaped.
2. The marginal cost curve passes through the minimum point of the average fixed cost curve.
3. 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.
4. The cost function C(y) = 10 + 3y has marginal cost less than average cost for all levels of output.
5. The cost function C(y) = 100 + 3y2 has marginal cost less than average cost for all positive levels of
output.
6. 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.
7. Average cost can never rise while marginal costs are declining.
8. The area under the marginal cost curve measures total fixed costs.
9. If marginal costs increase as output increases, then the average fixed cost curve will be U-shaped.
10. Average fixed cost curves will be U-shaped if the marginal cost curve is upward sloping.
MULTIPLE CHOICE
1. 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.
2. 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.
3. 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.
4. 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
5. 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
6. 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.
7. 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.
8. 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.
9. 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.
10. 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
a.
constant and equal to .50.
b.
constant and equal to 3.
c.
increasing.
d.
decreasing.
e.
None of the above.
11. The production function of a competitive firm is described by the equation y = 4x1/2 1x1/2 2. The factor
prices are p1 = $1 and p2 = $36 and the firm can hire as much of either factor it wants at these prices.
The firm’s marginal cost is
a.
decreasing.
b.
constant and equal to 19.
c.
constant and equal to 3.
d.
increasing.
e.
None of the above.
12. A firm has the short-run total cost function c(y) = 4y2 + 100. At what quantity of output is short-run
average cost minimized?
a.
5
b.
2
c.
25
d.
0.40
e.
None of the above.
13. A firm has the short-run total cost function c(y) = 9y2 + 144. At what quantity of output is short-run
average cost minimized?
a.
4
b.
16
c.
0.75
d.
3
e.
None of the above.
14. A firm has the production function Q = X1/21X2. In the short run it must use exactly 15 units of factor 2.
The price of factor 1 is $75 per unit and the price of factor 2 is $2 per unit. The firm’s short-run
marginal cost function is
a.
MC(Q) = 10Q/15.
b.
MC(Q) = 30Q1/2.
c.
MC(Q) = 30 + 75Q2.
d.
MC(Q) = 2Q.
e.
MC(Q) = 15Q1/2.
15. A firm has the production function Q = X1/21X2. In the short run it must use exactly 35 units of factor 2.
The price of factor 1 is $105 per unit and the price of factor 2 is $3 per unit. The firm’s short-run
marginal cost function is
a.
MC(Q) = 105Q-1/2.
b.
MC(Q) = 6Q/35.
c.
MC(Q) = 105 + 105Q2.
d.
MC(Q) = 3Q.
e.
MC(Q) = 35Q-1/2.
16. Mr. Dent Carr’s total costs are 2s2 + 40s + 40. If he repairs 10 cars, his average variable costs will be
a.
$60.
b.
$64.
c.
$80.
d.
$120.
e.
$40.
17. Mr. Dent Carr’s total costs are 2s2 + 45s + 30. If he repairs 15 cars, his average variable costs will be
a.
$77.
b.
$75.
c.
$150.
d.
$105.
e.
$52.50.
18. Rex Carr could pay $10 for a shovel that lasts one year and pay $5 a car to his brother Scoop to bury
the cars, or he could buy a low-quality car smasher that costs $200 a year to own and that smashes cars
at a marginal cost of $1 per car. If it were also possible for Rex to buy a high-quality hydraulic car
smasher that cost $650 per year to own and if with this smasher he could dispose of cars at a cost of
$.67 per car, it would be worthwhile for him to buy this high-quality smasher if he needed to dispose
of
a.
at least 1,350 cars per year.
b.
no more than 675 cars per year.
c.
at least 1,360 cars per year.
d.
no more than 1,350 cars per year.
e.
at least 675 cars per year.
19. Rex Carr could pay $10 for a shovel that lasts one year and pay $5 a car to his brother Scoop to bury
the cars, or he could buy a low-quality car smasher that costs $200 a year to own and that smashes cars
at a marginal cost of $1 per car. If it were also possible for Rex to buy a high-quality hydraulic car
smasher that cost $550 per year to own and if with this smasher he could dispose of cars at a cost of
$.67 per car, it would be worthwhile for him to buy this high-quality smasher if he needed to dispose
of
a.
no more than 525 cars per year.
b.
no more than 1,050 cars per year.
c.
at least 1,060 cars per year.
d.
at least 1,050 cars per year.
e.
at least 525 cars per year.
20. Mary Magnolia from your workbook has variable costs equal to y2/F, where y is the number of
bouquets she sells per month and where F is the number of square feet of space in her shop. If Mary
has signed a lease for a shop with 200 square feet, if she is not able to get out of the lease or to expand
her store in the short run, and if the price of a bouquet is $6 per unit, how many bouquets per month
should she sell in the short run?
a.
200
b.
100
c.
600
d.
900
e.
660
21. Mary Magnolia from your workbook has variable costs equal to y2/F, where y is the number of
bouquets she sells per month and where F is the number of square feet of space in her shop. If Mary
has signed a lease for a shop with 600 square feet, if she is not able to get out of the lease or to expand
her store in the short run, and if the price of a bouquet is $4 per unit, how many bouquets per month
should she sell in the short run?
a.
600
b.
1,800
c.
300
d.
1,200
e.
1,320
22. Touchie McFeelie from your workbook has a production function (0.1)J1/2 J3/4, where J is the number
of old jokes used and L is the number of hours of cartoonists’ labor. Touchie is stuck with 400 old
jokes for which he paid 4 dollars each. If the hourly wage rate for cartoonists is 5 dollars, then the total
cost of producing 16 comics books is
a.
1,680 dollars.
b.
840 dollars.
c.
2,520 dollars.
d.
1,696 dollars.
e.
420 dollars.
23. Touchie McFeelie from your workbook has a production function (0.1)J1/2 J3/4, where J is the number
of old jokes used and L is the number of hours of cartoonists’ labor. Touchie is stuck with 400 old
jokes for which he paid 6 dollars each. If the hourly wage rate for cartoonists is 4 dollars, then the total
cost of producing 16 comics books is
a.
2,464 dollars.
b.
1,232 dollars.
c.
2,480 dollars.
d.
3,696 dollars.
e.
616 dollars.
24. Touchie McFeelie’s production function for comic books is (0.1)J1/2 J3/4, where J is the number of
jokes and L is the number of hours of cartoonists labor that he uses. If Touchie can vary both jokes and
cartoonists’ labor and if old jokes cost $3 each and cartoonists’ labor costs $18 per hour, then the
cheapest way to produce comics books requires using jokes and labor in the ratio J/L =
a.
6.
b.
8.
c.
2.
d.
2/3.
e.
4.
25. Touchie McFeelie’s production function for comic books is (0.1)J1/2 J3/4, where J is the number of
jokes and L is the number of hours of cartoonists labor that he uses. If Touchie can vary both jokes and
cartoonists’ labor and if old jokes cost $2 each and cartoonists’ labor costs $18 per hour, then the
cheapest way to produce comics books requires using jokes and labor in the ratio J/L =
a.
3.
b.
12.
c.
9.
d.
2/3.
e.
6.
26. A firm’s production function is given by q = minM, L1/2, where M is the number of machines and L
is the amount of labor that it uses. The price of labor is $1and the price of machines is $2 per unit. The
firm’s long-run marginal cost curve is
a.
a straight line with slope 2.
b.
upward sloping and gets flatter as Q increases.
c.
upward sloping and gets steeper as Q increases.
d.
a straight line with slope 1.
e.
a straight line with slope 2.
27. A firm’s production function is given by q = minM, L1/2, where M is the number of machines and L
is the amount of labor that it uses. The price of labor is $1and the price of machines is $4 per unit. The
firm’s long-run marginal cost curve is
a.
upward sloping and gets flatter as Q increases.
b.
a straight line with slope 2.
c.
a straight line with slope 1.
d.
upward sloping and gets steeper as Q increases.
e.
a straight line with slope 4.
28. In the reclining chair industry (which is perfectly competitive), two different technologies of
production exist. These technologies exhibit the following total cost functions:
C1(Q) = 1,000 + 600Q − 40Q2 + Q3
C2(Q) = 200 + 145Q− 10Q2 + Q3
Due to foreign competition, the market price of reclining chairs has fallen to $190. In the short run,
firms using technology 1
a.
and firms using technology 2 will remain in business.
b.
will remain in business and firms using technology 2 will shut down.
c.
will shut down and firms using technology 2 will remain in business.
d.
and firms using technology 2 will shut down.
e.
More information is needed to make a judgment.
29. In the reclining chair industry (which is perfectly competitive), two different technologies of
production exist. These technologies exhibit the following total cost functions:
C1(Q) = 500 + 560Q − 40Q2 + Q3
C2(Q) = 600 + 280Q − 20Q2 + Q3
Due to foreign competition, the market price of reclining chairs has fallen to $170. In the short run,
firms using technology 1
a.
and firms using technology 2 will remain in business.
b.
will remain in business and firms using technology 2 will shut down.
c.
will shut down and firms using technology 2 will remain in business.
d.
and firms using technology 2 will shut down.
e.
More information is needed to make a judgment.
30. A firm has the long-run cost function C(Q) = 4Q2 + 64.In the long run, it will supply a positive amount
of output, so long as the price is greater than
a.
$64.
b.
$72.
c.
$16.
d.
$32.
e.
$37.
31. A firm has the long-run cost function C(Q) = 4Q2 + 196. In the long run, it will supply a positive
amount of output, so long as the price is greater than
a.
$120.
b.
$112.
c.
$56.
d.
$28.
e.
$61.
32. The VCR manufacturing business is perfectly competitive.Suppose that currently, firms that
manufacture VCRs utilize either technology 1 or technology 2,whose cost functions are
TC1(Q) = 340 − 20Q + Q2
TC2(Q) = 405 − 30Q + Q2
In the long run, assuming no new manufacturing technologies,what will happen in this industry?
a.
Firms utilizing technology 1 and firms utilizing technology 2 will stay in business.
b.
Firms utilizing technology 1 will stay in business, but firms utilizing technology 2 will
shut down.
c.
Firms utilizing technology 1 will shut down, but firms utilizing technology 2 will stay in
business.
d.
Firms utilizing technology 1 and firms utilizing technology 2 will shut down.
e.
None of the above.
33. The VCR manufacturing business is perfectly competitive. Suppose that currently, firms that
manufacture VCRs utilize either technology 1 or technology 2, whose cost functions are
TC1(Q) = 1,120 − 60Q + Q2
TC2(Q) = 300 − 20Q + Q2
In the long run, assuming no new manufacturing technologies,what will happen in this industry?
a.
Firms utilizing technology 1 and firms utilizing technology 2 will stay in business.
b.
Firms utilizing technology 1 will shut down, but firms utilizing technology 2 will stay in
business.
c.
Firms utilizing technology 1 will stay in business, but firms utilizing technology 2 will
shut down.
d.
Firms utilizing technology 1 and firms utilizing technology 2 will shut down.
e.
None of the above.
34. The snow removal business in East Icicle, Minnesota,is a competitive industry. All snowplow
operators have the cost function C = Q2 + 4, where Q is the number of driveways cleared. Demand for
snow removal in the town is given by Qd = 120 − P. The long-run equilibrium number of firms in this
industry is
a.
29.
b.
58.
c.
56.
d.
120.
e.
59.
35. The snow removal business in East Icicle, Minnesota,is a competitive industry. All snowplow
operators have the cost function C = Q2 + 4, where Q is the number of driveways cleared. Demand for
snow removal in the town is given by Qd = 120 − P. The long-run equilibrium number of firms in this
industry is
a.
120.
b.
29.
c.
56.
d.
58.
e.
59.
36. Florence’s Restaurant estimates that its total costs of providing Q meals per month is given by
TC = 8,000 + 6Q. If Florence charges $7 per meal, what is its break even level of output?
a.
1,333.33 meals
b.
1,142.86 meals
c.
615.38 meals
d.
16,000 meals
e.
8,000 meals
37. Florence’s Restaurant estimates that its total costs of providing Q meals per month is given by
TC = 8,000 + 5Q. If Florence charges $9 per meal, what is its break even level of output?
a.
4,000 meals
b.
571.43 meals
c.
888.89 meals
d.
1,600 meals
e.
2,000 meals
38. If Green Acres Turf Farm’s total cost of producing acres of sod is TC = 4Q2 + 25Q + 30, the marginal
cost of producing the 20th acre of sod is
a.
$30.
b.
$25.
c.
$105.
d.
$185.
e.
$345.
39. If Green Acres Turf Farm’s total cost of producing acres of sod is TC = 5Q2 + 25Q + 40, the marginal
cost of producing the 10th acre of sod is
a.
$125.
b.
$40.
c.
$25.
d.
$75.
e.
$275.
PROBLEM
1. Not long ago, the Canadian edition of a famous textbook on principles of economics had a diagram
depicting a U-shaped average fixed cost curve. This occasioned great mirth around the campfires of
some economists in the Great White North and did much to shorten a long hard winter. Explain what is
wrong with drawing a U-shaped average fixed cost curve.
2. Hildegard, an intelligent and charming Holstein cow,grazes in a very large, mostly barren pasture with
a few patches of lush grass. When she finds a new grassy area, the amount of grass she gets from it is
equal to the square root of the number of hours, h, that she spends grazing there. Finding a new patch
of grass on which to graze takes her 1 hour. Since Hildegard does not have pockets, the currency in
which her costs are measured is time.
a. What is the total cost to Hildegard of finding a new plot of grass and getting y units of grass from
it?
b. Find an expression for her marginal costs and her average cost per patch of grass as a function of
the amount of grass she gets from each patch.
c. How much time would she spend in each plot if she wanted to maximize her food intake? (Hint:
Minimize average costs per unit of grass eaten.)
3. A competitive firm has the short-run cost function c(y) = y3 −2y2 + 5y + 6. Write down equations for:
a. The firm’s average variable cost function
b. The firm’s marginal cost function
c. At what level of output is average variable cost minimized?
d. Graph the short-run supply function for this firm, being careful to label the key points on the graph
with the numbers specifying the exact prices and quantities at these points.
4. North American Manufacturing has the production function Q = min0.25K, 0.5L, where K is units of
capital and L is hours of labor.
a. Without any warning, the price of capital doubles.What should North American Manufacturing do
in response?
b. If North American were planning a new manufacturing plant, would there be any advantages to a
larger facility?