CHAPTER 21: Cost Minimization
MULTIPLE CHOICE
1. Suppose that Nadine in Problem 1 has a production function 3x1 + x2. If the factor prices are $3 for
factor 1 and $3 for factor 2, how much will it cost her to produce 80 units of output?
a.
$960
b.
$80
c.
$240
d.
$600
e.
$160
2. Suppose that Nadine in Problem 1 has a production function 4x1 + x2. If the factor prices are $4 for
factor 1 and $2 for factor 2, how much will it cost her to produce 70 units of output?
a.
$700
b.
$1,260
c.
$140
d.
$70
e.
$105
3. Suppose that Nadine in Problem 1 has a production function 3x1 + x2. If the factor prices are $12 for
factor 1 and $3 for factor 2, how much will it cost her to produce 20 units of output?
a.
$430
b.
$780
c.
$60
d.
$80
e.
$70
4. Suppose that Nadine in Problem 1 has a production function 4x1 + x2. If the factor prices are $12 for
factor 1 and $2 for factor 2, how much will it cost her to produce 50 units of output?
a.
$100
b.
$2,500
c.
$150
d.
$1,325
e.
$125
5. Suppose that Nadine in Problem 1 has a production function 5x1 + x2. If the factor prices are $10 for
factor 1 and $3 for factor 2, how much will it cost her to produce 70 units of output?
a.
$1,960
b.
$3,710
c.
$140
d.
$210
e.
$175
6. In Problem 2, suppose that a new alloy is invented which uses copper and zinc in fixed proportions
where 1 unit of output requires 3 units of copper and 3 units of zinc for each unit of alloy produced. If
no other inputs are needed, the price of copper is $3, and the price of zinc is $3, what is the average
cost per unit when 4,000 units of the alloy are produced?
a.
$9.50
b.
$1,000
c.
$1
d.
$18
e.
$9,500
7. In Problem 2, suppose that a new alloy is invented which uses copper and zinc in fixed proportions
where 1 unit of output requires 5 units of copper and 3 units of zinc for each unit of alloy produced. If
no other inputs are needed, the price of copper is $4, and the price of zinc is $2, what is the average
cost per unit when 3,000 units of the alloy are produced?
a.
$26
b.
$13.33
c.
$666.67
d.
$.67
e.
$13,333.33
8. In Problem 2, suppose that a new alloy is invented which uses copper and zinc in fixed proportions
where 1 unit of output requires 4 units of copper and 4 units of zinc for each unit of alloy produced. If
no other inputs are needed, the price of copper is $5, and the price of zinc is $2, what is the average
cost per unit when 2,000 units of the alloy are produced?
a.
$14.25
b.
$.50
c.
$28
d.
$500
e.
$14,250
9. In Problem 2, suppose that a new alloy is invented which uses copper and zinc in fixed proportions
where 1 unit of output requires 3 units of copper and 3 units of zinc for each unit of alloy produced. If
no other inputs are needed, the price of copper is $4, and the price of zinc is $5, what is the average
cost per unit when 4,000 units of the alloy are produced?
a.
$1.33
b.
$14.17
c.
$1,333.33
d.
$27
e.
$14,166.67
10. In Problem 2, suppose that a new alloy is invented which uses copper and zinc in fixed proportions
where 1 unit of output requires 3 units of copper and 4 units of zinc for each unit of alloy produced. If
no other inputs are needed, the price of copper is $2, and the price of zinc is $3, what is the average
cost per unit when 3,000 units of the alloy are produced?
a.
$18
b.
$.67
c.
$666.67
d.
$9.33
e.
$9,333.33
11. In Problem 3, the production function is f(L, M) = 4L1/2 M1/2, where L is the number of units of labor
and M is the number of machines used. If the cost of labor is $100 per unit and the cost of machines is
$16 per unit, then the total cost of producing 7 units of output will be
a.
$140.
b.
$406.
c.
$112.
d.
$280.
e.
None of the above.
12. In Problem 3, the production function is f(L, M) = 4L1/2 M1/2, where L is the number of units of labor
and M is the number of machines used. If the cost of labor is $9 per unit and the cost of machines is
$81 per unit, then the total cost of producing 10 units of output will be
a.
$270.
b.
$90.
c.
$135.
d.
$450.
e.
None of the above.
13. In Problem 3, the production function is f(L, M) = 4L1/2 M1/2, where L is the number of units of labor
and M is the number of machines used. If the cost of labor is $49 per unit and the cost of machines is
$25 per unit, then the total cost of producing 7 units of output will be
a.
$122.50.
b.
$259.
c.
$175.
d.
$245.
e.
None of the above.
14. In Problem 3, the production function is f(L, M) = 4L1/2 M1/2, where L is the number of units of labor
and M is the number of machines used. If the cost of labor is $25 per unit and the cost of machines is
$64 per unit, then the total cost of producing 6 units of output will be
a.
$240.
b.
$150.
c.
$267.
d.
$120.
e.
None of the above.
15. In Problem 3, the production function is f(L, M) = 4L1/2 M1/2, where L is the number of units of labor
and M is the number of machines used. If the cost of labor is $49 per unit and the cost of machines is
$36 per unit, then the total cost of producing 4 units of output will be
a.
$84.
b.
$170.
c.
$144.
d.
$168.
e.
None of the above.
16. Suppose that in the short run, the firm in Problem 3 which has production function F(L, M) = 4L1/2M1/2
must use 4 machines. If the cost of labor is $10 per unit and the cost of machines is $6 per unit, the
short-run total cost of producing 64 units of output is
a.
$512.
b.
$384.
c.
$640.
d.
$1,328.
e.
$664.
17. Suppose that in the short run, the firm in Problem 3 which has production function F(L, M) = 4L1/2M1/2
must use 9 machines. If the cost of labor is $5 per unit and the cost of machines is $6 per unit, the
short-run total cost of producing 84 units of output is
a.
$598.
b.
$420.
c.
$462.
d.
$504.
e.
$299.
18. Suppose that in the short run, the firm in Problem 3 which has production function F(L, M) = 4L1/2M1/2
must use 9 machines. If the cost of labor is $10 per unit and the cost of machines is $4 per unit, the
short-run total cost of producing 60 units of output is
a.
$420.
b.
$600.
c.
$240.
d.
$572.
e.
$286.
19. Suppose that in the short run, the firm in Problem 3 which has production function F(L, M) = 4L1/2M1/2
must use 9 machines. If the cost of labor is $5 per unit and the cost of machines is $5 per unit, the
short-run total cost of producing 108 units of output is
a.
$900.
b.
$540.
c.
$540.
d.
$540.
e.
$450.
20. Suppose that in the short run, the firm in Problem 3 which has production function F(L, M) = 4L1/2M1/2
must use 9 machines. If the cost of labor is $7 per unit and the cost of machines is $9 per unit, the
short-run total cost of producing 96 units of output is
a.
$1,058.
b.
$672.
c.
$864.
d.
$768.
e.
$529.
21. In Problem 12, Al’s production function for deer is f(x1, x2) = (2x1 + x2)1/2, where x1 is the amount of
plastic and x2 is the amount of wood used. If the cost of plastic is $8 per unit and the cost of wood is $1
per unit, then the cost of producing 7 deer is
a.
$49.
b.
$119.
c.
$196.
d.
$7.
e.
$28.
22. In Problem 12, Al’s production function for deer is f(x1, x2) = (2x1 + x2)1/2, where x1 is the amount of
plastic and x2 is the amount of wood used. If the cost of plastic is $4 per unit and the cost of wood is $4
per unit, then the cost of producing 8 deer is
a.
$16.
b.
$96.
c.
$256.
d.
$128.
e.
$32.
23. In Problem 12, Al’s production function for deer is f(x1, x2) = (2x1 + x2)1/2, where x1 is the amount of
plastic and x2 is the amount of wood used. If the cost of plastic is $4 per unit and the cost of wood is $1
per unit, then the cost of producing 4 deer is
a.
$32.
b.
$16.
c.
$36.
d.
$4.
e.
$8.
24. In Problem 12, Al’s production function for deer is f(x1, x2) = (2x1 + x2)1/2, where x1 is the amount of
plastic and x2 is the amount of wood used. If the cost of plastic is $8 per unit and the cost of wood is $3
per unit, then the cost of producing 5 deer is
a.
$15.
b.
$100.
c.
$95.
d.
$75.
e.
$20.
25. In Problem 12, Al’s production function for deer is f(x1, x2) = (2x1 + x2)1/2, where x1 is the amount of
plastic and x2 is the amount of wood used. If the cost of plastic is $4 per unit and the cost of wood is $3
per unit, then the cost of producing 5 deer is
a.
$55.
b.
$10.
c.
$50.
d.
$75.
e.
$15.
26. Two firms, Wickedly Efficient Widgets (WEW) and Wildly Nepotistic Widgets (WNW), both produce
widgets with the same production function y = K1/2L1/2, where K is the input of capital and L is the
input of labor. Each company can hire labor at $1 per unit and capital at $1 per unit. WEW produces
10 widgets per week, choosing its input combination so as to produce these 10 widgets in the cheapest
way possible. WNW also produces 10 widgets per week, but its dotty CEO requires it to use twice as
much labor as WEW uses. Given that it must use twice as many laborers as WEW does and must
produce the same output, how much larger are WNW’s total costs than WEW’s?
a.
$10 per week
b.
$20 per week
c.
$15 per week
d.
$5 per week
e.
$2 per week