Deck 21: B: Cost Minimization

Question 1

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

Answer 1

$18

Question 2

In Problem 3,the production function is f(L,M)=4L^1/2 M^1/2,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.

Answer 2

$140.

Question 3

Suppose that in the short run,the firm in Problem 3 which has production function F(L,M)=4L^1/2M^1/2 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.

Answer 3

$664.

Question 4

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

Question 5

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

Question 6

In Problem 3,the production function is f(L,M)= 4L^1/2 M^1/2,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.

Question 7

Suppose that in the short run,the firm in Problem 3 which has production function F(L,M)=4L^1/2M^1/2 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.

Question 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 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

Question 9

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

Question 10

Suppose that in the short run,the firm in Problem 3 which has production function F(L,M)=4L^1/2M^1/2 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.

Question 11

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

Question 12

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

Question 13

In Problem 3,the production function is f(L,M)=4L^1/2 M^1/2,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.

Question 14

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

Question 15

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

Question 16

In Problem 3,the production function is f(L,M)= 4L^1/2 M^1/2,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.

Question 17

Suppose that in the short run,the firm in Problem 3 which has production function F(L,M)=4L^1/2M^1/2 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) -$900.
E) $450.

Question 18

In Problem 3,the production function is f(L,M)= 4L^1/2 M^1/2,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.

Question 19

Suppose that in the short run,the firm in Problem 3 which has production function F(L,M)=4L^1/2M^1/2 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.

Question 20

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

Question 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 $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.

Question 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 $1 per unit,then the cost of producing 4 deer is

A) $32.
B) $16.
C) $36.
D) $4.
E) $8.

Question 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 $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.

Question 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 $1 per unit,then the cost of producing 7 deer is

A) $49.
B) $119.
C) $196.
D) $7.
E) $28.

Question 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.

Question 26

Two firms,Wickedly Efficient Widgets (WEW)and Wildly Nepotistic Widgets (WNW),both produce widgets with the same production function y =K^1/2L^1/2,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