Question

Assume that a firm that manufactures widgets can produce them with one of the three processes, used alone or in combination. The following table indicates the amounts of capital and labor required by each of the three processes to produce one widget.

	Units of Labor	Units of Capital
Process 1	1	4
Process 2	2	2
Process 3	4	1

a) Assume capital costs $5 per unit and labor costs $15 per unit. Which process will be employed?

b) Determine the variable costs for quantities 10, 30, and 50 for each process.

c) For each of three output levels, how much capital and labor will be demanded?

d) Repeat numbers 1 and 3 assuming the price of capital is $10 and the price of labor is $8 per unit.

e) Explain how you can use numbers 1 and 3 of this problem to explain the impact of organized labor asking for a wage increase.

Answer 1

Answer.

1. A firm will use that process which costs least to produce one widget.

Cost of capital = $5

Cost of labor = $15

Process 1

1 unit of labor and 4 unit of capital

Total cost = 1*15 + 5*4

                   = 35

Process 2

2 unit of labor and 2 unit of capital

Total cost = 2*15 + 5*2

                   = 40

Process 3

4 unit of labor and 1 unit of capital

Total cost = 4*15 + 5*1

                   = 65

The firm will choose process 1 because it will cost least.

1. Labor employment is a variable cost for a firm

At output level 10

Process 1

Variable cost = 1*15*10

                         = 150

Process 2

Variable cost = 2*15*10

                         = 300

Process 3

Variable cost = 4*15*10

                         = 600

At output level 30

Process 1

Variable cost = 1*15*30

                         = 450

Process 2

Variable cost = 2*15*30

                         = 900

Process 3

Variable cost = 4*15*30

                         = 1800

At output level 50

Process 1

Variable cost = 1*15*50

                         = 750

Process 2

Variable cost = 2*15*50

                         = 1500

Process 3

Variable cost = 4*15*50

                         = 3500

1. Capital and labor demanded at all three levels of output

The firm will demand combination which cost the least.

Process 1 will always cost least as the cost of labor very high relative to the cost of capital

For output level 10

The firm will demand 1 unit of labor and 4 unit of capital to produce 1 unit of a widget

So to produce 10 widgets, the firm will demand

1*10, 4*10

So firm will demand 10 units of labor and 40 units of capital

For output level 30

The firm will demand 1 unit of labor and 4 unit of capital to produce 1 unit of a widget

So to produce 30 widgets, a firm will demand

1*30, 4*30

So firm will demand 30 units of labor and 120 units of capital

For output level 50

The firm will demand 1 unit of labor and 4 unit of capital to produce 1 unit of a widget

So to produce 30 widgets, a firm will demand

1*50, 4*50

So firm will demand 50 units of labor and 200 units of capital

1. If the cost of labor changes to $8 and capital $8

Process 1

1 unit of labor and 4 unit of capital

Total cost = 1*8 + 10*4

                   = 48

Process 2

2 unit of labor and 2 unit of capital

Total cost = 2*8 + 10*2

                   = 36

Process 3

4 unit of labor and 1 unit of capital

Total cost = 4*8 + 5*10

                   = 42

The firm will choose process2 because it will cost least.

Process 2 will always cost least as the cost of labor very high relative to the cost of capital

For output level 10

The firm will demand 1 unit of labor and 4 unit of capital to produce 1 unit of a widget

So to produce 10 widgets, a firm will demand

2*10, 2*10

So firm will demand 20 units of labor and 20 units of capital

For output level 30

The firm will demand 2 unit of labor and 2 unit of capital to produce 1 unit of a widget

So to produce 30 widgets, a firm will demand

2*30, 2*30

So firm will demand 60 units of labor and 60 units of capital

For output level 50

A firm will demand 2 unit of labor and 2 unit of capital to produce 1 unit of a widget

So to produce 30 widgets, a firm will demand

2*50, 2*50

So firm will demand 100 units of labor and 100 units of capital