Question

Problem 05-02 A firm's product sells for $4 per unit in a highly competitive market. The firm produces output using capital (which it rents at $25 per hour) and labor (which is paid a wage of $30 per hour under a contract for 20 hours of labor services). Complete the following table and use that information to answer the questions that follow. Instruction: Round your answers for Average Product of Capital and Average Product of Labor to 2 decimal places. V5) 67) Marginal Average Average Value Marginal Product of Product of Product of Product of Capital Capital MPK Capital APK Labor APL VMPK Capital Labor Output 100 300 150 a. Identify the fixed and variable inputs. Labor is the fixed input and capital is the variable input. Capital and labor are fixed inputs. Capital and labor are variable inputs. Capital is the fixed input and labor is the variable input. b. What are the firm's fixed costs? $ c. What is the variable cost of producing 475 units of output? $ d. How many units of the variable input should be used to maximize profits? e. What are the maximum profits this firm can earn? $ f. Over what range of the variable input usage do increasing marginal returns exist? From g. Over what range of the variable input usage do decreasing marginal returns exist? From t o

Answer 1

Capital	labor	Output	MPk	APK	APL	VMPk
0	20	0	NA	NA	NA	NA
1	20	50	50	50.0	2.5	200
2	20	150	100	75.0	7.5	400
3	20	300	150	100.0	15	600
4	20	400	100	100.0	20	400
5	20	450	50	90.0	22.5	200
6	20	475	25	79.2	23.75	100
7	20	475	0	67.9	23.75	0
8	20	450	-25	56.3	22.5	-100
9	20	400	-50	44.4	20	-200
10	20	300	-100	30.0	15	-400
11	20	150	-150	13.6	7.5	-600

Note: MPk = (Change in output) / (change in Capital)

APk = Output / Capital

APL = Output / Labor

VMPk = (Price of output) * (MPk)

(a) Labor is fixed input and capital is variable input

answer: Option (A)

(b) Wage rate is $30 per hour

labor is fixed at 20 hours

fixed cost = ($30) * (20)

Fixed cost = $600

Answer: $600

(c) 7 Units of capital are required to produce 475 units of output. The capital rental rate is $25.

The variable cost of producing 475 units of output = ($25) * (7)

The variable cost of producing 475 units of output = $175

Answer: $175

(d) the number of capital which maximizes the profit occurs at the point where MPk = rental rate

MPk = rental rate = $25 corresponding to 6 units of capital.

Answer: 6 units

(e) 6 units of capital with 20 units of labor are producing 475 units of output.

variable cost = ($25) (6) = $150

Fixed cost = $600

Total cost of producing 475 units = $150 + $600 = $750

Total revenue from 475 units = (475) * ($4) = $1900

Profit = TR -TC

Profit = $1900 - $600

Profit = $1300

answer: $1300

(f) Increasing marginal returns exist from 1 unit of capital to 4 units of capital.

the MPk is increasing between 1 unit to 4 units of capital

(g) decreasing marginal returns exist from 5 units of capiatl to 7 units of capital.

In this range, MPk is decreasing but remains positive.

Answer 2

e) 6 units of capital with 20 units of labor are producing 475 units of output.

variable cost = ($25) (6) = $150

Fixed cost = $600

Total cost of producing 475 units = $150 + $600 = $750

Total revenue from 475 units = (475) * ($4) = $1900

Profit = TR -TC

Profit = $1900 - $750

Profit = $1150

answer: $1150