# Calculating various production costs

Use the following information on a hypothetical short-run production function to answer questions a-d.

Units of Labor/Day 5 6 7 8 9

Units of Output/Day 120 140 155 165 168

The price of labor is $20 per day. Ten units of capital are used each day, regardless of output level. The price of capital is $50 per unit.

a. Calculate the marginal and average variable product of each unit of labor input. Hint: plot your Units of labor and Units of Output vertically.

b. Calculate total, average total, average variable, and marginal costs.

c. Can you tell where diminishing marginal returns sets in?

d. Graph the resulting cost curves similar to the graph 5.2 on Page 141 of the textbook.

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#### Solution Preview

Please refer attached file for better clarity of tables and graphs. Graphs are not visible in this section.

Solution:

a. Calculate the marginal and average variable product of each unit of labor input. Hint: plot your Units of labor and Units of Output vertically

Table 1

Output Labor Capital Marginal Product of labor Average Variable Product

Change in Output/Change in labor Output/Labor

120 5 10 24.0

140 6 10 20 ...

#### Solution Summary

Solution describes the steps for calculating variable costs, fixed costs, total costs, average variable cost, average fixed cost and maginal costs. It also explains where diminishing returns take place.

Analyzing and Calculating Production Costs

Please refer attached file for better clarity of tables and expressions.

1. Consider the following table of numbers, which represents demand and cost conditions for a competitive firm.

(a) Fill in the missing values.

(b) What level of output should the firm produce? Explain.

P = MR Q TFC AFC TVC AVC TC ATC MC TR Total Profit

600 0 - 0 - 570 -

600 1 570 240

600 2 430

600 3 670

600 4 960

600 5 1350

600 6 1840

600 7 2430

600 8 3120

600 9 3910

600 10 4800

2. You own four firms that produce different products. The following table summarizes the conditions in each firm. After calculating the missing numbers for each firm, make one of the following four decisions regarding operations in each firm, and explain why a particular decision is reached.

(a) continue producing the same output level

(b) shut down

(c) increase output

(d) decrease output

Firm P MR TR Q TC MC ATC AVC

A 11 8 20 200 5 9

B 3 1 100 1.5 2.5 2

C 4 2 200 2 7 5

D 8 5 10 70 5 6

3. Given the market share information in the table below, calculate the four firm concentration ratio and the Herfindahl index.

Firm

Number Market Share

(%)

1 35

2 25

3 15

4 15

5 10