Total, Average, and Marginal Cost Derivation

Once we know a firm’s production behavior, and we know what each factor of production costs, we can derive the firm’s total, average, and marginal costs. Below we have copied the firm’s production behavior from the first table in the previous section (Section 2).

Number of Workers
Amount of Land in Acres
Number of Machines
Total Production of Cars Average Production of Labor
Marginal Production of Labor
0 2 5 0
1 2 5 3 3 3
2 2 5 7 3.5 4
3 2 5 15 5 8
4 2 5 19 4.75 4
5 2 5 22 4.4 3
6 2 5 23 3.83 1

Let’s assume that the three factors of production used to produce the products in the table are workers, land, and machines. The cost of these factors of production are as follows:
1. Each worker costs the firm $4,000 per month.
2. Each acre of land costs the firm $1,000 per month.
3. Each machine costs the firm $600 per month.

The table below illustrates the total cost at each number of workers.

Number of Workers Total
Worker
Cost
Amount
of
Land
in
Acres
Total Land Cost
Number of Machines
Total Machine
Cost
Total Cost of All Factors in Dollars Total Production of Cars Average Cost Per Car in Dollars
Marginal
Cost Per Car in Dollars
0 0 2 2,000 5 3,000 5,000 0
1 4,000 2 2,000 5 3,000 9,000 3 3,000 1,333
2 8,000 2 2,000 5 3,000 13,000 7 1,857 1,000
3 12,000 2 2,000 5 3,000 17,000 15 1,133 500
4 16000 2 2,000 5 3,000 21,000 19 1,105 1,000
5 20,000 2 2,000 5 3,000 25,000 22 1,136 1,333
6 24,000 2 2,000 5 3,000 29,000 23 1,261 4,000

Total monthly worker cost is the number of workers times the cost per worker. For example, at 3 workers, the total worker cost is 3 times $4,000, or $12,000.

Total monthly land cost is the number of acres used times the cost per acre. The firm uses 2 acres, so the total monthly land cost is 2 times $1,000, or $2,000. This cost is fixed in the short run, regardless of the number of workers employed and the number of products produced.

Total monthly machine cost is the number of machines times the cost per machine. The firm uses 5 machines, so the total monthly machine cost is 5 times $600, or $3,000. This cost is fixed in the short run, regardless of the number of workers used and the number of products produced.

Total monthly cost of all factors of production is the sum of the three factor costs. For example, at 3 workers, the total cost is $12,000 plus $2,000 plus $3,000, or $17,000.

Average monthly cost is the total monthly cost per car. For example, at 3 workers, total production is 15 cars. Total monthly cost is $17,000. Therefore, the average cost is $17,000 divided by 15, or $1,133 (rounded to whole dollars).

Marginal monthly cost is the additional cost per car. For example, at 3 workers, the total cost increases by $4,000 compared to what it is at 2 workers. Total production increases by 8 products (from 7 to 15). Therefore, marginal cost is $4,000 divided by 8, or $500.

The next unit (Unit 5) elaborates on the various cost functions, discusses the difference between implicit and explicit costs, illustrates graphs of these functions, and discusses long-run cost behavior.

Video Explanation
For a video explanation of how production and costs are related, please watch: