Question

A firm has a possibility to produce output using either one or two units of capital. Capital costs $10 per unit. Labor is always variable. If it uses 1 unit of capital, marginal cost is constant (no diminishing returns) at $3. If it uses 2 units of capital, marginal cost is constant at $1.

For the output quantities of 1 to 10, create the firm’s short run average total cost curves. Also create the firm’s long-run average total cost curve.

Does the firm exhibit economies of scale, diseconomies of scale, or constant returns to scale? Explain your answer.

Answer 1

Total cost = Cost of capital*capital hired + cost of labor*labor hired

Below are cost schedule-

Output	Capital	Labor	Total Cost (TC1)
1	1	1	13
2	1	2	16
3	1	3	19
4	1	4	22
5	1	5	25
6	1	6	28
7	1	7	31
8	1	8	34
9	1	9	37
10	1	10	40

Output	Capital	Labor	Total Cost (TC2)
1	2	1	21
2	2	2	22
3	2	3	23
4	2	4	24
5	2	5	25
6	2	6	26
7	2	7	27
8	2	8	28
9	2	9	29
10	2	10	30

Below is how the Short run average total cost (ATC) for both capital will look like -

Output	TC1	TC2	ATC1	ATC2
1	13	21	13	21
2	16	22	8	11
3	19	23	6.333333	7.666667
4	22	24	5.5	6
5	25	25	5	5
6	28	26	4.666667	4.333333
7	31	27	4.428571	3.857143
8	34	28	4.25	3.5
9	37	29	4.111111	3.222222
10	40	30	4	3

where ATC = TC/output.

Long run cost function = minimum of ATC1 and ATC2. That is, the firm will choose the plant where the short run cost is least-

Output	TC1	TC2	ATC1	ATC2	LRATC
1	13	21	13	21	13
2	16	22	8	11	8
3	19	23	6.333333	7.666667	6.333333
4	22	24	5.5	6	5.5
5	25	25	5	5	5
6	28	26	4.666667	4.333333	4.333333
7	31	27	4.428571	3.857143	3.857143
8	34	28	4.25	3.5	3.5
9	37	29	4.111111	3.222222	3.222222
10	40	30	4	3	3

The firm exhibits economies of scale. This is because the long run average total cost keeps falling as the output level increases which is an indication of economies of scale.