Question

Below are the short-run average-total-cost schedules for three plants of different size that a firm
might build to produce its product. Assume that these are the only possible sizes of plants that the
firm might build. (10 points)
a) What is the long-run average-cost schedule for the firm? Show it in the second table below.
Plant size X Plant size Y Plant size Z
Output ATC Output ATC Output ATC
5 $10 5 $13 5 $72
10 9 10 12 10 65
15 8 15 11 15 52
20 7 20 10 20 41
25 6 25 8 25 33
30 9 30 7 30 20
35 12 35 9 35 15
40 18 40 12 40 14
45 20 45 17 45 12
50 23 50 19 50 14
55 29 55 25 55 20
60 31 60 33 60 30
Output Average cost
5 $_____
10 _____
15 _____
20 _____
25 _____
30 _____
35 _____
40 _____
45 _____
50 _____
55 _____
60 _____
b) For what output levels should the firm build plant X, plant Y, and plant Z?

Answer 1

Solution,

a). The average cost is equal to the sum of the cost of all plant on a specific output, such as average cost at output 5 is equal to the sum of the average cost of all plant at output 5 divided by the number of firm/plant

Average Cost = (ATC_x + ATC_y + ATC_z)/3

Plant size X	Plant Size Y	Plant Size Z	Industry
Output	ATC	Output	ATC	Output	ATC	Output	Average Cost
5	10	5	13	5	72	5	31.66666667
10	9	10	12	10	65	10	28.66666667
15	8	15	11	15	52	15	23.66666667
20	7	20	10	20	41	20	19.33333333
25	6	25	8	25	33	25	15.66666667
30	9	30	7	30	20	30	12
35	12	35	9	35	15	35	12
40	18	40	12	40	14	40	14.66666667
45	20	45	17	45	12	45	16.33333333
50	23	50	19	50	14	50	18.66666667
55	29	55	25	55	20	55	24.66666667
60	31	60	33	60	30	60	31.33333333

b).

the output level the firm build where each plant have lowest cost

long-run cost is passed through the point where plants have a minimum cost.

Plant X produced output 25 where the average cost is lowest 6 and Plant Y produced output 30 where the average cost is lowest 7 and Plant Z produced output 45 where the average cost is lowest 12.

Plant X - 25

Plant Y - 30

Plant Z - 45