Long-Run Cost Functions
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1. The Haverford Company is considering three types of plants to make a particular electronic device. Plant A is much more highly automated than plant B, which is in turn more highly automated than plant C. For each type of plant, average variable cost is constant so long as output is less than capacity, which is the maximum output of the plant. The cost structure for each type of plant is as follows:
Plant A Plant B Plant C
Average Variable Costs
Labor $1.10 $2.40 $3.70
Materials 0.90 1.20 1.80
Other 0.50 2.40 2.00
Total $2.50 $6.00 $7.50
Total Fixed Costs $300,000 $75,000 $25,000
Annual Capacity 200,000 100,000 50,000
a. Derive the average cost of producing 100,000, 200,000, 300,000 and 400,000 devices per year for plant A. (For outputs exceeding the capacity of a single plant, assume that more than one plant of this type is built.)
b. Derive the average cost of producing 100,000, 200,000, 300,000 and 400,000 devices per year for plant B.
c. Derive the average cost of producing 100,000, 200,000, 300,000 and 400,000 devices per year for plant C.
d. Using the results of parts a through c, plot the points on the long-run average cost curve for the production of these electronic devices for outputs of 100,000, 200,000, and 400,000 devices per year.
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