Haverford Company and Roosevelt Laboratories

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 in turn is 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 .90 1.20 1.80
Other .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 with 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 with Plant B.
c. Derive the average cost of producing 100,000, 200,000, 300,000 and 400,000 devices per year with Plant C.
d. Using the results of parts a through c, plot the points on the long-run outputs of 100,000, 200,000 and 400,000 devices per year.

2. The chief scientist at the Roosevelt Laboratories estimates that the cost (in million of dollars) of developing and introducing a new type of antiulcer drug equals:

C=100-19t = 0.5t21 for 1< t < 6

Where t is the number of years taken to develop and introduce the new drug. The discounted profit (gross of innovation cost) from a new drug of this type (in millions of dollars) is estimated to equal

R = 110 - 15t for 1< t < 6

a. The managers of the Roosevelt Laboratories are committed to developing and introducing this new drug within six years, and it is impossible to develop and introduce it in less than year. What project durations would minimize cost?
b. Why does R decline as t increase?
c. What is the optimal project duration? Why?