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Substitution of labor and capital

A. Problem III: (each part counts for 5 points)

Semiconductor integrated circuits (ICs or "chips") are manufactured by building up layers of circuitry on silicon wafers. To fabricate chips, each layer must line up precisely with the patterns of other layers. To align layers, firms employ a combination of capital equipment and labor.

One technology, the least capital intensive, involves the use of an aligner machine. Employees use a microscope to line up layers by hand and process the wafer. Each worker uses one aligner machine and can produce chips at the rate of 3.125 per hour.

A second technology, which is more capital intensive, involves the use of a stepper machine to automatically align layers of the chip. Each worker can operate two steppers simultaneously and can produce chips at the rate of 6.25 per hour.

The proportions of capital and labor in these two technologies are rigid (one aligner per employee and two steppers per employee). Any other proportions mean that either the machine or the employee has significant idle time.

a. The P&R text discusses the cases of perfect substitutes and fixed proportion technologies.
Which case applies to each of the chip fabrication technologies described above? Explain, and please describe (you do not need to draw a graph) the shape of an isoquant.

b. A manager must plan for a production rate target of 200 chips per hour. If you adopt the aligner
process, how many workers and aligners (per hour) will you need to meet the target rate? If you adopt the stepper process, how many workers and steppers will you need?
c. The P&R text describes a fixed-proportion technology as one where it is "difficult to
substitute" (p. 205). Do you agree or disagree with this assessment when a firm can choose between technologies? Explain.

d. Suppose you manufacture chips in Europe where labor costs are W=4 (per hour). Capital
equipment costs are given by (on a per hour basis) Ra= 1 for aligners and Rs=2 for steppers. Do you recommend aligners or steppers as the best choice for minimizing costs of producing at the target rate of 200 chips per hour? What total cost do you achieve and what input choices are needed?

e. Another facility manufactures chips in Malaysia where labor costs are much lower at W=1. Capital costs are still given by Ra=1 and Rs=2. What do you recommend for cost minimizing input choices and what total cost do you achieve?

f. Given the ability to plan ahead, which location would you choose, Europe or Malaysia? Explain, using the ideas of cost minimization and substitution, why it does or does not make sense to use different techniques in different locations.


Solution Preview

a. Labor and capital are not perfect substitutes in this case, because the machines cannot make chips with workers, and workers cannot make chips without machines. Fixed proportions of labor and capital must be used, so the company faces fixed proportion technologies. fixed proportion technologies. The isoquants of a production function with fixed proportions are L-shaped.

b. If each worker produces chips at the rate of 3.125 per hour with one aligner, ...

Solution Summary

Finding most efficient combinations of labor and capital.