Do the following functions exhibit increasing, constant, or
decreasing returns to scale? What...

Question

Do the following functions exhibit increasing, constant, or
decreasing returns to scale? What happens to the marginal product of each
individual factor as that factor is increased and the other factor held
constant?

a. q = 3L + 2K

b. q = (2L + 2K)1/2

c. q = 3LK2

d. q = L1/2K1/2

e. q = 4L1/2 + 4K

The production function for the personal computers of DISK,
Inc., is given by

q = 10K0.5L0.5

where q is the number of computers produced per day, K is
hours of machine time, and L is hours of labor input. DISK’s competitor,
FLOPPY, Inc., is using the production function

q = 10K0.6L0.4

a. If both companies use the same amounts of capital and
labor, which will generate more output?

b. Assume that capital is limited to 9 machine hours, but
labor is unlimited in supply. In which company is the marginal product of labor
greater? Explain.

Komalavalli · Accepted Answer

Production function 
a. q = 3L+2K is a constant returns to scale, For example, if L and K are both one, then q equals five. If L and K are both 2, then q is 10. When the inputs are multiplied by two, the result is multiplied by two. For this production function, each marginal product is constant. When L rises by one, q increases by three. When K goes up by one, q goes up by two.
b. q = (2L+2K)1/2 is a decreasing returns to scale. If L and K are both 2, then q equals 2.8. If L and K are both 4, then q is also 4.

Do the following functions exhibit increasing, constant, or decreasing returns to scale? What happens to the marginal product of each individual factor as that factor is increased and the other factor...

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