Question

The production technology is given by q = 600L2 ? 10L3 where output is given by q and labor by L.

a. Are there values of labor where output is negative. Show your logic.

b. Calculate the marginal product of labor.

c. Does the marginal product of labor diminish?

d. Are there values of labor where its marginal product is negative? Show your logic.

e. Calculate the average product of labor. Show your logic.

f. Does the average product of labor diminish? Show your logic.

g. Does the average product of labor reach a maximum? If so, compute the value of labor at which its marginal product is maximized.

h. Check the second-order condition for a maximum. Is it satisfied? Show your calculations.

Answer 1

A) Assuming that the production function is q=600L2/10L3. ( Just in case ,the function is different, reply to this thread. I will reply. The methodology will remain the same regardless of the specification)

Q= 60/L. There is no value of L for which q is negative as labor cannot be negative. If denominator is non negative and since the expression is positive, the answer will be non negative.

2. MPL is calculated by derivating the output with respect to labour.

Mpl = dq/dL = -60/L2.

C) The marginal product of labour is diminishing because as L increases MPL diminshes.

D) Marginal product will be negative for any non zero value of labour as the denominator has L2 which can never be negative and the expression has a minus sign.

E) APL= Q/L = (60/L)/L = 60/L2.

F) The average product of labour is diminishing because as L increases, APL falls.