Question

5) A firm's short-run production function is given by Q=50 L-.02 L^{2}

Where L denotes the number of workers.

1. Find the size of the workforce that maximizes output.

2. Find marginal product of labor (M PL)

3. Find the average product of labor (APL)

4. Find the size of the workforce which maximizes the average product of labor. Calculate M PL and A PL at this value. What do you observe.

6) Find and classify the critical (stationary) points of the following function and state the range where it is convex or concave

f(x)=-2 x^{3}+15 x^{2}-36 x+27

Answer 1

(5)

Q = 50L - 0.02L²

(1)

Output is maximized when dQ/dL = 0

dQ/dL = 50 - 0.04L = 0

0.04L = 50

L = 1250

(2)

MPL = dQ/dL = 50 - 0.04L

(3)

APL = Q/L = 50 - 0.02L

(4)

APL is maximized when L = 0 (since L is non-negative).

When L = 0,

APL = 50

MPL = 50

Therefore, when APL is maximized, MPL equals APL.

NOTE: As per Answering Policy, 1st question is answered.