Answer to Question #158708 in Macroeconomics for Iqra

Question

You have been hired by Kia as manager for its Pakistan operations. Assume following is the short￾run production function at their assembly plant outside Karachi:

Q = 10L2 – 0.5 L3

 where L is variable input labor, Q is output of Cars assembled

b. Demonstrate the relationship between Total Production, Marginal Product and 

AverageProduct in a hypothetical graph and clearly label the three stages as per the 

values of Lyou observed in 

Answer 1

Part A

$Q$ $=$ $10L$$^2$ $-0.5L^3$

Average Product, $AP=$ $Q/L$

$10L^2-0.5L^3/L$

$10L-0.5L^2$

At maximization we equate to zero & differentiate with respect to L.

$d(AP)/dL=0$

$10-1.5*2L=0$

$L=10$

Stage 1 is as a result of average product increase. The range is from L=0 to L=10

Marginal product,

$MP=dQ/dL$

$MP=10*2L-0.5*3L^2$

$MP=20L-1.5L^2$

At Stage 2 margin product decreases but still remains positive.

At Stage 3 marginal product is equal to zero

$MP=0$

$20L-1.5L^2=0$

$20=1.5L$

$L=20/1.5$

$L=13.33$

Part B