Answer to Question #157979 in Macroeconomics for Qurban Ali

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 = 10L^2 – 0.5L^3 where L is variable input labor, Q is output of Cars assembled

a. Find the ranges of the three stages of production.

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 (a) above.

c. At the end of the year it is expected that output will double with purchase ofnew equipment and machinery. The production function is estimated to be

Q = 60L^.30K^.70 where L is labor and K is capital.

Suppose initial L1 = 1 and K1 = 1. When inputs are in increased to L2 = 2 and K2 = 2,

do you observe increasing, decreasing or constant returns to scale?

d. Assume Kia Head Office is considering hiring more laborers either at their Gwadarplant or alternatively at the Karachi plant. What will be your advice if workers’ marginal product is 40 at wage of Rs=5/hour in Karachi and marginal product is 28 at wage of Rs=4/hour in Gawdar?

Answer 1

a.

the ranges of the three stages of production

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

Assume L = 1,2,3,4, .....n

units of labor TP AP MP

1 9.5 9.5 9.5

2 36 18 26.5

3 76.5 25.5 40.5

4 128 32 51.5

5 187.5 37.5 59.5

6 252 42 64.5

7 318.5 45.5 66.5

8 384 48 65.5

9 445.5 49.5 61.5

10 500 50 54.5

11 544.5 49.5 44.5

12 576 48 31.5

13 591.5 45.5 15.5

14 588 42 -3.5

Stage I

holds from at L = 1 until L= 7.

known as the stage of increasing returns. marginal product increases reaching maximum at L = 7.

Stage II

holds from L=8 until L=13

known as the stage of diminishing returns. marginal product starts diminishing until it reaches zero.

Stage III

holds beyond L=13

stage of declining returns. MP is negative

b)

c)

When inputs are in increased to L2 = 2 and K2 = 2 we observe increasing returns to scale  

d)

I would advice that the workers be paid Rs5/hour to increase production