Answer to Question #157992 in Microeconomics for Syed Qasim

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

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)short run stage 1 arises due to to increasing average product. As more of the variable input is added to the fixed input, the marginal product of the variable input increases. Most importantly, marginal product is greater than average product, which causes average product to increase. This is directly illustrated by the slope of the average product curve.

Stage II, short-run production is characterized by decreasing, but positive marginal returns. As more of the variable input is added to the fixed input, the marginal product of the variable input decreases. Most important of all, Stage II is driven by the law of diminishing marginal returns.

The onset of Stage III results due to negative marginal returns. In this stage of short-run production, the law of diminishing marginal returns causes marginal product to decrease so much that it becomes negative.

Stage III production is most obvious for the marginal product curve, but is also indicated by the total product curve.

b)The average product (AP)=total producr(TP)/ Labour (L). It denotes the addition of variable factor to total product.Thus, marginal product =Changed output/ changed input. In other ways, marginal product leads to an increase of total product help of average product = total product /Labour. It denotes the addition of variable factor to total product. Thus, Marginal product= Changed output/ changed input. In other ways,marginal product leads to an increase of total product with the help of additional worker or input.worker or input.

c)For the Karachi plant, the Marginal product is 40 ,

The marginal labour is therefore