Answer to Question #158364 in Macroeconomics for ria

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. (2 Marks)

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     (2 Marks)

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?     (1 Mark)

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?(1 Mark)

Answer 1

Answer :

10L²+ 0.5L³

$AP= 10L2- 0.5L3/Q$

L² = 9.5

L= 3.75

10L² - 0.5L^{3 . . }By this represents..

Out as more as unit of variable input labour, add to fixed stock of capital short prodution function for radio.

$MP = \Delta Q / \Delta L$

According above table :

First range

$93-0/3.75=24.8$

Second range

$114-93/5-3.75=16.8$

Third range

$82.5-114/1=-31.5$

First stage output increase at the increasing rate as few unit is added

TP increase, MP and AP also increase.

2) At AP- 3.75, TP increases but decreasing way till top other hand MP also increase but faster than AP

3) TP is decreased positively, AP also fall but positive but MP will be negative.

According question (c)

This is indicator of long run

So.. Purchased machinery and equipment for double production in future

1)if we change in scale, then output change

.

Both are same increasing it is constant

2)

Out put is not up to the increase labour

3)

Increasing labour increase less but output increases more

Q= 60L³⁰k⁷

60*1³⁰ 1⁷⁰ =60

60*2¹⁰⁰

120

Yes it will become double

D) 40*5=200 cost

28*4=112 cost

Gwadar plant is good for yoy