Question

Task 2: Short-Run Production: One Variable and One Fixed Input II.... Consider the following production function: q=8LK + 5L2 - L. Assume capital is fixed at K = 25. (a) At what level of employment does the marginal product of labor equal zero? (Hint: To answer this question mathematically, you will have to use the quadratic formula.) (b) Illustrate the above production function for values of L € [1,30] (Note: Your graph does not necessarily have to be precise at any L). Where can you see your result from part (a) in the graph? (c) In what range of your graph does the marginal product of labor exhibit diminishing marginal returns? (Hint: To answer this question mathematically, you will have to analyze the sign of the first-order derivative of the marginal product of labor with respect to L.) Illustrate your result in a suitable diagram.

Answer 1

A).q=8L*25+5L2-1/3*L3

Q=200L+5L2-1/3*L3

MPL=200+10L-L2

Putting MPL=0

0=200+10L-L2

-L2+20L-10L+200=0

-L(L-20) -10(L-20)=0

(L-20)(-L-10)=0

L-20=0

L=20

-L-10=0

L=-10(not possible)

So L=20 where MPL=0

B)

AMPLO Total Detput highest 51223 Labour Suantity

C).

AMPEO Totat owent highest decreasiny MPL Total ant! decreedsing Bucuzeul 5 to is go z 30 Labour quantity