Question

1) “A firm will never find it optimal to employ so much of an input that its marginal product is negative.” Is this statement true or false? Explain your answer.

2) As a production manager, your job depends on your ability to minimize the cost of production.

You hire a consulting firm, and its report suggests that you have plenty to worry about: The cost of capital is $200 per hour, the wage paid to your workers is $16 per hour, the marginal product of capital is 10 units per hour, and the marginal product of labor is 32 units per hour. What is the consulting firm going to recommend, and why?

Answer 1

1)TRUE A firm will never find it optimal to employ so much output that the MP is negative.

MP of a variable is declining to due "law of dim inishing marginal returns" which states that "as units of one input are added (with ceterus paribus) a point will be reached where the resulting additions to output will begin to decrease; that is marginal product will decline" . so this means that even when the total returns from a variable increases , it increases at a decreasing rate when marginal product is declining.

a stage will be reached when the marginal product would be negative ie the marginal returns from an additional unit would decrease the total returns . in that case the additional unit employed would do no extra addition , instead it would decline the total cost of the previous units as well.

so the statement is true

2) For minimising the cost of production , we need to look at the optimal condition of the production which is given by the tangency condition of slope of isocost curve and of isoquant

The MRTS is the slope of isoquant which explins how the two variables can be subsituted given the output constant.

MRTS= -(change in K/change in L) =MP_L/MP_k

the slope of the isocost curve is given by ratio of input prices

which is -( w/r) =change in K/change in L

equating these two we get

w/r = MP_L/MP_k

so substituting the values given in the question we have

wages paid = w=$16

cost of capital per hour is $200= r

MP of labour is 32= MPl

MP of capital is 10 =MPk

w/r=  MP_L/MP_k

16/200 =w/r= 2/25

MP_L/MP_k = 32/10 = 16/5

the ratio is far from equal so as a consul;ting firm we need to consider several facts

if wr assume that the wages and rental cost remains the same then , only a change in the marginal products could bring about an equality in the ratios. this means that for that we need to decrease the units of capital employed so that the marginal product increases .

as we know that as more and more additional units of a variable is employed the MP of it declines . so by employing less of the variable we can increase the MP of capital and hence stabilise or equalise the ratios.

or we can increase the units of labour so that the MP of labour reduces and simulatneously reduce units of capital to bring the ratio equal to w/r = 2/25

so by increasing or by substituting more of labour and reducing capital the optimal or minimum cost can be achieved.