Q=60L^2 K^1/2 - 4L^2 K(K bar)=9 After what quantity of labor does diminishing marginal returns now...

Q=60L^2 K^1/2 - 4L^2

K(K bar)=9

After what quantity of labor does diminishing marginal returns now occur?

What is the maximum output the firm can now produce?

Solutions

Expert Solution

Solution:

We are given the production function as: Q = 60L^2 K^1/2 - 4L^2 ; where Q is output, K is capital and L is labor

With K as constant at 9, the function becomes: Q = 60*L^2*(9)^1/2 - 4L^2

Q = 180L^2 - 4L^2 = 176L^2

Marginal returns = dQ/dL = 2*176*L = 352*L

So, with increase in L, marginal return is increasing, and not diminishing here (unlike well behaved production function). With no diminishing, the maximum output can go till infinite.

PS: parameters of production function could be different than actual, resulting in not diminishing marginal returns, kindly recheck.

Rahul Sunny answered 2 years ago

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