Question

4. Suppose a firm's production function is well behaved and strictly suppose the firm is operating at some point where T'RS(L, K)| < PL/pK, where "h indicates absolute value of some number h. Explain how this firm can inercase its out convex. Additionally put without changing its total expenditure for why inputs. Provide an additional argument firm operating at a point where 1TRS(L, K)| PL/PK is not maximizing a profit.

The question doesn't give TRS.

Answer 1

As MRTS = MPL / MPK

Now as MRTS < PL/PK

MPL / MPK < PL / PK

Thus MPL / PL < MPK / PK

So firm should hire more capital & less Labor, which results in rising MPL & falling MPK

till the MPL/ PL = MPK / PK

Which is the eqm profit maximization condition

now when MRTS not equals input price ratio, then firm is not maximizing the profit,

bcoz when MPL/PL < MPK/ PK

then for every additional dollar spending on production input, marginal productivity of Labor is lower than that of the capital , hence employ more K & less L