Topic 2: Profit Maximization and Employment of Factors

Profit Function

profit = TR(Q)-TC(Q) or TR(K.L) - TC(K,L)

Profit Maximizing Condition

MR=MC or MRP = MFC

Marginal Revenue Product

additional revenue gained from the output produced by the additional input used (marginal revenue multiplied by marginal product)

Marginal Factor Cost

additional cost incurred by using an additional input (equal to wage or rent)

Marginal Value Product

value of the additional output produced by the additional input used (marginal product multiplied by price)

What is the relationship between wage and the amount of labor employed by a firm?

the cheaper the cost of hiring an input, the greater the amount of that input a firm can purchase, cet. par. (w and L are inversely related)

The effect on the inputs can be broken into two parts:

Factor Substitution Effect (FSE) and Output Effect (OE)

Relationships of w to L and K (via FSE)

w is negatively-related to L and positively-related to K

Relationships of r to L and K (via FSE)

r is negatively-related to K and positively-related to L

How does a change in the price of inputs affect the firm’s profit maximization?

The demand for factors does not depend only on cost minimization (the firm’s main objective is to maximize profit). Meaning, the change in the price of an input results in a change in the marginal cost structure of the firm and thus, affects the firm’s profit maximizing condition

Explain the FSE of an increase in wage

As wage increases, the ratio w and and r (w/r) also increases, so L becomes more expensive than before meaning the original combination of L and K is no longer cost-minimizing (MRTS < w/r). The firm shifts to the relatively less expensive input K

Explain the OE of an increase in wage

increase in w will increase the cost of producing Q - the MC of producing Q is now higher at w’ - MC is now greater than MR (MC>MR) and thus it will be profit maximizing to decrease Q - less Q requires less L and K

Relationships of w to L and K (via OE)

Both L and K are negatively related to w because Q is negatively-related to w