Douglas A. Ruby
A Producer Optimum
In describing a producer optimum, we have defined the profit maximization condition with respect the variable factor input (labor) as:
MPL = w/P.or
P = w/MPL = MC.For the competitive firm (a price taker), we can write:
Revenue (TR) = P x Qand
Marginal Revenue (MR) = dTR/dQ = P!Thus an alternative expression for profit maximization for a competitive firm is:
P = MC.
If P (MR) > MC then additions to revenue exceed the additions to cost (via the production and sale of one more unit of output) and the firm will be able to increase profits by selling that additional unit.
If the opposite is true, P (MR) < MC then additions to costs exceed the additions to revenue (via the production and sale of one more unit of output) and the firm will be able to increase profits by reducing output by one additional unit.
Imperfectly Competitive Firms
In the case of a firm with market (monopoly) power -- a price maker, the market demand curve is also the demand curve for that firm's output. Assuming that the demand curve is linear we find:
P = a - bQ -- the inverse demand curveand
TR = PxQ = aQ - bQ2 -- Total Revenue -- a quadratic equation!and
Marginal Revenue (MR) = dTR/dQ = a - 2bQThe equation for Marginal Revenue has the same intercept 'a' and is twice as steep as the slope of inverse demand. The condition for profit maximization still holds:
MR = MC.
Concepts for Review: