# Profit maximization

Profit maximization is the mechanism, entrepreneurs adapt to in a market economy, its production volume, so that a market equilibrium is reached. In the situation of maximum profit and marginal cost is the marginal revenue.

In the Business Administration profit maximization is considered as an important corporate goal; but precisely speaks Wilhelm Rieger here of maximizing the return on equity of a company.

## Formulas to maximize profits

The gain is the difference between the proceeds and the costs, that is, G = E - K. The maximum profit is the point at which the marginal revenue E 'is equal to the marginal cost C ' is, so to the E '= K' applies. From G '= E' - K ' it follows that the boundary gain G ' at this point is 0, that is, G ' = 0. Could formally at point G '= 0 and a local minimum are present, the condition G ' = 0 is therefore necessary, but not sufficient. At point G '= 0 must continue to G " <0 apply (G " is the second derivative of G ) to guarantee a local maximum formal (G' = 0 and G " <0 is a sufficient condition for a local maximum ).

Example:

Where are the price-demand function

And a linear cost function

It follows

With 1,200 units of the gain maximum is reached at a height of 52,000 monetary units. The price per unit amounts to 90 monetary units.

, The condition that G " is <0, is always satisfied in this case, since