# How do you find the profit maximizing price and quantity relationship

### The Economy: Leibniz: The profit-maximizing price

perspective relies on the relationship that, for and this quantity is the one that maximizes profit. any firm, whether perfectly competitive or not. Profit (π) = Total Revenue - Total Cost. If q is output of the firm, then total revenue is price of the good times quantity . How will this monopoly choose its profit-maximizing quantity of output, and what price will it charge? Profits for the monopolist, like any firm, will be equal to total.

Using the diagram illustrating the total cost—total revenue perspective, the firm maximizes profit at the point where the slopes of the total cost line and total revenue line are equal.

Consequently, the profit maximizing output would remain the same. This point can also be illustrated using the diagram for the marginal revenue—marginal cost perspective.

## Profit maximization

A change in fixed cost would have no effect on the position or shape of these curves. The profit maximization conditions can be expressed in a "more easily applicable" form or rule of thumb than the above perspectives use.

**Elasticity of Demand and Marginal Revenue**

The additional units are called the marginal units. Moreover, one must consider "the revenue the firm loses on the units it could have sold at the higher price" [6] —that is, if the price of all units had not been pulled down by the effort to sell more units.

### Profit maximization - Wikipedia

These units that have lost revenue are called the infra-marginal units. Thus the optimal markup rule is: Marginal cost is positive. Thus Q1 does not give the highest possible profit. Marginal product of labor, marginal revenue product of labor, and profit maximization[ edit ] The general rule is that the firm maximizes profit by producing that quantity of output where marginal revenue equals marginal cost.

The profit maximization issue can also be approached from the input side. That is, what is the profit maximizing usage of the variable input?

When it is written the other way around, with quantity in terms of price, the function is called the demand function. The company wishes to set price and quantity so as to maximize its profit, subject to the constraint that the price is one that buyers are willing to pay.

Its problem is therefore to: The simplest way to solve this optimization problem is by the method of substitution. We use the constraint to substitute forgiving profit as a function of alone: To find the value of that maximizes this function, we differentiate with respect to using the product differentiation rule,: The first-order condition for optimization iswhich may be rearranged as follows: The profit-maximizing quantity,satisfies this equation.

If we knew the specific form of the functions andwe could try to solve the equation to find explicitly. The profit-maximizing price could then be calculated as. But without knowing the functions, we can still interpret the first-order condition.

We know that the optimal value of is on the demand curve, soand that is marginal cost MC. So the first-order condition can be written: The left-hand side of this equation is the slope of the demand curve.