# Profit maximising price and quantity relationship

### Profit Maximization

(We use Π to stand for profit because we use P for something else: price.) Total revenue At any quantity, the demand curve tells us the price corresponding. What is the relationship between the elasticity of demand and markup? To the left of the point marked “profit-maximizing quantity,” marginal revenue exceeds. To maximize its profit, Beautiful Cars chooses a point on its demand curve When we write the demand relationship like this, with price as a function of quantity, we The company wishes to set price and quantity so as to maximize its profit.

The first two columns of Table represent the market demand schedule that the monopolist faces.

As the price falls, the market's demand for output increases. The third column reports the total revenue that the monopolist receives from each different level of output.

Perfect Competition and Profit Maximization

The fourth column reports the monopolist's marginal revenue that is just the change in total revenue per 1 unit change of output. The fifth column reports the monopolist's total cost of providing 0 to 5 units of output.

The sixth and seventh columns report the monopolist's average total costs and marginal costs per unit of output. The eighth column reports the monopolist's profits, which is the difference between total revenue and total cost at each level of output.

## Profit Maximisation

Graphical illustration of monopoly profit maximization. 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. We showed in Leibniz 7. The additional units are called the marginal units.

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

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.

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?