# Profit maximizing price and quantity relationship

### Profit maximization - Wikipedia

An equivalent perspective relies on the relationship that, for each unit sold, marginal profit. An explanation of profit maximisation with diagrams - Profit max. But, to maximise profit, it involves setting a higher price and lower quantity. A firm maximizes its profits by choosing to supply the level of output where its marginal At the market price, P 1, the firm's profit maximizing quantity is Q 1.

The firm's equilibrium supply of 29 units of output is determined by the intersection of the marginal cost and marginal revenue curves point d in Figure. The firm's profits are therefore given by the area of the shaded rectangle labeled abed.

The area of this rectangle is easily calculated.

The length of the rectangle is In general, the firm makes positive profits whenever its average total cost curve lies below its marginal revenue curve. When the firm's average total cost curve lies above its marginal revenue curve at the profit maximizing level of output, the firm is experiencing losses and will have to consider whether to shut down its operations.

In making this determination, the firm will take into account its average variable costs rather than its average total costs.

The difference between the firm's average total costs and its average variable costs is its average fixed costs.

The firm must pay its fixed costs for example, its purchases of factory space and equipmentregardless of whether it produces any output. Hence, the firm's fixed costs are considered sunk costs and will not have any bearing on whether the firm decides to shut down.

Thus, the firm will focus on its average variable costs in determining whether to shut down.

### Profit Maximization

The firm is better off continuing its operations because it can cover its variable costs and use any remaining revenues to pay off some of its fixed costs. Of course, the firm will not continue to incur losses indefinitely. The profit-maximizing price could then be calculated as.

**Marginal Cost and Marginal Revenue**

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.

## Profit Maximization

Thus the first-order condition tells us precisely that the profit-maximizing choice lies at a point of tangency between the demand and isoprofit curves. For Beautiful Cars, this is point E in Figure 7. The profit-maximizing choice of price and quantity for Beautiful Cars. Note, the firm could produce more and still make a normal profit.

## Short-Run Supply

Therefore, in a monopoly profit maximisation involves selling a lower quantity and at a higher price. Diagram of monopoly Profit Maximisation in Perfect Competition In perfect competition, the same rule for profit maximisation still applies. Profit Maximisation in the Real World Limitations of Profit Maximisation In the real world, it is not so easy to know exactly your marginal revenue and the marginal cost of last goods sold.

For example, it is difficult for firms to know the price elasticity of demand for their good — which determines the MR. It also depends on how other firms react.

If they increase the price, and other firms follow, demand may be inelastic.