# Determine the profit maximizing price and quantity have a relationship

### Profit Maximisation | Economics Help

When a firm has monopoly, the leeway in setting prices as well as the importance of Relationship between marginal revenue and price-elasticity of demand Determining the profit-maximizing quantity of production. If a retail store has fixed cost of Rs and variable cost per unit is Rs and sells its product at Rs. Find the profit function, and determine the profit when units are sold. iv Marginal revenue is the change in total revenue from increasing quantity by one unit. Find the profit revenue-maximizing output level. The typical demand curve has the price on the y-axis and the quantity the relationship between the price level and the quantity demanded at each price level. Joan's next step was to determine the quantity where profits are maximized.

What's left is to choose the quantity produced so as to maximize the firm's profits. Definition of marginal revenue Now that we have determined the firm's price as a function of the quantity produced, the firm's total revenue also becomes a function of the quantity produced.

Thus, we can take the derivative of total revenue with respect to quantity produced. This derivative is called marginal revenue and is abbreviated MR.

Geometrically, the marginal revenue is the derivative with respect to the quantity produced of the area of the rectangle between the axes and the quantity, price point on the demand curve.

Note that marginal revenue depends, not on the firm's production technologies, but rather, completely on the firm's market demand curve. Moreover, in analogy terms: Average variable cost curve Relationship between marginal revenue curve and market demand curve The marginal revenue curve lies below the market demand curve everywhere. This follows from the law of demand: In particular, this means that increasing the quantity demanded requires reducing the price somewhat.

### Profit maximization - Wikipedia

The derivative of total revenue with respect to quantity is therefore less than the price. The extent to which the marginal revenue curve diverges from the market demand curve is directly related to the extent of deadweight loss created in the situation. Relationship between marginal revenue and price-elasticity of demand The relationship is below: Condition on price-elasticity of demand Conclusion for marginal revenue note that this is the derivative with respect to quantity, not price.

Thus, the price is highly sensitive to the quantity demanded by the inverse function theoremthe sensitivies are reciprocal. A small increase in quantity demanded leads to a larger compensating decrease in the price that can be charged to sell out the quantity, causing the total revenue to decrease.

Here price and quantity are inversely proportional to each other. This, the price is insensitive to the quantity demanded. A small increase in quantity demanded leads to a smaller compensating decrease in the price that can be charged to sell out the quantity, causing the total revenue to increase.

## Profit Maximisation

In many cases, this is an accurate description of pricing behavior. When a grocery store posts a price, that price holds for every unit on the shelf. But sometimes firms charge different prices for different units—by either charging different prices to different customers or offering individual units at different prices to the same customer.

You have undoubtedly encountered examples. Firms sometimes offer quantity discounts, so the price is lower if you buy more units. Sometimes they offer discounts to certain groups of customers, such as cheap movie tickets for students. We could easily fill an entire chapter with other examples—some of which are remarkably sophisticated.

Firms can have pricing strategies that call for the price to change over time. For example, firms sometimes engage in a strategy known as penetration pricing, whereby they start off by charging a low price in an attempt to develop or expand the market.

It might decide to offer the cereal at a low price to induce people to try the product. Only after it has developed a group of loyal customers would it start setting their prices according to the markup principle. Pricing plays a role in the overall marketing and branding strategy of a firm. Some firms position themselves in the marketplace as suppliers of high-end offerings. They may choose to set high prices for their products to ensure that customers perceive them appropriately.

Consider a luxury hotel that is contemplating setting a very low price in the off-season.

### Determination of price and quantity supplied by monopolistic firm in the short run - Market

Psychologists who study marketing have found that demand is sensitive at certain price points. Such consumer behavior does not seem completely rational, but there is little doubt that it is a real phenomenon. Throughout this chapter, we have said that there is no difference between a firm choosing its price and taking as given the implied quantity or choosing its quantity and taking as given the implied price.

Either way, the firm is picking a point on the demand curve.

## Profit maximization

This is true, but there is a footnote that we should add. See Chapter 14 "Busting Up Monopolies" for discussion of this. We should also note that firms often do not know their demand curves with complete certainty.

If the firm sets the price, it will end up with an unexpectedly large quantity being demanded.

If the firm sets the quantity, it will end up with an unexpectedly high price. We have focused our attention on the market power of firms as sellers, as reflected in the downward-sloping demand curves they face.

Firms can also have market power as buyers.

Walmart is such an important customer for many of its suppliers that it can use its position to negotiate lower prices for the goods it buys. Governments are also often powerful buyers and may be able to influence the prices they pay for goods and services. For example, government-run health-care systems may be able to negotiate favorable prices with pharmaceutical companies. Key Takeaways At the profit-maximizing price, marginal revenue equals marginal cost.

The airline would maximize profit by filling all the seats.

Perfect Competition and Profit Maximization

Changes in total costs and profit maximization[ edit ] A firm maximizes profit by operating where marginal revenue equals marginal cost. In the short run, a change in fixed costs has no effect on the profit maximizing output or price. 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. 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.

The additional units are called the marginal units.

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