91Ó°ÊÓ

Price elasticity of demand is a measure of how responsive the quantity demanded of a good is to a change in its price. It tells us the degree to which the quantity demanded will change if the price of the product changes. The mathematical expression for price elasticity of demand is given by:\[ E^D = \frac{\Delta Q / Q}{\Delta P / P} \]Here:

• \( \Delta Q \) is the change in quantity demanded,
• \( Q \) is the initial quantity demanded,
• \( \Delta P \) is the change in price, and
• \( P \) is the initial price.

When the price elasticity of demand is greater than one, the demand is said to be elastic, meaning consumers are responsive to changes in price.
If it is less than one, demand is inelastic, indicating that consumers are less responsive to price changes.
Understanding this concept is crucial because it helps firms determine how a change in price might affect their total revenue and sales volumes.

Perfect competition is an idealized market structure where many firms sell identical products, and no single seller can affect the market price. Because each firm in a perfectly competitive market faces a perfectly elastic demand curve, their price elasticity of demand tends toward infinity.
This means that even the slightest increase in price would lead to consumers buying from another seller, hence demand is extremely sensitive to price.
In such a market, the marginal revenue a firm receives is equal to the price of the product. Mathematically, this is expressed as:\[ MR = P \]Since each additional unit sold does not impact the prevailing market price, firms will continue to sell additional units as long as the price covers the cost of production.
Thus, their goal is to produce the quantity where marginal cost equals the market price, maximizing their profit and efficiency.

Market power refers to the ability of a firm to influence the price of its product, a feature not present in the model of perfect competition. Firms with market power face downward-sloping demand curves, meaning they can set prices above marginal cost.
This ability allows them to increase prices without losing all of their customers, unlike in perfectly competitive markets.
Firms with market power exhibit price elasticity of demand values less than infinity, indicating that demand does not respond substantially to price changes.
The relationship between price elasticity and marginal revenue can be expressed as:\[ MR = P \left( 1 + \frac{1}{E^D} \right) \]Here, \( 1 + \frac{1}{E^D} \) is always less than one when \( E^D \) is greater than 1, meaning that marginal revenue is always less than the price.
This enables firms to set prices strategically, maximizing profit while maintaining market power. Such firms engage in pricing strategies that may maximize revenue at the expense of producing the socially optimal output level.