Problem 703 What is marginal revenue? How do... [FREE SOLUTION]

Chapter 19: Problem 703

What is marginal revenue? How does the elasticity of demand affect marginal revenue?

Short Answer

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Marginal revenue (MR) is the additional revenue a firm earns when it sells one more unit of its product, calculated as \( MR = \Delta TR / \Delta Q \). The elasticity of demand affects marginal revenue as follows: 1) For elastic demand (E > 1), marginal revenue is positive, encouraging the firm to lower its price to increase total revenue. 2) For inelastic demand (E < 1), marginal revenue is also positive, encouraging the firm to raise its price to increase total revenue. 3) For unitary elastic demand (E = 1), marginal revenue is zero, and changing the price does not affect total revenue. Understanding a product's demand elasticity helps firms make informed pricing decisions to optimize their total revenue.

Step by step solution

Definition of Marginal Revenue

Marginal revenue is the additional revenue that a firm earns when it sells one more unit of its product. In other words, it is the change in total revenue divided by the change in quantity sold. Mathematically, it can be expressed as: \( MR = \Delta TR / \Delta Q \) Where MR stands for marginal revenue, 螖TR stands for the change in total revenue, and 螖Q stands for the change in quantity sold.

Relationship between Price and Revenue

In order to understand the effect of elasticity of demand on marginal revenue, we should first understand the relationship between price and revenue. Total revenue (TR) can be represented as: \( TR = P \times Q \) Where P is the price of the product and Q is the quantity sold.

Definition of Elasticity of Demand

Elasticity of demand is a measure of how sensitive the quantity demanded of a product or service is to a change in its price. It is calculated as: \( E = \dfrac{\% \Delta Q}{\% \Delta P} \) Where E is the elasticity of demand, %螖Q is the percentage change in quantity demanded, and %螖P is the percentage change in price.

Effect of Elasticity of Demand on Marginal Revenue

Now, we can analyze the effect of elasticity of demand on marginal revenue. There are three main cases to consider: 1. Elastic Demand: When the elasticity of demand is greater than 1, an increase in price will result in a decrease in total revenue. This is because the percentage decrease in quantity demanded is larger than the percentage increase in price. In this case, the marginal revenue will be positive, encouraging the firm to lower its price to increase total revenue. 2. Inelastic Demand: When the elasticity of demand is less than 1, an increase in price will result in an increase in total revenue. This is because the percentage decrease in quantity demanded is smaller than the percentage increase in price. In this case, the marginal revenue will also be positive, encouraging the firm to raise its price to increase total revenue. 3. Unitary Elastic Demand: When the elasticity of demand is equal to 1, a change in price will not affect total revenue. In this case, the marginal revenue will be zero, and changing the price will not make any difference to total revenue. In conclusion, the elasticity of demand plays a crucial role in determining the marginal revenue. A firm must understand its product's demand elasticity to make informed decisions about pricing to optimize its total revenue.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Elasticity of Demand

Elasticity of demand refers to how much the quantity demanded of a good responds to a change in its price. It is an essential concept in economics as it helps businesses understand consumer behavior and make pricing decisions. To calculate elasticity of demand, we use the formula: \[ E = \dfrac{\% \Delta Q}{\% \Delta P} \] where \( E \) is elasticity, \( \% \Delta Q \) is the percentage change in quantity demanded, and \( \% \Delta P \) is the percentage change in price.

Elastic Demand: This occurs when the elasticity is greater than 1, meaning consumers are highly responsive to price changes.
Inelastic Demand: This is when elasticity is less than 1, indicating consumers are not very responsive to price changes.
Unitary Elastic Demand: Here, elasticity equals 1, and total revenue remains constant when the price changes.

Knowing the elasticity of demand helps businesses predict how changes in price will affect their sales volume and revenue.

Price Elasticity

Price elasticity is a specific measure of elasticity that examines the relationship between changes in price and changes in quantity demanded. It is crucial for setting optimal pricing strategies. Price elasticity directly affects decisions related to pricing policies and marketing strategies.

Highly elastic demand means slight changes in price lead to significant changes in quantity demanded.
Inelastic demand suggests that considerable price changes are needed to influence demand.

Understanding price elasticity helps firms forecast the effects of their pricing decisions and find the balance where the product's price maximizes their revenue.

Total Revenue

Total Revenue (TR) is the total amount of money a company earns from selling its goods or services. It's calculated by multiplying the price per unit by the quantity sold:\[ TR = P \times Q \]where \( TR \) is total revenue, \( P \) is the price, and \( Q \) is the quantity sold.

In an elastic market, lowering the price can increase total revenue.
In inelastic scenarios, raising prices might be the correct approach to boost total revenue.
Understanding the elasticity of demand is crucial because it directly impacts how changes in price will affect total revenue.

Effective revenue management requires an understanding of this relationship to make informed financial decisions.

Economic Concepts

Economic concepts such as marginal revenue, elasticity of demand, and total revenue are interconnected and influence each other. Marginal revenue is the extra income earned from selling one more unit of a product. It is key to understanding how to optimize pricing strategy.

Elasticity of demand affects whether marginal revenue is positive, negative, or zero.
In elastic demand conditions, lowering prices raises total revenue by increasing sales sufficiently.
In inelastic conditions, the opposite holds true, where raising prices boosts revenue when sales decrease only slightly.
Unitary elasticity means sales volume changes proportionally with price, keeping total revenue unchanged.

A solid grasp of these concepts allows businesses to craft strategies that enhance profitability by understanding and predicting consumer reactions to pricing decisions.

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