Question

The own-price elasticity of demand for food is negative. The demand for food is inelastic. A higher food price increases spending on food. Higher food prices imply less is spent on all other goods. The quantity demanded of each of these other goods falls. Discuss each statement. Are they all correct?

Short answer

All statements are correct given the assumptions.

Step-by-step solution

Understand Own-Price Elasticity of Demand

Own-price elasticity of demand measures how the quantity demanded of a good responds to changes in its price. It's given by the formula \( E_d = \frac{\%\text{ change in quantity demanded}}{\%\text{ change in price}} \). A negative value indicates that demand decreases as price increases, which is typical for most goods.

Inelastic Demand Defined

Demand is inelastic when the absolute value of own-price elasticity is less than 1. This means that a percentage change in price results in a smaller percentage change in quantity demanded. Therefore, consumers do not reduce their quantity demanded significantly when prices increase.

Impact of Higher Prices on Spending for Inelastic Goods

For inelastic goods, an increase in price leads to an increase in total revenue because the percentage decrease in quantity demanded is less than the percentage increase in price. This implies that spending (price times quantity) on such goods rises as prices rise.

Consequences on Budget and Other Goods

If spending on food (an inelastic good) increases with price, consumers have less budget left for other goods. This is a result of the budget constraint. As a consequence, the demand for other goods, which are presumably elastic, will decrease since consumers have fewer resources to allocate to them.

Verifying Each Statement

1. The own-price elasticity of demand for food is negative: Correct, as most goods have a negative elasticity due to the inverse relationship between price and demand. 2. The demand for food is inelastic: Correct by given assumption. 3. A higher food price increases spending on food: Correct for inelastic demand. 4. Higher food prices imply less is spent on all other goods: Correct, due to a limited budget. 5. The quantity demanded of each of these other goods falls: Correct if other goods are elastic or if they belong to normal or luxury goods category.

Key concepts

Inelastic Demand

Inelastic demand refers to a situation where the demand for a product does not significantly change even when its price goes up or down. This happens when the absolute value of the own-price elasticity is less than 1. In simpler terms, if prices increase by a certain percentage, the quantity demanded drops by a smaller percentage.

For instance, if the price of bread increases, people will generally continue to purchase it because it is a necessity. They cannot easily reduce the quantity they buy, unless there are substitute goods that are significantly cheaper and similar in quality.

• The demand for necessities, like food, is typically inelastic.
• Consumers continue purchasing despite changes in price.

Budget Constraint

A budget constraint represents the limited amount of income available to consumers to spend on goods and services. Every consumer faces this limit, impacting how they allocate their spending across different items.

When prices rise, especially for an inelastic good like food, consumers may be forced to adjust their spending habits due to their budget constraint. This often means spending more of their available income on the inelastic good, leaving less for other items.

• Consumers have limited income to allocate across various goods and services.
• Rising prices of inelastic goods can reduce spending flexibility on other items.

Price and Demand Relationship

The relationship between price and demand is a fundamental concept in economics. Typically, demand decreases as prices increase. This inverse relationship is why the own-price elasticity of demand is generally negative.

In the case of inelastic goods, even though prices go up, the quantity demanded doesn't drop much. This results in higher total revenue for sellers, since consumers continue buying nearly the same amount, despite the higher costs. Thus, for inelastic goods, higher prices generally lead to increased spending.

• Price increase usually leads to demand decrease; however, less so for inelastic goods.
• Inelastic goods can result in increased revenue due to consistent demand.

Spending Behavior

Spending behavior reflects how consumers allocate their money in different situations. When faced with higher prices for inelastic goods, consumers may adapt their spending in various ways.

For example, if the cost of food goes up significantly, consumers might cut back on non-essential purchases such as entertainment or luxury goods. Even though the quantity demanded for food remains relatively stable, because of the necessity, spending on other flexible or luxury items tends to decrease.

• People adjust spending based on necessities and available budget.
• Higher prices for inelastic goods lead to reduced spending on non-essentials.