Question

The data below refer to the market for cheese: $$ \begin{array}{|l|l|} \hline \text { Quantity } & \text { Price } \\ \hline 130 & 10 \\ \hline 110 & 20 \\ \hline 80 & 35 \\ \hline 70 & 40 \\ \hline 58 & 46 \\ \hline 50 & 50 \\ \hline \end{array} $$ Plot the demand for cheese. Given that the demand for cheese is unit elastic at \(37 \mathrm{p}\), for which prices is the demand for cheese elastic? For which ones is the demand for cheese inelastic?

Short answer

Demand is elastic at prices lower than 37 and inelastic at prices higher than 37.

Step-by-step solution

Interpret the Data

The table provides quantity and price information for the market for cheese. It is crucial to understand how a change in price affects the quantity demanded. The given data points are the quantity demanded at different price levels.

Plot the Demand Curve

Plot the given data points on a graph with Quantity on the x-axis and Price on the y-axis. Connect these points to form the demand curve. - Point (130, 10) - Point (110, 20) - Point (80, 35) - Point (70, 40) - Point (58, 46) - Point (50, 50)

Understand Elasticity

Elasticity measures how responsive the quantity demanded is to a change in price. Define these key terms: - **Elastic Demand**: When elasticity > 1, a price change leads to a larger percentage change in quantity demanded. - **Inelastic Demand**: When elasticity < 1, a price change leads to a smaller percentage change in quantity demanded. - **Unit Elastic Demand**: When elasticity = 1, a price change leads to an equal percentage change in quantity demanded.

Identify Unit Elastic Point

The demand is unit elastic at the price of 37. This means if the price changes from 37, the percentage change in quantity is exactly matched by the percentage change in price. At this point, the elasticity is exactly 1.

Determine Elastic and Inelastic Prices

Analyze the points relative to the unit elastic point: - **Elastic**: Price movements towards 37 from lower prices (e.g., 10 and 20) are likely elastic, since quantity changes drastically compared to price changes. - **Inelastic**: Price movements towards 37 from higher prices (e.g., 46 and 50) are inelastic, as the quantity change is less sensitive to price changes.

Key concepts

Demand Curve

The demand curve is a graphical representation showing the relationship between the price of a product and the quantity demanded. In this scenario, we're looking at the demand for cheese. This curve is constructed by plotting the given price and quantity pairs on a graph. The x-axis usually represents quantity, while the y-axis shows price.

Each point on the demand curve indicates a specific quantity that consumers are willing to purchase at a given price. By connecting these points, the curve typically slopes downwards from left to right.

This downward slope illustrates the law of demand, which states that, all else being equal, as the price of a good increases, the quantity demanded decreases. In other words, cheese becomes more expensive, people buy less of it.

Elastic Demand

Elastic demand refers to a situation where a small change in price leads to a significant change in the quantity demanded. For a product with elastic demand, consumers are highly responsive to price changes. This implies that if the price of cheese drops slightly, the quantity demanded rises quickly, and vice versa.

From the step-by-step solution, it is evident that when prices move towards 37 from lower prices such as those at 10 and 20, the demand is elastic. In this range, a small decrease in price results in a noticeable increase in the quantity of cheese demanded.

Some characteristics of elastic demand include:

• Availability of substitutes: If cheese has other alternatives, the demand becomes more elastic.
• Larger portion of income: If cheese represents a more significant portion of consumer expenses, they might react more to a price change.

Inelastic Demand

Contrary to elastic demand, inelastic demand occurs when a change in price causes a relatively smaller change in the quantity demanded. Products with inelastic demand are less sensitive to price changes.

In our cheese market example, when the price increases towards 37 from higher levels like 46 and 50, the demand is considered inelastic. This means that even as prices continue to rise, the quantity demanded doesn't decrease significantly.

Key features of inelastic demand often involve:

• Necessity goods: Products that are essential like cheese might have less elastic demand, especially if consumers see it as a necessity.
• Lack of substitutes: If there are fewer substitutes for cheese, consumers may be less responsive to price hikes.

Unit Elastic Demand

Unit elastic demand is when a change in price leads to an equivalent percentage change in the quantity demanded, resulting in an elasticity value of 1. In this particular exercise, the demand for cheese at the price of 37 is unit elastic.

Unit elastic demand means that both revenue and price adjustments move proportionally. If the price of cheese shifts slightly, the effect on quantity demanded is just enough to keep the total expenditure the same. This balance is unique and often considered a midpoint or a transition zone between elastic and inelastic ranges.

Recognizing unit elastic demand is crucial for businesses. Knowing this equality helps them understand how much they can adjust prices without affecting total revenue negatively.