Question

Write the formula for the price elasticity of supply. If an increase of 10 percent in the price of frozen pizzas results in a 9 percent increase in the quantity of frozen pizzas supplied, what is the price elasticity of supply for frozen pizzas? Is the supply of pizzas elastic or inelastic?

Short answer

The price elasticity of supply for frozen pizzas is 0.9. The supply for frozen pizzas is inelastic as the calculated elasticity is less than 1.

Step-by-step solution

Understanding Price Elasticity of Supply Formula

The formula for price elasticity of supply (Es) is given by: \(Es = \frac{\% \Delta Q_s}{\% \Delta P}\) where: \n- %ΔP is the percentage change in price \n- %ΔQs is the percentage change in quantity supplied.

Substituting the Given Values into the Formula

Given that there is a 10 percent increase in the price of pizzas (\%ΔP = 10%) and 9 percent increase in the quantity of pizzas supplied (\%ΔQs = 9%), the formula becomes: \(Es = \frac{9}{10}\)

Calculate the Price Elasticity of Supply

Solving the equation gives the price elasticity of supply for the frozen pizzas. \(Es = 0.9\)

Determining the Nature of Price Elasticity of Supply

To determine whether the supply is elastic or inelastic, one needs to compare the calculated elasticity with 1. If Es > 1, the supply is elastic. If Es < 1, the supply is inelastic. Since the calculated Es is less than 1, the supply for frozen pizzas is inelastic.

Key concepts

Percentage Change in Quantity Supplied

The percentage change in quantity supplied is a critical concept when evaluating price elasticity of supply. It represents how much the quantity of a good or service changes as a response to a price alteration in the market. To find this percentage change, you use the formula: \[ \% \Delta Q_s = \frac{(Q_f - Q_i)}{Q_i} \times 100 \] where:

• \(Q_f\) is the final quantity supplied.
• \(Q_i\) is the initial quantity supplied.

This formula tells us the percentage change, which you can then use in more complex calculations, like finding the price elasticity of supply. In the frozen pizza example, a 9% increase in quantity supplied indicates that suppliers are able to produce and offer more pizzas in response to a price increase. Understanding how much the supply shifts with price helps businesses and economists predict how markets respond to changes in demand and costs.

Percentage Change in Price

Percentage change in price measures how much the price of a product has increased or decreased over a certain period of time. It is calculated with the formula: \[ \% \Delta P = \frac{(P_f - P_i)}{P_i} \times 100 \] where:

• \(P_f\) is the final price.
• \(P_i\) is the initial price.

Calculating the percentage change in price is essential to understand the overall effect on supply and demand. In the context of frozen pizzas, a 10% increase in price implies a considerable shift in market dynamics that could influence buyers' and suppliers' behavior. Such calculations help economists determine market conditions and analyze the potential burden on consumers versus the benefits for producers.

Elasticity vs Inelasticity

Elasticity vs. inelasticity describes how the quantity supplied reacts to changes in price. **Elastic supply** means that a small change in price leads to a significant change in the quantity supplied. **Inelastic supply**, on the other hand, implies that quantity supplied is less responsive to price changes. The price elasticity of supply (\(Es\)) can be calculated using:\[ Es = \frac{\% \Delta Q_s}{\% \Delta P}\]

• If \(Es > 1\), supply is elastic.
• If \(Es < 1\), supply is inelastic.
• If \(Es = 1\), supply is unitary elastic, meaning changes in price are proportionally matched by changes in quantity supplied.

For frozen pizzas, the calculated \(Es\) of 0.9 indicates inelastic supply. This character means the producers do not significantly increase their output when the price rises. Understanding these concepts helps assess how supply chains and availability might react to shifts in market prices, useful for both producers and policymakers in crafting strategies and policies.