Math Problem Statement

  1. Calculate the elasticity of demand when the price of a coffee rises from ​$4 to ​$6 a cup.
  2. At what price is the elasticity of demand for coffee equal to​ 1?

Question 28 options:

$4; $3

$5; $3

$5; $4

$3; $5

1. Calculate the elasticity of demand when the price of a coffee rises from $4 to $6 a cup. 2. At what price is the elasticity of demand for coffee equal to 1?

Solution

To answer your questions based on the provided graph:

1. Calculate the elasticity of demand when the price of coffee rises from $4 to $6 a cup.

Elasticity of demand is given by the formula:

E=% change in quantity demanded% change in priceE = \frac{\% \text{ change in quantity demanded}}{\% \text{ change in price}}

From the graph, we can observe the following:

  • When the price rises from $4 to $6, the quantity demanded decreases from 150 cups to about 125 cups.

We can compute the percentage change in price and quantity demanded:

  • Percentage change in price: % change in price=644×100=50%\% \text{ change in price} = \frac{6 - 4}{4} \times 100 = 50\%

  • Percentage change in quantity demanded: % change in quantity demanded=125150150×100=16.67%\% \text{ change in quantity demanded} = \frac{125 - 150}{150} \times 100 = -16.67\%

Now we calculate the elasticity: E=16.6750=0.333E = \frac{-16.67}{50} = -0.333

Thus, the demand elasticity is inelastic because the absolute value of the elasticity is less than 1.

2. At what price is the elasticity of demand for coffee equal to 1?

Elasticity of demand is 1 at the point where the demand curve passes through the unitary elasticity point. Based on the graph, the price at which the elasticity equals 1 appears to be around $5.

Correct Answer:

  • The correct answer is $5; $4, where the elasticity of demand equals 1 at $5 and the elasticity when price rises from $4 to $6 is calculated as inelastic.

Do you need further details or have any other questions?

Here are 5 related questions:

  1. How is elasticity calculated using the midpoint formula?
  2. What are the factors that determine whether demand is elastic or inelastic?
  3. How does a price change affect total revenue when demand is elastic vs. inelastic?
  4. What happens to demand when the price of a good increases and demand is elastic?
  5. What are examples of goods with perfectly inelastic and perfectly elastic demand?

Tip: When calculating elasticity, always check the absolute value. If it's greater than 1, demand is elastic, and if it's less than 1, demand is inelastic.

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Math Problem Analysis

Mathematical Concepts

Elasticity of Demand
Percentage Change
Inelastic and Elastic Demand

Formulas

E = (Percentage change in quantity demanded) / (Percentage change in price)
Percentage change = (New value - Old value) / Old value * 100

Theorems

Elasticity of Demand Theory

Suitable Grade Level

Grades 11-12