Question

b. Using the midpoint method (show your work), calculate the price elasticity of demand when the price of an ice cream cone rises from $3 to $4. What does this estimate imply about the price elasticity of demand for ice cream cones?

Answer 1

Answer on Question #50396 – Economics – Microeconomics

Using the midpoint method (show your work), calculate the price elasticity of demand when the price of an ice cream cone rises from $3 to $4. What does this estimate imply about the price elasticity of demand for ice cream cones?

We denote that:

$Q_{1}$ is the demand for ice cream cone with the price $3;

$Q_{2}$ is the demand for ice cream cone with the price $4.

The price elasticity of demand for ice cream cones is:

$$E = \frac {\left(Q _ {2} - Q _ {1}\right) / \frac {Q _ {1} + Q _ {2}}{2}}{\left(P _ {2} - P _ {1}\right) / \frac {P _ {1} + P _ {2}}{2}} = \frac {Q _ {2} - Q _ {1}}{Q _ {1} + Q _ {2}} * \frac {P _ {1} + P _ {2}}{P _ {2} - P _ {1}} = \frac {Q _ {2} - Q _ {1}}{Q _ {1} + Q _ {2}} * \frac {\$ 3 + \$ 4}{\$ 4 - \$ 3} = 7 * \frac {Q _ {2} - Q _ {1}}{Q _ {1} + Q _ {2}}$$

If $E < 1$, than the demand is inelastic: the product price growth largely overlaps the decline in demand and the gross income increases.

If $E = 1$, the product price growth only compensates the reduction of demand for it and income does not change.

If $E > 1$, than the demand is elastic: the product price growth does not cover a significant decrease in the demand for ice cream cone and, therefore, gross income of the seller reduces.

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