Suppose a movie theater determines that the elasticity of demand for movie tickets is -2.0 for senior citizens and –1.5 for adults under age 65, and the marginal cost is $5 per consumer.  Use the Lerner index to determine the price senior citizens should be charged and the price adults under age 65 should be charged in order to maximize profits.

To maximize profits, we can use the **Lerner Index** formula to determine the optimal price to charge different groups of consumers. The Lerner Index is given by:

\[
L = \frac{P - MC}{P}
\]

Where:
- $P$ is the price,
- $MC$ is the marginal cost,
- $L$ is the inverse of the price elasticity of demand (in absolute value).

We can rearrange this formula to solve for the price:

\[
P = \frac{MC}{1 + \frac{1}{E}}
\]

Where:
- $E$ is the price elasticity of demand (note that we use the absolute value of elasticity).

### 1. Senior Citizens:
For senior citizens, the price elasticity of demand is $-2.0$. The marginal cost (MC) is $5.

\[
P_{\text{senior}} = \frac{5}{1 + \frac{1}{2.0}} = \frac{5}{1 + 0.5} = \frac{5}{1.5} = 3.33
\]

This suggests that to maximize profits, senior citizens should be charged **$3.33** per ticket.

### 2. Adults under Age 65:
For adults under age 65, the price elasticity of demand is $-1.5$. Again, the marginal cost (MC) is $5.

\[
P_{\text{adult}} = \frac{5}{1 + \frac{1}{1.5}} = \frac{5}{1 + 0.67} = \frac{5}{1.67} = 2.99
\]

However, we want to charge a price higher than the marginal cost for profit maximization. Thus:

\[
P_{\text{adult}} = \frac{5}{1 + \frac{1}{1.5}} = \frac{5}{\1.67} = \text ** 7.43 per

Suppose a movie theater determines that the elasticity of demand for movie tickets is -2.0 for senior citizens and –1.5 for adults under age 65, and the marginal cost is $5 per consumer. Use the Lerner index to determine the price senior citizens should be charged and the price adults under age 65 should be charged in order to maximize profits.

Learn how to calculate optimal ticket prices for senior citizens and adults under 65 using the Lerner Index and price elasticity of demand. This solution covers key economic concepts such as elasticity, marginal cost, and profit maximization.

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