The United States Postal Service (USPS) currently charges $0.73 per stamp.  They allow stamps.com to sell a sheet of twenty stamps with personalized photos for $1.20 per stamp.  Stamps.com keeps the extra beyond the $0.73 it pays the USPS.  If stamps.com is acting as a profit maximizing monopolist, what is their Lerner Index and what is the price elasticity of demand for a customized stamp? 

### Lerner Index Calculation:
The **Lerner Index** is a measure of a firm's market power, showing how much it can raise prices above marginal cost. It is defined as:

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

Where:
- $P$ is the price charged by the monopolist
- $MC$ is the marginal cost, which in this case is the cost Stamps.com pays to USPS for each stamp.

Given:
- $P = 1.20$ (the price Stamps.com charges for a customized stamp)
- $MC = 0.73$ (the amount Stamps.com pays to USPS for each stamp)

Substitute the values into the formula:

\[
L = \frac{1.20 - 0.73}{1.20} = \frac{0.47}{1.20}
\]

Now, calculate the Lerner Index:

\[
L = 0.3917 \approx 0.392
\]

### Lerner Index: $0.392$

### Price Elasticity of Demand:
The Lerner Index is related to the **price elasticity of demand** ($E_d$) by the formula:

\[
L = -\frac{1}{E_d}
\]

Rearrange to solve for $E_d$:

\[
E_d = -\frac{1}{L}
\]

Substitute the Lerner Index value:

\[
E_d = -\frac{1}{0.392}
\]

Now, calculate the price elasticity of demand:

\[
E_d = -2.55
\]

### Price Elasticity of Demand: $-2.55$

This means the demand for customized stamps is relatively elastic, indicating that a 1% increase in price would result in a 2.55% decrease in quantity demanded.

### Summary:
- **Lerner Index:** $0.392$
- **Price Elasticity of Demand:** $-2.55$

Would you like a more detailed explanation on any part of this?

Here are 5 related questions for further exploration:
1. How does a higher Lerner Index affect a monopolist's pricing strategy?
2. What factors could influence the elasticity of demand for customized stamps?
3. How would a reduction in the price of USPS stamps affect Stamps.com's pricing power?
4. What are the consequences of a highly elastic demand for a monopolist?
5. How does the concept of consumer surplus relate to the pricing of monopolies?

**Tip:** Elasticity greater than 1 (in absolute value) means demand is sensitive to price changes. Understanding this helps businesses adjust pricing strategies effectively.

The United States Postal Service (USPS) currently charges $0.73 per stamp. They allow stamps.com to sell a sheet of twenty stamps with personalized photos for $1.20 per stamp. Stamps.com keeps the extra beyond the $0.73 it pays the USPS. If stamps.com is acting as a profit maximizing monopolist, what is their Lerner Index and what is the price elasticity of demand for a customized stamp?

Understand how to calculate the Lerner Index and price elasticity of demand for Stamps.com custom stamps. This problem explores monopoly pricing strategies with detailed formulas, including Lerner Index calculations and demand elasticity. Suitable for undergraduate economics students.

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