give answer in 2 step with explanation at the end of each step and final answer at the end: You are the owner of a local Honda dealership. Unlike other dealerships in the area, you take pride in your

Question

give answer in 2 step with explanation at the end of each step and final answer at the end: You are the owner of a local Honda dealership. Unlike other dealerships in the area, you take pride in your "No Haggle" sales policy. Last year, your dealership earned record profits of $1.7 million. In your market, you compete against two other dealers, and the market - level price elasticity of demand for midsized Honda automobiles is -1.4. In each of the last five years, your dealership has sold more midsized automobiles than any other Honda dealership in the nation. This entitled your dealership to an additional 20 percent off the manufacturer's suggested retail price (MSRP) in each year. Taking this into account, your marginal cost of a midsized automobile is $12, 000. What price should you charge for a midsized automobile if you expect to maintain your record sales?

VIPSolutions · Accepted Answer

# Step 1: Apply the Lerner Index Formula

The Lerner Index relates a firm's optimal markup to the price elasticity of demand ($E_d$):
$$
\frac{P - MC}{P} = -\frac{1}{E_d}
$$
where:
- $P$ is the profit-maximizing price,
- $MC$ is marginal cost ($12,000),
- $E_d$ is the price elasticity of demand (-1.4).

Plugging in the values:
$$
\frac{P - 12,000}{P} = -\frac{1}{-1.4} = .714
$$

**Explanation:**  
This equation shows the optimal markup as a function of marginal cost and demand elasticity.

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# Step 2: Solve for the Optimal Price

Rearrange the equation to solve for $P$:
$$
\frac{P - 12,000}{P} = .714 \implies P - 12,000 = .714P
$$
$$
P - .714P = 12,000
$$
$$
.286P = 12,000
$$
$$
P = \frac{12,000}{.286} \approx \$41,958
$$

**Explanation:**  
Solving the equation gives the profit-maximizing price your dealership should charge for a midsized Honda automobile, given the cost advantage and market elasticity.

---

# Final Answer

**You should charge approximately $41,958 for a midsized Honda automobile to maintain record sales while maximizing profit.**

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