Suppose that BMW can produce any quantity of cars at a...

Suppose that BMW can produce any quantity of cars at a constant marginal cost equal to $\$ 20,000$ and a fixed cost of $\$ 10$ billion. You are asked to advise the CEO as to what prices and quantities BMW should set for sales in Europe and in the United States, The demand for BMWs in each market is given by $$Q_{E}=4,000,000-100 P_{E}$$ and $$Q_{u}=1,000,000-20 P_{\mathrm{U}}$$ where the subscript $E$ denotes Europe, the subscript $u$ denotes the United States. Assume that BMW can restrict U.S. sales to authorized BMW dealers only. a. What quantity of BMWs should the firm sell in each market, and what should the price be in each market? What should the total profit be? b. If $\mathrm{BMW}$ were forced to charge the same price in each market, what would be the quantity sold in each market, the equilibrium price, and the company's profit?

Suppose that BMW can produce any quantity of cars at a constant marginal cost equal to $\$ 20,000$ and a fixed cost of $\$ 10$ billion. You are asked to advise the CEO as to what prices and quantities BMW should set for sales in Europe and in the United States, The demand for BMWs in each market is given by
$$Q_{E}=4,000,000-100 P_{E}$$ and $$Q_{u}=1,000,000-20 P_{\mathrm{U}}$$
where the subscript $E$ denotes Europe, the subscript
$u$ denotes the United States. Assume that BMW can restrict U.S. sales to authorized BMW dealers only.
a. What quantity of BMWs should the firm sell in each market, and what should the price be in each market? What should the total profit be?
b. If $\mathrm{BMW}$ were forced to charge the same price in each market, what would be the quantity sold in each market, the equilibrium price, and the company's profit?

Key Concepts

Cost Structures

Cost structures, comprising constant marginal cost and fixed cost elements, are important in determining profitability. The constant marginal cost influences the decision on how many units to produce, while the fixed cost must be covered by revenues, especially in high fixed cost industries, to ensure overall profitability.

Demand Analysis

Demand analysis entails studying how quantity demanded varies with price. By understanding the demand function for each market, firms can derive marginal revenue functions which are crucial in setting optimal prices and output levels in different markets.

Price Discrimination

This concept involves charging different prices to different consumer groups for the same product based on their willingness to pay. It requires an understanding of how market segmentation (separating different consumer groups) allows firms to maximize profits by capturing more consumer surplus. It also necessitates that the firm can prevent arbitrage between markets.

Profit Maximization

Profit maximization is the process of determining the output level where the difference between total revenue and total cost is the greatest. In the context of monopolistic or dominant firms, this is typically achieved by setting marginal revenue equal to marginal cost, taking into account both variable and fixed costs.

Market Segmentation

Market segmentation involves dividing a market into distinct subsets of consumers with different demand characteristics. In pricing strategies, effective segmentation enables a firm to tailor prices and output to each segment’s demand conditions, thereby enhancing overall profitability.

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