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Guided Analysis 6 In class we discussed vertical integration as means to price ...

Mar 25, 2024

Guided Analysis 6 In class we discussed vertical integration as means to price discriminate. With more practice, let's work out the details for the specific case Alcoa. Founded in 1888, Alcoa Cooperation (Aluminum Company of America) is an American industrial corporation. It is the world's eighth largest producer of aluminum, with corporate headquarters in Pittsburgh, Pennsylvania. Alcoa used vertical integration as a mechanism to price discriminate. Let's work this out more precisely in a numerical example. For simplicity, assume that Alcoa has a constant marginal cost of 20 per ingot. Also, assume Alcoa selling to only two customers: I. Electric Cable industry with a demand curve given by

Q_{E}(P)=60-P

II. Aircraft industry with a demand curve given by

Q_{A}(P)=100-P

1. At the time, the electric cable could use copper instead of aluminum while the aircraft industry had not alternative to use aluminum. Which of the two industries do you expect to have the more elastic demand curve? Why? 2. Compute the price elasticity of demand of both industries. Which one has the more elastic demand in this exercise? Is your result consistent with your answer in a., i.e., are our demand functions reasonable models (for now)? If not, can you adjust the model so that it is? 3. First, assume Alcoa cannot price discriminate. Determine the number of units sold to each industry and the overall profit Alcoa generates. To do so a. Determine the aggregate demand curve. (Hint: At any given price how many units does each of the industries want to purchase?) b. Find the MR-curve to solve the monopolist's production problem. c. Determine the price Alcoa would optimal charge and the profit it generates. 4. Now assume that Alcoa can engage in third degree price discrimination. What price would it charge in each of the two industries? How many units would it sell to each of the industries and how much profit would Alcoa make? To figure this out, a. Solve the monopolist's profit maximization problem as if Alcoa was only serving the Electric Cable industry. b. Solve the monopolist's profit maximization problem as if Alcoa was only serving the Aircraft industry. c. Determine Alcoa's profit from both industries. 5. Review the criteria necessary to sustain price discrimination. Do you think it is likely that Alcoa would be able to engage in third degree price discrimination? Why or why not? 6. Explain how Alcoa can implement third degree price discrimination through vertical integration. To implement it should Alcoa vertically integrate with the electric cable industry, the aircraft industry, or both?

Answer

The electric cable industry is expected to have the more elastic demand curve because they have an alternative (copper) to use instead of aluminum.

Solution

Electric Cable Industry Elasticity: Given the demand curve

Q_{E}(P) = 60 - P

, the price elasticity of demand at any price

P

\varepsilon_{E} = \frac{dQ_{E}/dP \cdot P}{Q_{E}} = \frac{-P}{60-P}

Aircraft Industry Elasticity: Given the demand curve

Q_{A}(P) = 100 - P

, the price elasticity of demand at any price

P

\varepsilon_{A} = \frac{dQ_{A}/dP \cdot P}{Q_{A}} = \frac{-P}{100-P}

Comparison of Elasticities: By comparing

\varepsilon_{E}

and

\varepsilon_{A}

, we can see that

\varepsilon_{E}

is more negative for any given price

P

, indicating that the electric cable industry has a more elastic demand

Key Concept

Price Elasticity of Demand

Explanation

The electric cable industry has a more elastic demand curve due to the availability of substitutes, which is consistent with the demand functions provided.

Answer

Without price discrimination, Alcoa would sell 40 units to the Electric Cable industry and 60 units to the Aircraft industry, generating a profit of $1600.

Solution

Marginal Revenue Curve: The MR curve is derived from the aggregate demand curve. For linear demand, MR has the same intercept but twice the slope

Monopolist's Production Problem: Set MR equal to MC to find the quantity where profit is maximized, then use the demand curve to find the price

Profit Calculation: Profit is calculated as

\pi = (P - MC) \times Q

, where

P

is the price and

Q

is the quantity sold

Key Concept

Monopolist's Profit Maximization without Price Discrimination

Explanation

Alcoa maximizes profit by equating marginal revenue to marginal cost, resulting in a specific quantity and price that maximizes profit without price discrimination.

Answer

With third-degree price discrimination, Alcoa would charge

40 to the Electric Cable industry and

60 to the Aircraft industry, selling 20 and 40 units respectively, and making a total profit of $2000.

Solution

Profit Maximization for Aircraft Industry: Solve the monopolist's problem for the Aircraft industry by setting MR equal to MC

Total Profit Calculation: Sum the profits from both industries to determine Alcoa's total profit with price discrimination

Key Concept

Third-Degree Price Discrimination

Explanation

Alcoa can increase its profit by charging different prices to different industries based on their respective demand elasticities, which is known as third-degree price discrimination.

Answer

It is likely that Alcoa would be able to engage in third-degree price discrimination because the two industries have different demand elasticities and Alcoa can prevent resale between them.

Solution

Key Concept

Feasibility of Price Discrimination

Explanation

Alcoa is likely to successfully implement price discrimination due to the different demand elasticities and the ability to segment the market and prevent resale.

Answer

Alcoa can implement third-degree price discrimination through vertical integration with either industry, but it would be more strategic to integrate with the electric cable industry due to its more elastic demand.

Solution

Strategic Choice of Integration: Integrating with the industry that has a more elastic demand (electric cable) would be more beneficial as it allows for greater price control and potentially higher profit margins

Key Concept

Vertical Integration and Price Discrimination

Explanation

Through vertical integration, Alcoa can better control the market and enforce price discrimination, especially in the industry with more elastic demand.