AskSia
Plus
Guided Analysis 6
In class we discussed vertical integration as means to price ...
Mar 26, 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 QE(P)=60−P
II. Aircraft industry with a demand curve given by QA(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
b
Electric Cable Industry Elasticity: Given the demand curve QE(P)=60−P, the price elasticity of demand at any price P is εE=QEdQE/dP⋅P=60−P−P
c
Aircraft Industry Elasticity: Given the demand curve QA(P)=100−P, the price elasticity of demand at any price P is εA=QAdQA/dP⋅P=100−P−P
d
Comparison of Elasticities: By comparing εE and εA, we can see that εE 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
b
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
c
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
d
Profit Calculation: Profit is calculated as π=(P−MC)×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 40totheElectricCableindustryand60 to the Aircraft industry, selling 20 and 40 units respectively, and making a total profit of $2000.
Solution
b
Profit Maximization for Aircraft Industry: Solve the monopolist's problem for the Aircraft industry by setting MR equal to MC
c
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
b
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.
Guided Analysis 9
A Strategic Horizontal Interaction
The week before Christmas is the best opening date for children's movies. Suppose Disney and DreamWorks have each a movie ready both of which have a priori the same expectations of becoming a hit. A movie that opens alone in that weekend in the US is expected to bring revenues from its cinema run of $150 m. The expected take per movie if two movies open at the same time against each other is $75 m. On the other hand, a studio can choose to move its opening to January, in which case the total expected take for an animated movie is $100 m, while if two open in January against each other each takes $50 m. Suppose that both studios are working on the same assumptions and projections.
1. Draw the pay-off matrix.
2. Keeping each player's actions fixed, identify the other player's best choice. Indicate this with arrows in the pay-off matrix.
3. Is there a stable outcome? If so, which one?
4. Is this a prisoners' dilemma? Why or why not?
Suppose now that DreamWorks publicizes a contract that allows Burger King and Wal-Mart to sell action figures related to the DreamWorks movie. The contract stipulates that DreamWorks has to pay a penalty of $30 m if the movie does not open for Christmas.
5. Draw the new pay-off matrix.
6. Keeping each player's actions fixed, identify the other player's best choice. Indicate this with arrows in the pay-off matrix.
7. Is there a stable outcome? If so, which one?
8. How likely do you think DreamWorks is to pay the penalty of $30 m ?
9. Do you think it is possible that during the negotiations with Burger King and Wal-Mart, DreamWorks suggested to put in the penalty clause? Why or why not?
Answer
The pay-off matrix for Disney (D) and DreamWorks (DW) is as follows:
| | DW: Christmas | DW: January |
|----------|---------------|-------------|
| D: Christmas | (75, 75) | (150, 100) |
| D: January | (100, 150) | (50, 50) |
Solution
a
Pay-off Matrix: The matrix represents the possible outcomes for Disney and DreamWorks based on their choices of releasing their movies either before Christmas or in January. The first number in each pair represents Disney's revenue in millions of dollars, and the second number represents DreamWorks' revenue
b
Best Choices: To identify the best choice for each player, we compare the pay-offs within each row for Disney and within each column for DreamWorks. For Disney, if DreamWorks releases at Christmas, Disney's best response is to release in January (100 > 75). If DreamWorks releases in January, Disney's best response is to release at Christmas (150 > 50). For DreamWorks, if Disney releases at Christmas, DreamWorks' best response is to release in January (150 > 75). If Disney releases in January, DreamWorks' best response is to release at Christmas (100 > 50)
c
Stable Outcome: A stable outcome, or Nash Equilibrium, occurs when neither player has an incentive to deviate from their strategy given the other player's choice. In this case, there are two Nash Equilibria: (Disney: Christmas, DreamWorks: January) and (Disney: January, DreamWorks: Christmas)
d
Prisoners' Dilemma: This situation is not a prisoners' dilemma because there are two Nash Equilibria and mutual cooperation (both releasing in January) does not lead to the highest individual pay-off for either player. In a prisoners' dilemma, players are typically worse off when they both defect, despite it being their dominant strategy
Key Concept
Nash Equilibrium
Explanation
A Nash Equilibrium is a situation where no player can benefit by changing their strategy while the other players keep theirs unchanged. In this case, there are two Nash Equilibria, indicating two stable outcomes where neither Disney nor DreamWorks would benefit from changing their release dates unilaterally.
Answer
The new pay-off matrix with the penalty clause for DreamWorks is:
| | DW: Christmas | DW: January |
|----------|---------------|-------------|
| D: Christmas | (75, 75) | (150, 70) |
| D: January | (100, 120) | (50, 20) |
Solution
a
New Pay-off Matrix: The penalty reduces DreamWorks' pay-offs by 30millioniftheydonotreleaseforChristmas.Thenewpay−offsforDreamWorkswhenreleasinginJanuaryarenow70 million (if Disney releases at Christmas) and $20 million (if Disney also releases in January)
b
Best Choices with Penalty: For Disney, the best response to DreamWorks releasing at Christmas remains releasing in January (100 > 75). If DreamWorks releases in January, Disney's best response is still to release at Christmas (150 > 50). For DreamWorks, the best response to Disney releasing at Christmas is now to release at Christmas as well (75 > 70), and if Disney releases in January, DreamWorks' best response is to release at Christmas (120 > 20)
c
Stable Outcome with Penalty: The stable outcome, or Nash Equilibrium, with the penalty is now (Disney: January, DreamWorks: Christmas). This is because DreamWorks has a disincentive to move to January due to the penalty
d
Likelihood of Paying Penalty: DreamWorks is unlikely to pay the penalty because their best response to any of Disney's actions is to release at Christmas, which avoids the penalty
e
Penalty Clause Suggestion: It is possible that DreamWorks suggested the penalty clause during negotiations to commit credibly to a Christmas release, thus deterring Disney from choosing the same date and avoiding a direct competition that would lower their revenues
Key Concept
Credible Commitment
Explanation
A credible commitment is an action taken by a firm to convince other players of its intended strategy. By publicizing the penalty clause, DreamWorks may have been attempting to make a credible commitment to a Christmas release, influencing Disney's decision-making process to avoid a simultaneous release.
© 2023 AskSia.AI all rights reserved