Acme Pharmaceutical Company Analysis

Scenario Overview:

Acme Pharmaceutical Company has discovered a vaccine for the common cold and holds a monopoly on the drug. The company can manufacture the drug in North America and Europe at a marginal cost of $10. There are no fixed costs.

Demands:

- Europe: [tex] Q_E = 70 - P_E [/tex]
- $ Q_E $ is the quantity demanded in Europe.
- $ P_E $ is the price in Europe.

- North America: [tex] Q_N = 110 - P_N [/tex]
- $ Q_N $ is the quantity demanded in North America.
- $ P_N $ is the price in North America.

Tasks:

a. Inverse Demand Functions:
- Derive the inverse demand function for each continent.

b. Third-Degree Price Discrimination:
- If the firm engages in third-degree price discrimination, determine the optimal quantity and price for each continent to maximize profit.
- Calculate the profits earned under this scenario.

c. Single Pricing:
- If price discrimination is illegal, determine the single price $ P $ the firm will charge on both continents.
- Calculate the profits under a single pricing strategy.

d. Surplus Calculation:
- Calculate consumer and producer surplus under both scenarios (b) and (c).
- Determine if total consumer and producer surplus is higher with or without price discrimination.
- Assess whether the firm will sell the drug on both continents in both scenarios.

e. Modified Demand in Europe:
- If European demand changes to [tex] Q_E = 30 - P_E [/tex], evaluate if the firm should sell on both continents without price discrimination.

f. Altered European Demand Function:
- If European demand changes to [tex] Q_E = 55 - 0.5P_E [/tex], determine if third-degree price discrimination increases profits.

g. Patent Expiration and Generic Competition:
- Analyze the scenario where the patent expires, allowing generic manufacturers to produce the drug at the same marginal cost.
- Assume high competition among many generic drug companies.
- Calculate the equilibrium price of the drug in this competitive market.
- Compare the total consumer and producer surplus in this case with the surpluses calculated in (d) and comment on the differences.

The firm should set a higher price and lower quantity in Europe compared to North America to maximize its profit through third-degree price discrimination.

By engaging in third-degree price discrimination, Acme Pharmaceutical Company can charge different prices for the same product in different markets. To maximize its profit, the firm should set a higher price and lower quantity in Europe compared to North America. This is because the demand function in Europe, QE = 70 - Pe, indicates that as the price decreases, the quantity demanded increases.

In contrast, the demand function in the United States, QN = 110 - Pn, shows that as the price decreases, the quantity demanded also increases. By charging a higher price in Europe and a lower price in North America, the company can capture a larger portion of consumer surplus in both markets and maximize its profits.

In terms of quantities and prices, the firm should determine the profit-maximizing quantities by setting the marginal cost equal to the marginal revenue in each market. In this case, since there are no fixed costs and the marginal cost is $10, the profit-maximizing price in Europe (Pe) would be $30, resulting in a quantity demanded of 40 units (QE = 70 - Pe = 70 - 30 = 40). In North America, the profit-maximizing price (Pn) would be $60, leading to a quantity demanded of 50 units (QN = 110 - Pn = 110 - 60 = 50).

By setting these prices and quantities, Acme Pharmaceutical Company can earn profits calculated as follows: Profit = (Price - Marginal Cost) * Quantity. In Europe, the profit would be (30 - 10) * 40 = $800, and in North America, the profit would be (60 - 10) * 50 = $2,500. Therefore, the total profit for the firm would be $800 + $2,500 = $3,300.

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