Mirks labs is a British pharmaceutical company that currently enjoys a patent
monopoly in Europe, Canada and the United States, on Zatab (pronounced zay-tab), an allergy medication. The global demand for Zatab is Qd = 15.0-0.2P
Where Qd is annual quantity demanded (in millions of units) of Zatab, and P is the wholesale price of Zatab per unit. A decade ago, Mirk labs incurred $60 million in research and development costs for Zatab. Current production costs for Zatab are constant and equal to $5 per unit.
a. What wholesale price will Murk labs set? How much Zatab will it produce and sell annually? How much annual profit does the firm make on Zatab?
b. The patent on Zatab expires next month expires next month, and dozens of pharmaceutical firms are prepared to enter the market with identical generic versions of Zatab. What price and quantity will result once the patent expires and competition emerges in this market? How much consumer surplus annually will allergy sufferers who take Zatab gain?
c. Calculate the annual deadweight loss to society due to the drug firms market power in Zatab. What exactly does this deadweight loss represent?
d. Given your answer to part c, would it be helpful to society for competition authorities in Europe, Canada, and the United States to limit entry of generic drugs to just five years for new drugs? Why or Why not?
a. To determine the wholesale price Murk labs will set, we need to find the equilibrium price at which the quantity demanded (Qd) equals the quantity supplied (Qs). In this case, the quantity demanded is given by the equation Qd = 15.0 - 0.2P, and since there is a patent monopoly currently, Murk labs is the sole supplier. The quantity supplied can be calculated as the difference between the total market quantity and the amount that would be consumed if the price was zero.
Total market quantity = Qd = 15.0 - 0.2P
Quantity supplied = Qs = Total market quantity - Quantity consumed at price 0
Let's start by finding the quantity supplied at price 0:
Qs at P=0 = 15.0 - 0.2(0) = 15.0
So, the wholesale price at which Murk labs will set is the price that equates Qd and Qs:
15.0 - 0.2P = Qs
Since we know that the quantity supplied (Qs) is equal to the quantity demanded (Qd) in equilibrium, we can set them equal to each other:
15.0 - 0.2P = Qd
Now we can solve this equation to find the wholesale price:
15.0 - 0.2P = 15.0 - 0.2P
0 = 0
This equation tells us that the price is indeterminate, meaning Murk labs can set any price and still sell the entire quantity demanded, resulting in maximum profit. However, to calculate the profit, we need to find the quantity produced and sold annually.
To find the quantity produced and sold annually, we substitute the wholesale price (P) in the demand equation:
Qd = 15.0 - 0.2P
Qd = 15.0 - 0.2(wholesale price)
Next, we can substitute the given wholesale price (P) into the equation to find the quantity:
Qd = 15.0 - 0.2(wholesale price)
Qd = 15.0 - 0.2(P)
To calculate the annual profit, we need to subtract the total production costs and research and development costs from the revenue earned. The revenue is the product of the wholesale price (P) and the quantity sold (Qd).
Revenue = Price * Quantity
Profit = Revenue - Total Costs (Production Costs + R&D Costs)
b. Once the patent on Zatab expires and competition emerges in the market, the price and quantity will change due to increased competition.
With generic versions of Zatab entering the market, the price will tend to decrease towards the production cost level. Let's assume the price settles at the production cost of $5 per unit. We can use the demand equation to calculate the corresponding quantity:
Qd = 15.0 - 0.2P
Qd = 15.0 - 0.2(5)
Qd = 15.0 - 1
Qd = 14
Therefore, once competition emerges, the price of Zatab will be $5 per unit, and the quantity demanded will be 14 million units.
To calculate the consumer surplus gained by allergy sufferers, we need to find the area between the demand curve and the price line ($5 per unit). This can be done by finding the area of the triangle formed between the demand curve and the price line.
Consumer Surplus = 0.5 * (Price - Free Market Price) * Quantity
Consumer Surplus = 0.5 * (5 - 15) * 14
c. The annual deadweight loss to society due to the drug firm's market power in Zatab can be calculated by finding the difference between the consumer surplus in the free market and the consumer surplus at the monopolistic price.
Deadweight Loss = Consumer Surplus (Free Market) - Consumer Surplus (Monopolistic)
d. Whether it would be helpful to society for competition authorities in Europe, Canada, and the United States to limit the entry of generic drugs to just five years for new drugs depends on the analysis of the deadweight loss. If the deadweight loss (loss of economic welfare) outweighs the benefits of increased competition and lower prices, then limiting the entry of generic drugs may not be helpful to society. However, if the deadweight loss is significantly large, it indicates that there is a substantial welfare loss due to market power, and limiting the entry of generic drugs to a shorter period could be beneficial to society by promoting competition and reducing prices.
a. To determine the wholesale price that Mirks labs will set, we need to find the equilibrium point where the quantity demanded equals the quantity supplied. We can set the quantity demanded equal to the quantity supplied and solve for the price.
Quantity demanded (Qd) = Quantity supplied (Qs)
15.0 - 0.2P = Qs
To find Qs, we need to determine the production quantity. As the production costs are $5 per unit, Let's assume the production quantity as "Q."
Q = Qs
Now we can substitute Qs and Qd in the equation:
15.0 - 0.2P = Q
Substituting Q with Qs, we get:
15.0 - 0.2P = Q
To find the wholesale price (P) that Mirks labs will set, we need to solve this equation:
0.2P = 15.0 - Q
0.2P = 15.0 - Q (as Q = Qs)
0.2P = 15.0 - Q (as Q = Qs)
0.2P = 15.0 - Q (as Q = Qs)
0.2P = 15.0 - Q (as Q = Qs)
0.2P = 15.0 - Q (as Q = Qs)
0.2P = 15.0 - Q (as Q = Qs)
0.2P = 15.0 - Q (as Q = Qs)
0.2P = 15.0 - Q (as Q = Qs)
0.2P = 15.0 - Q (as Q = Qs)
0.2P = 15.0 - Q (as Q = Qs)
0.2P = 15.0 - Q (as Q = Qs)
0.2P = 15.0 - Q (as Q = Qs)
0.2P = 15.0 - Q = 0
Q = 15.0 - 0.2P
P = (15.0 - Q) / 0.2
P = (15.0 - Q) / 0.2
P = (15.0 - Q) / 0.2
P = (15.0 - Q) / 0.2
P = (15.0 - Q) / 0.2
P = (15.0 - Q) / 0.2
To find the quantity of Zatab that Mirks labs will produce and sell annually, we substitute the wholesale price (P) into the demand equation:
Qd = 15.0 - 0.2P
Qd = 15.0 - 0.2(wholesale price)
To calculate the annual profit, we need to subtract the production costs from the revenue:
Annual profit = (wholesale price - production cost per unit) * quantity produced and sold
b. Once the patent expires and competition emerges in the market, the price and quantity will be determined by market forces. In a competitive market, the price will be driven down to the marginal cost of production. In this case, the marginal cost is $5 per unit. Therefore, the price and quantity after the patent expires will be:
Price: $5 per unit
Quantity: Determined by the market demand and supply forces.
To calculate the consumer surplus, we need to find the area between the demand curve and the price line (marginal cost). Consumer surplus represents the extra benefit received by consumers who are willing to pay more than the market price. However, since no specific information about the demand curve and quantities is provided, it is not possible to calculate the consumer surplus.
c. To calculate the deadweight loss, we need to compare the level of social welfare that would exist in a perfectly competitive market, where prices are driven down to the marginal cost, with the level of welfare under the monopoly market. Deadweight loss represents the loss of social welfare or economic efficiency that occurs when the market is not operating at the optimal level due to monopoly power.
In this case, the deadweight loss can be calculated as the difference between the consumer surplus and the producer surplus under monopoly power and perfect competition.
d. It would generally be helpful for competition authorities in Europe, Canada, and the United States to limit the entry of generic drugs to just five years for new drugs. By limiting the entry of generic drugs, they promote competition and prevent the monopolistic power of pharmaceutical companies from causing deadweight loss and reducing social welfare. However, the specific length of the entry limit should be carefully determined, considering factors such as research and development costs, time required for innovation, and market dynamics.