Mirk Labs is a pharmaceutical company that currently enjoys a patent monopoly in Europe, Canada, and the U.S. on Zatab, an allergy medication. The global demand for Zatab is Qd= 15.0- 0.2 P 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 cost for Zatab. Current production costs for Zatab are constant and equal to $5 per unit. (A) What wholesale price will Mirk 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 Zatb 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? Explain your answer.
(A) To find the wholesale price that Mirk Labs will set, we need to determine the point where the firm maximizes its profit. This occurs when the marginal cost equals the marginal revenue.
First, let's calculate the marginal revenue:
MR = d(Qd)/dP
MR = -0.2
Since the production cost per unit is constant at $5, the marginal cost is:
MC = $5
Setting MR = MC, we can solve for the wholesale price:
-0.2P = $5
P = $5 / -0.2
P = -$25 (not possible)
Since a negative price is not realistic, we need to reconsider our approach.
The demand function equation given is:
Qd = 15 - 0.2P
We can set this equation equal to the production cost per unit ($5) to find the quantity demanded at the wholesale price that covers the cost:
15 - 0.2P = $5
Solving for P:
0.2P = 15 - $5
0.2P = $10
P = $10 / 0.2
P = $50
Thus, Mirk Labs will set the wholesale price at $50 per unit.
To find the quantity of Zatab that will be produced and sold annually, we substitute this price into the demand equation:
Qd = 15 - 0.2P
Qd = 15 - 0.2($50)
Qd = 15 - $10
Qd = 5 million units
Therefore, Mirk Labs will produce and sell 5 million units of Zatab annually.
To calculate the annual profit, we need to subtract the total production costs from the total revenue:
Total revenue = P * Qd
Total revenue = $50 * 5 million
Total revenue = $250 million
Total production costs = Production cost per unit * Quantity produced
Total production costs = $5 * 5 million
Total production costs = $25 million
Profit = Total revenue - Total production costs
Profit = $250 million - $25 million
Profit = $225 million
Hence, the firm makes an annual profit of $225 million on Zatab.
(B) Once the patent on Zatab expires and competition emerges in the market, the price and quantity will adjust based on market forces. With the entry of generic versions, the market will become more competitive, leading to a downward pressure on prices.
Assuming perfect competition, the price will approach the marginal cost in the long run. Given that the production cost per unit is $5, we expect the price to gravitate towards the production cost level.
Therefore, once the patent on Zatab expires and competition emerges, the price is likely to decrease to around the $5 production cost per unit. The quantity demanded will depend on the new equilibrium reached between price and demand, as it will be determined by the intersection of the new demand curve and the new supply curve in the market.
To answer the questions, let's go step by step.
(A) What wholesale price will Mirk Labs set?
To find the wholesale price set by Mirk Labs, we need to equate the quantity demanded equation with the production cost equation. The production cost per unit is $5.
Qd = 15 - 0.2P (demand equation)
Cost per unit = $5
Setting Qd equal to the quantity that will be produced and sold (Qs) at a given price, and solving for P, we get:
Qs = 15 - 0.2P = Qd
15 - 0.2P = QS
0.2P = 15 - Qs
P = (15 - Qs) / 0.2
Now, let's determine the quantity produced and sold annually.
How much Zatab will it produce and sell annually?
To find the annual quantity produced and sold (Qs), we can substitute the wholesale price (P) into the quantity demanded equation.
Qs = 15 - 0.2P
Qs = 15 - 0.2((15 - Qs) / 0.2)
Qs = 15 - (15 - Qs)
Qs = Qs
The result shows that the quantity produced and sold annually (Qs) will equal the quantity demanded (Qd).
Now, let's calculate the annual profit made by the company.
How much annual profit does the firm make on Zatab?
To find the annual profit, we need to subtract the total cost (which includes the research and development cost) from the total revenue.
Total revenue = Wholesale price (P) * Quantity sold (Qs)
Total cost = Research and development cost + (Production cost per unit * Quantity sold)
Annual profit = Total revenue - Total cost
Total revenue = P * Qs
Total cost = $60 million + ($5 * Qs)
Annual profit = (P * Qs) - ($60 million + ($5 * Qs))
(B) What price and quantity will result once the patent expires and competition emerges in this market? Explain your answer.
Once the patent on Zatab expires and competition emerges in the market, pharmaceutical firms can produce identical generic versions of Zatab. This means that the market will no longer have a monopoly, leading to increased competition.
Under competitive conditions, firms tend to produce where price equals marginal cost. In this case, the marginal cost is constant at $5 (as stated earlier). Hence, in the long run, the price will settle at the marginal cost.
Therefore, once competition emerges, the price of Zatab would be expected to decrease to $5 per unit (assuming there are no other factors affecting price). As for the quantity sold, it will depend on the new demand and supply equilibrium in the market, which may differ from the initial quantity sold under the patent monopoly.
To determine the new equilibrium price and quantity, more information is needed about the demand and supply conditions after the patent expiration.