Qd=15.0-0.2P where Qd is annual quantity demanded in millions of units and P is the wholesale price. Incurred cost of $60 million. Production cost is $5/unit. (1) what is wholesale price, (2) production annually, (3) annual profit?
Given this is a monopoly with an expiring patent in 30 days, what price and quantity will result once the competition emerges in this market?
To find the wholesale price, we can rearrange the demand equation as:
Qd = 15.0 - 0.2P
Substituting the given incurred cost of $60 million, we can solve for the wholesale price:
Qd = 15.0 - 0.2P
60 = 15.0 - 0.2P
0.2P = 15.0 - 60
0.2P = -45
P = -45 / 0.2
P = -225
However, a negative price doesn't make sense in this context, so we need to consider that the price cannot be negative. In economics, price cannot be negative, so we have to revise our approach. The price is likely to be positive, so we can assume that Qd will be zero when P reaches its maximum value.
By substituting Qd = 0 into the demand equation, we can solve for P:
0 = 15.0 - 0.2P
0.2P = 15.0
P = 15.0 / 0.2
P = 75
Therefore, the wholesale price is $75.
To find the annual production, we need to calculate the quantity demanded when P = $75:
Qd = 15.0 - 0.2P
Qd = 15.0 - 0.2(75)
Qd = 15.0 - 15.0
Qd = 0
So, the annual production, represented by Qd, will be 0 units.
To calculate the annual profit, we need to subtract the production cost from the revenue (which is the wholesale price multiplied by the annual production):
Revenue = Wholesale Price × Annual Production
Revenue = $75 × 0 = $0
Production Cost = Production per unit × Annual Production
Production Cost = $5 × 0 = $0
Annual Profit = Revenue - Production Cost
Annual Profit = $0 - $0
Annual Profit = $0
Therefore, the annual profit is $0.
Now, let's consider the market once competition emerges after the patent expires in 30 days. In a competitive market, price is determined by the forces of supply and demand. The assumption of perfect competition implies that there are numerous buyers and sellers, and no single firm can influence the market price.
However, since we don't have information about the supply function, we cannot determine the exact price and quantity that will result once competition emerges. The specific price and quantity will depend on various factors, such as the market demand and the entry of new competitors.
If you have additional information about the supply function or any other relevant details, I can try to provide a more accurate answer.