Mirk Labs is a British pharmaceutical company that currently enjoys a patent monopoly in Europe, Canada, and the U.S on Zatab, an allergy medication. The global demand for Zatob 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.
Qd=15.0 - 0.2P where Qd is annual quantity demanded in millions of units and P is wholesale price per Zatab unit. Current production costs for Zatab are constant and equal to $5 per unit. What wholesale price will Mirk labs set? How much Zatab will it produce and see annually How much annual profit does the firm make on Zatab?
Qd=15.0 - 0.2P where Qd is annual quantity demanded in millions of units and P is wholesale price per Zatab unit. Current production costs for Zatab are constant and equal to $5 per unit. What wholesale price will Mirk labs set? How much Zatab will it produce and see annually How much annual profit does the firm make on Zatab?
Based on the information you provided, Mirk Labs incurs $60 million in research and development costs and $5 in production costs for each unit of Zatab. The global demand for Zatab is given by the equation Qd = 15.0 - 0.2P, where Qd is the annual quantity demanded in millions of units and P is the wholesale price per unit.
To determine Mirk Labs' profit-maximizing price for Zatab, we need to consider a few factors. Firstly, we need to calculate the total cost (TC) per unit, which is the sum of the production costs ($5) and the fraction of R&D costs allocated to each unit of Zatab. To do this, we divide the total R&D costs ($60 million) by the expected annual quantity demanded (Qd). Since Qd is in millions of units, we need to convert the R&D cost to millions by dividing it by one million.
Total Cost (TC) = Production Cost + (R&D Cost / Qd)
Now, let's substitute the values into the equation.
TC = $5 + ($60,000,000 / Qd)
Next, we can calculate the marginal cost (MC), which represents the change in total cost for each additional unit produced. In this case, since the production costs are constant, the marginal cost is equal to the production cost ($5).
Marginal Cost (MC) = $5
To maximize profit, Mirk Labs should set the price (P) at a level where the marginal cost (MC) equals the marginal revenue (MR). Since the demand equation is linear, the marginal revenue (MR) is equal to the change in total revenue for each additional unit sold. Mathematically, it can be calculated as the derivative of the total revenue function.
Marginal Revenue (MR) = d(TR) / dQd
To calculate the marginal revenue, we differentiate the total revenue equation with respect to quantity demanded (Qd). Since the demand function is given as Qd = 15.0 - 0.2P, we need to solve for P in terms of Qd and substitute it into the total revenue equation.
Qd = 15.0 - 0.2P
0.2P = 15.0 - Qd
P = (15.0 - Qd) / 0.2
Now, we can substitute the expression for P into the total revenue equation.
TR = P * Qd
TR = [(15.0 - Qd) / 0.2] * Qd
Lastly, we differentiate the total revenue equation with respect to Qd to find the marginal revenue.
MR = d([(15.0 - Qd) / 0.2] * Qd) / dQd
To determine the profit-maximizing price, we need to set the marginal cost equal to the marginal revenue.
MC = MR
Once we solve this equation, we can find the price (P) that maximizes Mirk Labs' profit for the allergy medication Zatab.