Demand function for Zatab:
Qd = 15.0 - 0.2P
Q = annual quantity demanded
P = wholesale price of one Zatab unit
Production cost per unit: $5
Mirk Lab incurred a $60 million R&D cost a decade ago
1: What wholesale price will Mirk Labs set?
2: How much Zatab will it produce and
sell annually?
3: How much annual profit does the firm make on Zatab?
Demand function for Zatab:
Qd = 15.0 - 0.2P
Production cost per unit: $5
Mirk Labs incurred a $60 million R&D cost
1) What wholesale price will Mirk Labs set?
2) How much Zatab will it produce and sell annually?
3) How much annual profit does the firm make on Zatab?
what in the world is Zatab? And, what is your question?
Zatab is an allergy medication made by MIRK Labs [British pharmaceutical] that enjoys a patent monopoly in Europe, Canada, and USA.
To answer these questions, we need to use the given demand function and information about the production cost and R&D cost.
1: To determine the wholesale price that Mirk Labs will set, we need to find the price at which the quantity demanded equals the quantity produced. We set Qd equal to Q:
Qd = Q = 15.0 - 0.2P
Now, we substitute the production cost per unit ($5) into the equation and solve for P:
15.0 - 0.2P = Q
15.0 - 0.2P = Q = P + 5
10.0 = 1.2P
P = 10.0 / 1.2
P = 8.333
Mirk Labs will set the wholesale price of one Zatab unit to be approximately $8.333.
2: To find the annual quantity of Zatab that Mirk Labs will produce and sell, we substitute the wholesale price (P) into the demand function:
Qd = 15.0 - 0.2P
Q = 15.0 - 0.2(8.333)
Q = 15.0 - 1.667
Q = 13.333
Mirk Labs will produce and sell approximately 13.333 Zatab units annually.
3: To calculate the annual profit, we need to subtract the total cost from the total revenue. The total revenue is equal to the wholesale price (P) multiplied by the annual quantity (Q). The total cost includes both the production cost and R&D cost:
Total Revenue = P * Q
Total Cost = (Production Cost * Q) + R&D Cost
Annual Profit = Total Revenue - Total Cost
Using the values from the previous calculations:
Total Revenue = $8.333 * 13.333
Total Cost = ($5 * 13.333) + $60 million
Annual Profit = ($8.333 * 13.333) - (($5 * 13.333) + $60 million)
Performing the calculations will give you the annual profit that the firm makes on Zatab.