The demand for health club services is Q = 350 − 2P and the marginal cost of providing these services is MC = 110 + 2Q. If a two-part tariff pricing system is used, what is the optimal price and quantity combination?
a.P = 52 and Q = 240
b.P = 199 and Q = 52
c.P = 26 and Q = 162
d.P = 162 and Q = 26
e.none of the above
To find the optimal price and quantity combination in a two-part tariff pricing system, we need to first understand what a two-part tariff is.
In a two-part tariff pricing system, the seller charges a fixed fee upfront (part one) and then charges a per-unit price for each unit sold (part two). This is commonly seen in the form of membership fees combined with a usage fee, like in health clubs.
To determine the optimal price and quantity combination, we follow these steps:
Step 1: Calculate the profit-maximizing quantity.
To find the profit-maximizing quantity, we need to set the marginal cost (MC) equal to the per-unit price (P).
MC = 110 + 2Q
P = 110 + 2Q
Now, we substitute the demand equation (Q = 350 - 2P) into the per-unit price equation:
P = 110 + 2(350 - 2P)
P = 110 + 700 - 4P
5P = 810
P = 162
Step 2: Calculate the quantity.
We substitute the optimal price (P = 162) back into the demand equation to find the quantity:
Q = 350 - 2P
Q = 350 - 2(162)
Q = 350 - 324
Q = 26
Therefore, the optimal price and quantity combination for this two-part tariff pricing system is P = 162 and Q = 26.
So, the correct answer is d. P = 162 and Q = 26.