Two Part Tariffs

Simple Profit Maximization

1. Find marginal revenue of the product (which is the derivative of the multiplication of the demand curve and quantity).
2. Find the marginal cost of the product
3. Set marginal cost equal to marginal revenue and solve for the quantity

Two Part Tariff when Consumer Demand is Homogeneous

1. Find the intersection between the marginal cost curve and the demand curve.
2. Solve for Q and P.
3. The fee to charge for each unit purchased should be this value of P.
4. Draw a line from the intersection of the marginal cost and demand curves to the y axis. The area above this line and below the demand curve is the consumer surplus.
5. The entrance fee should be equal to the consumer surplus.

Two Part Tariff with Different Consumer Types

There are two ways in which a firm can optimize profit in this case:

1. The firm can decide to price the entrance fee such that none of the "casual" customers will purchase any of the good. Therefore, the firm will try to maximize profit catering to just the "serious" customers.
2. The firm can try to cater to both the "serious" and "casual" customers by setting a lower entrance fee.

How do you calculate the profit in each of these two scenarios?

1. Find the intersection between the marginal cost curve and the "serious" customers demand curve. A profit is simply equal to the entire customer surplus of the serious customers.
2. In the second case
   1. first we calculate the membership fee. This will be area of the consumer surplus for the "casual" customers demand curve given a price P.
   2. next we calculate the usage profits for the "serious" and "casual" customers.
   3. third, we add up two times the membership fee, plus the usage fees for the serious and casual customers.
   4. fourth, we take the derivative of this profit function and set it equal to zero and solve for P
   5. finally, this P can be used to solve for the quantity sold to both the serious and casual customers and what the usage fee should be.