monopolies

1st degree price discrimination

charge everyone their maximum willingness to pay (auctions, bartering)

3rd degree price discrimination

charge different prices to different groups of people (students, veterans, senior pricing, amazon student)

2nd degree price discrimination

menu pricing; seller knows the distribution of customers but can’t tell them apart, set prices and customers self sort. Cover charge or tariff.

monopoly w/ uniform pricing

1. find inverse D

2. from inverse D find MR

3. set MC = MR to find Q*

4. Plug Q* into inverse D to find P*

solve 3rd degree price discrimination

1. start with 2 inverse demand functions

2. set MR = MC for both demand functions

3. solve for the optimal q1 and q2 for both

4. Find price by substituting the optimal quantities into their inverse demand functions

3rd degree price discrimination if prices had to be uniform

1. find total demand

2. find inverse total demand

3. set MR = MC

4. solve for Q*

5. plug into inverse demand to solve for P

with uniform pricing

it could happen that only the high WTP consumers are served.

2nd degree price discrimination with single type of consumer

1. set P = MC

2. Set T* equal to consumer surplus

2nd degree price discrimination with multiple types of consumers

1. write the profit function with T(P), the cover charge as a function of price originating from the consumer surplus of the low WTP group

2. maximize profit with respect to price

3. set equal to 0 and solve for P*

4. plug P* into demand functions of each type of consumers Q1 and Q2

5. Plug P* into T(P) to determine the cover charge T*