Mikroøkonomi prisdiskriminaion

Hej alle,

Jeg sidder her med en eksamensopgave jeg fik til eksamen. Jeg er i tvivl om hvorvidt det udleverede rettevejledning er korrekt og tyder derfor til jeres hjælp.

opgaven er som følger og er taget på Mikro B, polit studiet:

Consider a monopolist who has the possibility to charge a two-part tariff from its product:
P(x)=F+px. The fixed (F) and the variable (p) unit part of the tarif fare are for now assumed to be
equal across the two different types of consumers.
The consumers are assumed to have a preferences over the good that can be represented by utility
functions:
 

U₁=(3/2) - (3/2)*(1-x)²-P(X)

U₂=1 -(1-x)²-P(X)

The marginal costs for the monopolist are constant and equal to c.
Finally assume that a fraction q of the customers that the monopolist is facing are type 1.
a) Write up the constraint the monopolist must consider if she wants both the customer types to
consume of the good.
b) If the monopolist can only charge one single two-part tariff, what is the optimal per-unit charge
then?
c) Explain what the incentive compatibility constraint that the monopolist would have to consider if
the monopolist could charge two different two-part tariffs, is. You do not have to find it, but you
may argue using diagrams etc. Morover, should the monopolist always choose to differentiate the
tariffs this way?