Microeconomics/Industrial Organization with group pricing problem

Heya,

I'm doing a problem on group pricing, and this individual problem really got me stuck. I don't even know where to start. I was wondering if someone could please help me out, and I will understand it afterwards. Thanks!

It's a problem about a monopolist purposely creating an inferior product so that consumers will self-select their preferred product, allowing the monopolist to charge different prices for different consumers. This is favorable even though marginal costs for the inferior product are higher.

There are 10 consumers, from i=1 to 10. Consumer i derives its utility from a uniform distribution on the interval 10-20, independent of all other consumers. The selling price is p(1), marginal cost c=6.

I first have to derive the (expected) demand function, and this is where I already get stuck. Further on I also need the (expected) profit maximizing price, and consumer surplus.

That is just the start, but the expectations and probabilities really get me confused.

The second part of the problem requires me to introduce an 'inferior' product, for which valuation of consumer i equals 0.5Vi+5, and marginal cost c=6 as well.

And here I have to show that the demand for the standard and inferior product are, respectively;

D(1)= 2P(2) - 2P(1) + 10
D(2)= 2P(1) - 4P(2) + 20

And again I have to find the profit maximizing price, profit and consumer surplus.

You would be my hero if you can help me out with this one, so I have something to fall back on when trying to solve the other problems.

Thanks a lot!