Isi 2008. Monopoly and two types of demands

[Spiti]

For sub question (i), when i calculate market price, at that price for type I consumers demand is negative. So what to do? I'm stuck.
Here are the demand curves : market demand q= 20-3p/2. Solving FOC would give q=10/7 and p=12.38. But at this market price q1 is negative.

[Dreyfus]

I think in that case whole supply will supplied to group 2!

[The Villain]

@Spiti...i got the same  
q=10/7 and p=260/21.
I guess we need not calculate individual qantitites..and whole to grup 2 i guess
n how did u solve part 2...

[Dreyfus]

Ron...its 3rd degree price discrimination

[The Villain]

ohkk thanxx..got confused..

[Spiti]

Even in (ii) i am getting q1 as negative. q1=-5/7 and q2=15/7.

[Dreyfus]

Spiti...in part 2 I m getting q1 as 0.56

[Spiti]

When you say whole supply, at what price?

[Dreyfus]

At p=12.38....but there will be excess supply in dat case...

[Spiti]

Oh.. You just need to equate MR of both type consumers to MC right.
Heres what i did.
For type I MR : 10-2q1 and MC =8(q1+q2).  And similarly for type 2. I got two simultaneous equations.

[Dreyfus]

After solving these simultaneous eqs....I m getting q1=q2=0.556

[Spiti]

My two equations are 5q1+4q2=5 and 2q1+3q2=5

[Spiti]

We get q1=q2 when we equate MR1=MR2 but these values do not satisfy MR2=MC. shouldn't they? Because in 2nd type market, MR2>MC. So it pays the monopolist to increase production.