MICRO Doubt

[Shefali]

Suppose that a monopolist operates in a domestic market facing a
demand curve p= 5 - 3/2 qi, where p is the domestic price and  qi is
the quantity sold in the domestic market. This monopolist also has the
option of selling the product in the foreign market at a constant price
of 3. The monopolist has a cost function given by C(q) = q2 , where q
is the total quantity that the monopolist produces. Now, answer the
following questions.
(a) How much will the monopolist sell in the domestic market and
how much will it sell in the foreign market?

[Homer Simpson]

Monopolist will export 5/6 and produce 2/3 units domestically. Domestic price is 5.

[Shefali]

How did u solve it Tsuki??I'm not getting it

[Homer Simpson]

if we apply the usual MR=MC rule for domestic markets, we see that 5-3q = q and p>3 so the monopolist can sell cheaper overseas anyway. this is a case for dumping.

So, i equate foreign price with MC to get maximum quantity produced. I have total q now. However, we know that monopolist will charge some other price in the domestic market.

Thus to find domestic production, equate MR = Foreign price and find domestic q. calculate domestic p through the demand function.

The difference between total production and domestic production would be your exports.

[Shefali]

Thanx a lot tsuki..
Bt how did u get price as 5?When we put 2/3 in dd fn we get 4 ..then??

[Homer Simpson]

oh yes, price is 4. silly mistake while calculating. thanking you for pointing out :)

[Shefali]

Its okk..thanxx ..