mathematical economics
posted by ismail .
suppose a monopolist produces and sells a product ona 2 diferent markets. demand function on the two markets are repectively i=market 1 / ii=market 2
Pi= 2002Qi Pii=1804Qii
cost function is C=20(Qi+Qii)
A) what Quantities and price that maximize the firm's profit
B) how much profit is lost if price discrimination becomes illigal?
C)discuss the consequences on the optimal quantities, prices and profits of the introduction of a tax of 5 per unit sold in market 1
==i just seem to be getting very very weird answers === please i need help!!!

Always Always Always, set MC=MR
MC with respect to Qi and/or Qii is 20.
In market i:
TR is Pi*Qi = 200Qi  2Qi^2. MR is the first derivitive. So MR = 2004Qi
MR=MC = 2004Qi = 20. Solve for Qi.
Repeat for market ii. With Qi and Qii known, solve for total profit
Now for the tricky part. Derive the demand functions in a combined market (where price discrimination is illegal). P = 2002Q for Q<= 10 and P=180  6*(Q10) for Q> 10. If we extend this latter line back to the origion, the demand equation becomes 2406Q for Q>10. So, MR is 24012Q. Again, solve for optimal Q, and then total profit.
For Part C, I need some clarification. Is the 5 perunit tax apply in scenario A with price discrimination or scenario B without price discrimination. If B, can the tax be tacked on to the price, so that in market 1, consumers pay 5 more than in market 2. Or does the price after taxes still need to be the same in both markets.
I hope this helps.