# mathematical economics

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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= 200-2Qi Pii=180-4Qii

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!!!

• mathematical economics -

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 = 200-4Qi
MR=MC = 200-4Qi = 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 = 200-2Q for Q<= 10 and P=180 - 6*(Q-10) for Q> 10. If we extend this latter line back to the origion, the demand equation becomes 240-6Q for Q>10. So, MR is 240-12Q. Again, solve for optimal Q, and then total profit.

For Part C, I need some clarification. Is the 5 per-unit 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.

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