Cournot duopolists face demand MWTP 50 2Q If firm 1 will p

Cournot duopolists face demand MWTP = 50 - 2Q. If firm 1 will produce 5 units, what is firm 2’s marginal revenue from increasing its production from 9 to 10? (Remember, do not enter the $, and enter the - sign if negative.)

The answer is 2 but I don\'t know how.

Solution

We know P=50-2Q

When firm 1 produces 5units and firm 2 produces 9units then P=50-2(9+5)=50-2(14)=22 and Total revenue=22*9=198

When firm 2 increases production to 10 then price=20-2(15)=20 and tital revenue of firm 2 is 20*10=200

Thus Marginal revenue of 10unit is 200-198=$2