Answer:
The monopolist's net profit function would be:
[tex]N(y)=198\,y\,-\,2.5\,y^2[/tex]
Step-by-step explanation:
Recall that perfect price discrimination means that the monopolist would be able to get the maximum price that consumers are willing to pay for his products.
Therefore, if the demand curve is given by the function:
[tex]P(y)=200-2y[/tex]
P stands for the price the consumers are willing to pay for the commodity and "y" stands for the quantity of units demanded at that price.
Then, the total income function (I) for the monopolist would be the product of the price the customers are willing to pay (that is function P) times the number of units that are sold at that price (y):
[tex]I(y)=y*P(y)\\I(y)=y\,(200-2y)\\I(y)= 200y-2y^2[/tex]
Therefore, the net profit (N) for the monopolist would be the difference between the Income and Cost functions (Income minus Cost):
[tex]N(y)=I(y)-C(y)\\N(y)=(200\,y-2y^2)-(2y+0.5y^2)\\N(y)=198\,y\,-\,2.5\,y^2[/tex]
