Exercise 2 | Wiskunde op Tilburg University

A producer is a monopolist in the market and therefore he sets the price of the good. The demand function of this market is given by

$y(p)=25-p$ ,

$(0\leq p \leq 25)$ . The cost function of the producer is given by

$C(y)=y^2+5y$ . Determine the maximum profit for this monopolist.

Antwoord 1 correct

Correct

Antwoord 2 optie

$0$

Antwoord 2 correct

Fout

Antwoord 3 optie

$34$

Antwoord 3 correct

Fout

Antwoord 4 optie

$112\frac{1}{2}$

Antwoord 4 correct

Fout

Antwoord 1 optie

$50$

Antwoord 1 feedback

Correct:

$p(y)=25-y$ and hence,

$R(y)=p(y)\cdot y=-y^2+25y$ . Therefore,

$\pi(y)=-2y^2+20y$ . Then

$\pi'(y)=-4y+20=0$ gives

$y=5$ . A sign survey shows that this is a maximum location. Then

$\pi(5)=50$ .

Go on.

Antwoord 2 feedback

Wrong: This monopolist can make a positive profit.

See Example.

Antwoord 3 feedback

Wrong:

$y$ cannot be negative. Note that

$R(y)=-y^2+25y$ .

Try again.

Antwoord 4 feedback

Wrong: Consider the minus-signs:

$\pi(y)\neq-2y^2+30y$ .

Try again.