The demand function for a good is given as $$P = 50 - 2Q$$
- Write down expressions for the TR and MR functions.
- Find and classify the type of the point price elasticity at price $P = 10$
- Calculate the output at which TR is a maximum, and use
$\hspace{0.4cm}$ second order conditions to confirm that it is maximum. - Confirm that marginal revenue is zero at maximum point.
$ TR = P×Q \Rightarrow TR=(50−2Q)Q=50Q-2Q^2$
The marginal revenue function is the first derivative of the total revenue function
$MR=50-4Q$
When the derivative of TR=0 in that point it reachs its maximum value($Q=\frac{50}{4}$)
The Price elasticity($e_p=\frac{P_o}{Q_o}*Q(P_o)'$)
$e_p=\frac{10}{20}*0.5=1/4=0.25$ which means Relatively Inelastic