Question

The following is the demand curve for widgets

P=120 - 1.5Q

Total revenue= 120Q - 1.5Q^2

Marginal revenue = 120 - 3Q

1) At what level of output is total revenue maximized and what is the corresponding price?

2) what is the value of marginal revenue when the price is $90?

3) what is the point price elasticity when the price is $90?

Answer 1

1) At what level of output is total revenue maximized and what is the corresponding price?

the TR is maximum when the MR=0

120-3Q=0

3Q=120

Q=40

and

P=120-1.5*40=60

the price is $60 and the quantity is 40

2) what is the value of marginal revenue when the price is $90?

P=120-1.5Q

converting it to normal function

1.5Q=120-P

Q=80-(2/3)P

P=90

Q=80-(2/3)*90

Q=20

MR=120-3*20=60

the MR is $60

3) what is the point price elasticity when the price is $90?

the formula is:

$E=\frac{\partial Q}{\partial P}*\frac{P}{Q}\\ P=90\\ Q=20\\ \frac{\partial Q}{\partial P}=\frac{\partial \left ( 80-\frac{2}{3} P\right )}{\partial P}=-\frac{2}{3}\\ E=-\frac{2}{3}*\frac{90}{20}=-3$

the elasticity is -3.