Answer:
E = -2. The demand is going down by 2% per 1% increase in price at that price level.
The price that gives a maximum revenue is $22.5. The maximum revenue is $9112.5
Step-by-step explanation:
The overall demand formula: Q = aP + b
Q = 990 - 22P
Demand elasticity:
At P = $30, the Q = 990 - 22×30 = 330. a = [tex]\frac{dQ}{dP}[/tex] = -22
The formula for demand elasticity: E = [tex]\frac{dQ}{dP}[/tex]×[tex]\frac{P}{Q}[/tex]
Demand elasticity at $30: E = -22 × [tex]\frac{30}{330}[/tex] = -2
So, The demand will be going down by 2% if 1% increase in price.
Revenue:
R = P×Q = P×(990 - 22P) = -22P² - 990P
R' = -44P - 990. The revenue is maximum when R' = 0
⇔0 = -44P - 990 ⇔ P = $22.5
At the P = $22.5, the Q = 990 - 22×22.5 = 495.
The maximum revenue = $22.5×495 = $11,137.5
