Question

A manufacturer sells 50 boats per month at $25000 per boat, and each month demand is increasing at a rate of 4 boats per month. What is the fastest you could drop your price before your monthly revenue starts to drop

Answer 1

Answer:

For the revenue per month to drop, the price per boat per month has to drop more than $2,000

Explanation:

Given:

Number of boats sold per month = 50

Cost of each boat = $25,000

Each month demand increases at a rate of 4 boats per month.

Required:

Find the fastest price could drop before monthly revenue starts to drop.

Revenue, R = Price × Quantity

R = P × Q

Differntiate both sides with respect to time, t:

$\frac{dR}{dt} = \frac{dP}{dt} Q + \frac{dQ}{dt} P$

$= \frac{dP}{dt} 50 + 4 * 25,000$

For the fastest price could drop before monthly revenue starts to drop, $\frac{dR}{dt} < 0$

Thus,

$= \frac{dP}{dt} 50 + 4 * 25,000 < 0$

$= \frac{dP}{dt} 50 + 100,000 < 0$

$= \frac{dP}{dt} 50 < -100,000$

$\frac{dP}{dt} = \frac{-100,000}{50}$

$\frac{dP}{dt} = -2,000$

Since the answer is negative, it indicates a drop in price.

Therefore, for the revenue per month to drop, the price per boat per month has to drop more than $2,000