# Marginal revenue as a function of *price* instead of quantity?

1. Oct 4, 2009

### glass.shards

1. The problem statement, all variables and given/known data
Mondo Inc. estimates that it can sell 3400 of its premium espresso machine, the Caffeinator, at a price of $900 each, but it will lose 100 sales for each$50 increase in price of the machine. Let p be the price and q be the number of machines sold.
(a) Write q as a linear function of p.
(b) Write the revenue R as a function of p, and find the marginal revenue, MR, with respect to p.

2. Relevant equations
This is straight out of an exam so I'm guessing it's not a typo. Isn't revenue usually a function of the quantity produced, not the price? I can solve for an equation for part a), but part b) eludes me.

3. The attempt at a solution
I got q = -2p + 5200 for a), but have no idea how to do b).

Am I reading the question wrong? Any help would be very much appreciated, thanks so much in advance! =)

2. Oct 4, 2009

### lanedance

you have a direct relation between q & p, q(p) , so should first write total revenue as

R(p) = q(p).p

then substitue for q(p) in terms of p

ie because of the direct relation, you should be able to express it in terms of either, R(q) = R (p)