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

  1. Oct 4, 2009 #1
    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. jcsd
  3. Oct 4, 2009 #2

    lanedance

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    Homework Helper

    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)
     
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