Results 1 to 2 of 2

Math Help - Price Elasticity with Differentiation

  1. #1
    Newbie
    Joined
    Apr 2013
    From
    San jose
    Posts
    1

    Price Elasticity with Differentiation

    I'm having trouble with this problem from a review sheet of mine.

    Problem 2
    Consider the price-demand equation x=f(p)=(144-2p)^(1/2) , 0>p>72.

    a) Calculate the elasticity of demand at p 20, 40 and 60. Describe each case as
    elastic or inelastic. For what value of p is demand unit elastic?

    b) Express total revenue as a function of price p and find the value of p which
    maximizes total revenue.

    c) Explain, for the given price-demand equation, the connection between elasticity of
    demand and the increasing/decreasing behaviour of the total revenue function
    depending on price p !



    What I'm really struggling with is converting the equation to the correct one for a). The answer given by the review is E=(p)/(144-2p). But the closest I've come was E=1/(144-2p)

    Any help is great!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    May 2010
    Posts
    1,028
    Thanks
    28

    Re: Price Elasticity with Differentiation

    the price elasticity of demand is defined as \epsilon = \frac{dx}{dP} \frac{P}{x}

    Evaluating the derivative:
    \epsilon = \left( \frac{-1}{(144-2p)^{0.5}}   \right) \frac{p}{x}

    This is technically an answer, but it isn't much help as we have two unknowns (x,p) on the right. However you are given the demand function, so you know the relationship between x and p. subsitute x = (144-2p)^{0.5}



    \epsilon = \left( \frac{-1}{(144-2p)^{0.5}}   \right) \frac{p}{(144-2p)^{0.5}}

    which simplifies to:

    \epsilon = \frac{-p}{(144-2p)}

    i assume this is what your text book says (remember own price elasticity is almost always negative)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. price elasticity of demand
    Posted in the Business Math Forum
    Replies: 9
    Last Post: July 22nd 2010, 01:45 AM
  2. Finding Price Elasticity through differentiation
    Posted in the Business Math Forum
    Replies: 1
    Last Post: March 7th 2010, 06:39 PM
  3. own price elasticity question....
    Posted in the Business Math Forum
    Replies: 1
    Last Post: January 31st 2010, 02:51 PM
  4. price elasticity of demand of -0.5
    Posted in the Advanced Math Topics Forum
    Replies: 1
    Last Post: September 4th 2007, 07:48 PM
  5. price elasticity of demand
    Posted in the Business Math Forum
    Replies: 1
    Last Post: January 28th 2007, 08:53 PM

Search Tags


/mathhelpforum @mathhelpforum