Results 1 to 5 of 5

Math Help - Need help on Elasticity

  1. #1
    Newbie
    Joined
    Dec 2010
    Posts
    3

    Need help on Elasticity

    Consider the market for widgets. The quantity of widgets demanded by consumers is
    QD = 24 − 3PC ,
    and the quantity of widgets offered by suppliers is given by the function
    QS = 15+6PP ,
    where QD and QS are the quantity of widgets demanded and supplied, respectively, and PC and PS are the consumers’ and producers’ prices. The relationship between consumers’ and producers’ prices can be defined by the function PC = PP +T, where T denotes a tax.
    (a) Assume, initially, that there is no tax so that PP = PC = P . What is the
    equilibrium price and quantity in the widget market?
    (b) Assuming that Dε < 0, determine the elasticity of demand at the original
    equilibrium price and quantity. ( denotes the elasticity.)
    (c) Assuming that Sε> 0, determine the elasticity of supply at the original equilibrium price and quantity.
    (d) Now assume that a tax of T = 0.3 has been levied on widget production.
    Determine the impact that a change in T has on producers’ prices with the formula

    Determine the impact on consumers’ prices with the formula
    (e) Which price, PC or PP , responds more to the increase in T? Why? Calculate
    the new equilibrium quantity, consumers’ price, and producers’ price
    Last edited by silentbang; December 18th 2010 at 05:31 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Nov 2010
    From
    Clarksville, ARk
    Posts
    398

    Move this to Business Math.

    This probably belongs in the Business Math section.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    May 2010
    Posts
    1,030
    Thanks
    28
    I assume you're stuck on part (b), which is the first part involving elasticity.

    (a)
    Equilibrium: Demand = Supply
    QD=QS
    24-3PC=15+6PP

    You're told that PC=PP
    24-3P=15+6P

    Solve for P. Use the demand function to get QD. Now you have the equilibrium price (P=PC=PS) and quantity (Q=QD=QS)

    (b)
    Use the elasticity formula, which you should look up. from memory i think it is:
    D\epsilon = \frac{dQD}{dPC} \times \frac{PC}{QD}

    \frac{dQD}{dPC} comes from differentiating the demand function, and you just calculated the values of PC and QD.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Dec 2010
    Posts
    3
    thank you . I have a question: in part c/ and d/ can I use the Dε and Sε of part b . and how to solve e/
    Quote Originally Posted by SpringFan25 View Post
    I assume you're stuck on part (b), which is the first part involving elasticity.

    (a)
    Equilibrium: Demand = Supply
    QD=QS
    24-3PC=15+6PP

    You're told that PC=PP
    24-3P=15+6P

    Solve for P. Use the demand function to get QD. Now you have the equilibrium price (P=PC=PS) and quantity (Q=QD=QS)

    (b)
    Use the elasticity formula, which you should look up. from memory i think it is:
    D\epsilon = \frac{dQD}{dPC} \times \frac{PC}{QD}

    \frac{dQD}{dPC} comes from differentiating the demand function, and you just calculated the values of PC and QD.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    May 2010
    Posts
    1,030
    Thanks
    28
    in part c/ I use the Dε and Sε of part b
    if you already compued Sε [which i assume is your notation for price elasticity of supply] then thats the answer


    in part d/ I use the Dε and Sε of part b
    no, for (d) you'll need to find the new equilibrium price and quantity, and the new elasticities at that equlibrium. Use those with the formulae provided.

    how to solve e/
    Your answer to (d) will tell you which price responds most to changes in tax. Its an elasticity question....so the reason probably has something to do with that, see if you can work it out.


    all of the above comes with an "I think" caveat as i haven't actually seen the formulae in part d before.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. elasticity of demand
    Posted in the Calculus Forum
    Replies: 7
    Last Post: November 9th 2010, 06:19 PM
  2. elasticity
    Posted in the Business Math Forum
    Replies: 0
    Last Post: January 28th 2010, 06:17 PM
  3. Elasticity
    Posted in the Calculus Forum
    Replies: 6
    Last Post: September 4th 2009, 01:27 AM
  4. Elasticity
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 6th 2008, 02:10 PM
  5. Arc elasticity
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: February 12th 2008, 07:56 PM

Search Tags


/mathhelpforum @mathhelpforum