Question

Mrs. Smith has the following demand equation for certain product: Q = 30 - 2P
A. At a price of $7, what is the point elasticity?
B. Between prices of $5 and $6 what is the arc elasticity?
C. If the market is made up of 100 individuals with demand curves identical to Mrs. Smiths what will be the point and arc elasticity for the conditions specified in parts A and B?

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A. At P = $7, Q = 30-2(7) = $16
A 1% change in price is %7.07 (up) or $$6.93 (down)
A 1% change in price results in a quantity of $15.86 or $16.14 (using Q=30-2P)
% Change in Q = (16.14-16)/16 = .0875; same thing if price decreases.
Point elasticity is then (% change in Q)/(% change in P) = .0875/.01 = .875...

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