About four years ago, Kanye West performed at the UIC
Pavilion. General admission tickets were priced at $30. Concert promoters say
that price elasticity of demand for general admission concert tickets was-1.5. Although this show was sold out,
concert promoters estimate that they could have sold 30% more general admission
tickets if space allowed. How much could the concert promoters have raised the
price of a general admission ticket (in dollars) and still maintained a
sell-out (assuming all the other demand factors are held constant)?
solution: Given, price of general tkts=$ 30 Price el of demand = -1.5 Let the number of tkts sold be x. Total revenue = 30x Had they sold 30% more general tkts, number of tkts = x+0.3x = 1.3x Price of each = 30 Total rev = 30*1.3x II ) let the price be raised by m% Thus, new price = 30+(m% of 30) Qty will fall fown, new qty = (x-1.5m % x) Now, revenue = (30+(m% of 30)) ((x-1.5 m % x)) To earn the same revenue in the two cases…
it should happen that, 30*1.3x =(30+(m% of 30)) ((x-1.5 m % x)) => 39 x = (30x-0.45mx+0.30mx-0.0045m^2 x) Solving this equation quadratically, we have, m=24.83% Thus, the prices of the tickets could have been raised by 24.83% to earn revenues same as by hiking the number of tickets.