A retailer of an electronic game faces constant-elasticity price-response functi

Question

A retailer of an electronic game faces constant-elasticity price-response function with an elasticity of 3.0. It costs the retailer $45 a piece to purchase the game wholesale. At what price should the retailer sell the game to maximize total contribution? After a market study, the retailer realizes that the total market for the game consists of 50,000 people, and he loses 500 people for every $1 increase in the price of the game. At what price should the retailer price the game to maximize revenue? What is the elasticity at the revenue maximizing price?

Explanation / Answer

a) Price = MC(n/(n+1))

Price = 45(-3/-3+1) = $67.50

b) At price $72 the revenue is maximum =

If price is increased to $72, retailer would loose 13500 people.

Total Revenue = 72*(50000-13500) = $2,628,000

Price = MC(n/(n+1))

72=45(n/(n+1))

72/45=(n/(n+1))

n = 2.66 = New Elasticity is 2.66

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