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 SI 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

1) Maximize Total Contribution = Unit Margin × Demand for the product of a single seller as a function of the price offered by that seller

At the optium price , he should achieve a contribution margin of 1/3(elasicity=3)=33% per unit .This means he should price the game at (3/2)*45=$ 67.5 in order to maximise total conribution

2)500 people are lossed for every $ 1 increase in the price of the game.That means a 1% decrease in demand from a 1.5% increase in price.the revenue maximising price will occur where the elasticity of the price response function is equal to 1.That implies there is no unconstrained revenue maximising price aassociated with a constant elasticity price response function unless the price elasticiy happens to be 1.

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