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) If E: Elasticity of demand, then

Optimal price = [E / (1 + E)] x MC

= [- 3 / (1 - 3)] x $45 [Assuming the game follows law of demand, so its elasticity is -3]

= 3/2 x $45

= $67.5

(b)

Demand function is:

Q = 50,000 - 500P

Or, P = (50,000 - Q) / 500

Total revenue, TR = P x Q = (50,000Q - Q2) / 500

Marginal revenue, MR = dTR / dQ = (50,000 - 2Q) / 500

To maximize revenue, MR = 0

50,000 - 2Q = 0

2Q = 50,000

Q = 25,000

P = (50,000 - Q) / 500

= (50,000 - 25,000) / 500 = $50

Elasticity = (dQ / dP) x (P / Q)

= - 500 x (50 / 25,000)

= - 1

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