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Homework answers / question archive / Suppose that a manufacturer sells a product through an upscale boutique and, with a different brand name, through a discount retailer

Suppose that a manufacturer sells a product through an upscale boutique and, with a different brand name, through a discount retailer

Economics

Suppose that a manufacturer sells a product through an upscale boutique and, with a different brand name, through a discount retailer. The elasticity of demand at the boutique is -4, and at the discount retailer it is -3.

 

a) Write the formula that connects marginal revenue to price elasticity of demand through price of the good. [2 marks]

 

b) Use the formula from part a) to calculate marginal revenue in the boutique if the optimal price at the boutique is $72. [4 marks]

 

c) If the optimal price at the boutique is $72, what price should be charged at the discount retailer? [6 marks] (Hint: Consider marginal revenues in the two markets.)

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a) The relevant formula is as follows:

MR = P*(1+(1/Ep))

Here, 

MR = Marginal Revenue

P = Price of the Good

Ep = Price Elasticity of Demand

 

 

b) At the boutique, Ep = -4, and P = $72

Thus applying the formula,

MR = 72*(1+(1/-4))

MR = 63 * 0.75

MR = $54

Thus, at P = $72, MR = $54 at the boutique.

 

c) 

Lerner Index (LI) = - 1 / Elasticity

Again, LI = (P - MC) / P

For boutique,

LI = - 1 / - 4 = 0.25

So,

0.25 = (72 - MC) / 72

18 = 72 - MC

MC = 72-18 

MC = $54

 

For the discount retailer, 

LI = - 1 / - 3 = 0.3333

0.3333 = (P - 54) / P

0.3333P = P - 54

P - 0.3333P = 54

0.66667P = 54

P = 54/0.66667

P = 81

 

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