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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. 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.)
Expert Solution
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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