Question

Suppose a firm is the sole producer of unique type of surf board wax. The wax can be produced at a constant marginal cost of $4/ounce. The firm faces two types of customers for their product -- west coast surfers and east coast surfers-- and the demand for both groups is given by the following inverse demand functions: ???? = 20 − 0.1????, and ???? = 12 − 0.05????. Suppose this firm wishes to charge western and eastern customers different prices for the product. What is the profit maximizing price that should be charged in each market? At these prices, what are the elasticities of demand for both markets?

Answer 1

The firm is the sole producer thus the firm is a monopolist.

Marginal Cost, MC = $ 4 / ounce

First determine the Total Revenue, TR = PQ

Differentiating TR wrt qw

The monopolist can maximize profit by equating MR to MC

Now plug in this in the demand function of west coast we get

Elasticity can be determined using the following formula

the demand function of the west coast is,

Differentiating above equation wrt Pw we get

Now determining the elasticity for west coast market

Now determining the Price quantity and elasticity for east coast market

Now equate MR to MC

Plug in this in inverse demand function,

Now express the demand function in terms of P

Differentiating above equation wrt qe

Elasticity,

	Price	Quantity	Elasticity
West Coast	$ 12	$ 8	1.5
East Coast	80	80	2

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