Suppose a typical consumer\'s inverse demand function for bottled water at a res

Question

Suppose a typical consumer's inverse demand function for bottled water at a resort area where one firm owns all the rights to a local spring is given by P = 15 - 3Q. The marginal cost for gathering and bottling the water is $3 per gallon. Find the optimal number of bottles to package together for sale and the profit-maximizing price to charge for the package. Show the solution graphically.

Explanation / Answer

P = 15 – 3Q ==>Revenue=P*Q ==>Revenue=(15 – 3Q)*Q=15Q-3(Q^2) Marginal Revenue=15-6Q For optimal number of bottles MC=MR Given : MC=$3 ==>15-6Q=3 ==>Q=12/6=2 Optimum number of bottles=2 and Profit max. price=$9

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