Calculating profit maximizing price and output level
A high-end lamp monopolist operates in the Mid-West where
the demand for lamps is given by Q1=200-P1. Producing one lamp costs 10 per
unit.
(a) Derive the profit maximizing price and the profits at
this price.
(b)What is the demand elasticity at this price?
Suppose now that the monopolist has the opportunity to
expand to the East Coast.This would entail launching an advertising campaign at
a cost of 1000,a one time expense. The demand on the East Coast is given by Q2
=160-3P2.The per-unit cost of selling lamps on the East Coast is identical to
the cost of selling them in the Midwest.Suppose first that,because he is
thinking of selling from his website,the monopolist must charge the same price
in both markets .
(c) What is the total demand when the monopolist charges a
price P?
(d) Derive the profit maximizing price and the profits at
this price in the case where
the monopolist must charge the same price in both
markets.Would you recommend the monopolist to expand to this market?
Now suppose that the monopolist will sell through a network
of distributors,and can charge different prices on the East Coast and in the
Mid West .
(e)What price would the monopolist charge in the
Mid-West?What price would the
monopolist charge in the East?What are the total
profits?Would yo recommend the monopolist to expand in this case?
