Question

Why does the average revenue and marginal revenue curve seperate for a monopolist.

Answer 1

Monopoly is a market situation where there is a single firm selling the commodity and there is no close substitute of the commodity sold by the monopolist. The absence of close substitutes of the commodity implies that a monopolist faces an inelastic demand curve.

Since a monopoly firm is the only seller, it has substantial influence over the price of its product by manipulating its supply. But his influence over price is not total. Price is determined by forces of demand and supply and a monopolist can control only supply . Therefore, in monopoly, as output increases or decreases , price changes in accordance with what consumers are willing to pay along the demand curve. Thus, a monopolist firm can charge any price but it can’t sell any quantity at that price and hence , demand curve is a constraint.

As we know, the demand curve equals the AVERAGE REVENUE CURVE. The above discussion, implies that the AR curve facing a monopolist is negatively sloped which indicates that a monopolist can sell more by lowering price. In other words, price has to be reduced to sell additional units. Hence , AR curve is downward sloping.

Let the demand curve be given by

X = a-bP ....a,b>0 , X- quantity demanded P = price

or bP = a-X

P = a/b -X/b

The total revenue of the monopolist is given by-

TR = P.X

TR = (a/b -X/b ).X

TR = a/b.X - X^2/b

The average revenue (AR) is given by

AR = TR/X = PX/X = P = a-bX

AR = a-bX

The Marginal revenue is given by —

MR = dTR/dX = a/b — 2X /b

MR = a/b — 2X /b

Clearly, the MR is a straight line having the same intercept as that of the AR curve but it’s slope is twice the slope of the demand curve.