Question

Monopoly Discussion Total Revenue and Elasticity:

The total revenue test shows that the monopolist will avoid the inelastic segment of its demand schedule. As long as demand is elastic, total revenue will rise when the monopoly lowers its price, but this will not be true when demand becomes inelastic.

• At this point (inelastic), what happens to total revenue? Explain in detail use examples, data, and facts to support your argument.
• Monopolists will expand output only in the elastic portion of its demand curve. Why?
• How does the decision impact the firm's output, revenue, and or profit.

Answer 1

Monopoly always produces in the elastic portion of demand curve.

We know that quantity and price has negative relations, in the sense that if the monopolist sells an extra unit of good into the market the price for every unit of the good he sela will fall. Which means that increase in quantity will lead to decrease in price. Demand function is also downward , consumers will buy lesser and lesser units of good as price falls.

Total revenue (TR) = price* quantity = P*Q

Now let the demand function be P= f(Q) , where f'(Q) <0,

d(TR)/dQ = d(PQ)/dQ = d(f(Q)Q)/dQ  

dTR/dQ = Q*df(Q)/dQ + f(Q)*dQ/dQ

MR = Qf'(Q) + f(Q) , MR = Marginal revenue

MR = Q dP/dQ + P

MR/P = Q dP/PdQ + 1 = (1/e) +1

Where e = (d lnQ/d lnP)

MR = P( 1/e + 1 ) ..eq 1

Now as we have already discussed change in quantity sold due to change in price dQ/dP isls negative and that is why e is non positive real number. e 0

So for inelastic portion of demand function, -1<e < 0, infinity <1/e <-1 which implies , (1/e + 1) <0 and hence MR<0 since P>0 for -1<e<0 .

Now we know a monopolist sells at quantity levels at which MC = MR , now if MC is negative, monopolist can sell at inelastic portion of demand curve but that is highly unlikely.

Again when e = -1, MR = 0 from eq 1 , profit maximising condition of monopolist requires MC = MR . It is only possible in a monopoly set up to maximise profit by selling at a point in demand function where e = 1, and that is when MC = 0, which is also highly unlikely.

Hence there remains only one possibility that is e <-1 . I. This range of elasticity of demand, MR > 0. For any positive marginal cost , the monopolist will always sell at Elastic portion of demand curve.

Also intuitively, a monopolist would sell in the inelastic portion of demand curve because when demand is inelastic, the monopolist can at any time increase the price and earn higher Total revenue . This is because at the inelastic portion of demand curve, demand does not respond much to an increase in price, and hence total revenue increases. The monopoly will go on increasing price to earn even more revenue, hence more profit, till it moves to the elastic portion ,thus equilibrium can't settle at inelastic portion of demand curve.