Question

1 Explain using math why MR<=P for a monopoly? Show and explain graphically.

Answer 1

Monopolist decide both quantity and price. In order to sell more goods, monopolist must lower the price due to law of demand. Industry demand curve is downward sloping and monopolist is the industry as it is sole producer.

Since single price monopolist charges same price to all the consumers, in order to sell more, monopolist has to reduce price on all the units of goods sold. This means MR falls by twice the rate of price. For example- 1 shirt sells at $80 and 2 shirt sells at $79. MR=∆TR/∆Q= (158-80)/(2-1)= $78.

Price fell by $1 and MR fell by $2 (=$80-$78).

Demand curve reflects the price and MR curve is below the price level.

Another explanation-

Let Demand= P= a-bQ where slope = -b

TR=P*Q= (a-bQ)Q= aQ-b(Q)^2

MR=dTR/dQ= a-2bQ where slope= -2b

MR slope is twice the slope of Demand curve.

So in a monopoly MR≤P

Also, Average revenue = AR= TR/Q= (P*Q)/Q= P

So AR is the demand curve.

MR falls twice the Demand curve fall.

Hence Price will always be be more or equal to MR.