Behaviour of Revenue Monopoly

A firm under monopoly is required to reduce the price if it wants to sell more.

A monopolist by definition is price taker.

Being a single seller of the product in the market, he can fix whatever price he wishes to.

But he can sell more only if he lowers the price of his product.

Thus, there is a negative relationship between price of the product and demand for the product in a monopoly market.

Thus firms demand curve or AR curve (price line) slopes downwards.

Tabular Relationship between TR, AR and MR under Monopoly

Units of output (Q)	Price / AR  ( P)	TR	MR (TRn- TRn-1)
1 2 3 4 5 6 7	20 18 16 14 12 10 8	20 36 48 56 60 60 56	20 16 12 8 4 0 -4

1) When AR is not constant but declining, MR is also declining.

2) When AR is declining by Rs. 2, MR is declining by Rs. 4. 

This proves that under monopoly MR declines and declines faster than AR.

So that AR > MR

Reason:

When the price is reduced to increase the sale, price is reduced not only for additional unit but for all the units sold.

MR that a firm gets from selling one more unit equals the price it receives from the sale of one additional unit minus loss in revenues from the price reduction on all other units i.e.

MR = AR – Total Loss

Example: AR of 6^th unit is 10

                 AR of 7^th unit is 8

There is a loss Rs.2 (as price is reduced, when 7^th unit of product is sold)

Total Loss of all the above six units sold = 2 x 6 = Rs. 12

MR = AR (7th unit) – Total Loss

MR = 8 – 12 = -4

This proves the fact that AR > MR

3) When MR is declining, we are adding less and less to TR for every additional unit sold.

So that TR increases only at diminishing rate.

4) MR can be zero or negative at 6^th unit, as price keeps on declining.

This is not possible in perfect competition where price remains constant for a firm.

5) TR stops increasing when MR = 0 so that TR is maximum when MR = 0

6) TR starts declining when MR is negative.

The below graph illustrates the relationship between TR, AR and MR, when price (AR) is not constant, under monopoly.

revenue monopoly

Part (A) of the figure shows TR curve.

1) The TR curve is initially positively sloped rising from zero (at zero output) to a maximum at M, with OQ quantity of output and is falling thereafter.

2) TR is initially concave upwards and then after point M concave downwards.

3) Concavity means that TR is increasing at decreasing rate.

This is because in order to sell more and more output the producer has to reduce the price of the product, and this causes an increase in TR to get smaller.

As price falls to very low levels, the total revenue actually falls.

Part (B) of the figure shows AR and MR curve.

1) AR falls continuously as output increases, corresponding to OQ level of output.

However it cannot be negative because the price cannot be negative. 

AR curve is a negative sloping curve with a constant rate of change.

2) As AR is constantly falling, MR too is falling and AR > MR (explained above) 

3) When MR is positive, TR increases with an increase in output

When MR is zero at point Q, then TR is maximum.

When MR becomes negative, TR starts falling with an increase in output.