Question

A monopolist providing beryllium to the oil and gas sector has the following demand function Qd = 60 – P. The price and quantity demand is given in the table 3 below:

Table 3

P ($)	60	55	50	45	40	35	30	25	20	15	10	5	0
Qd	0	5	10	15	20	25	30	35	40	45	50	55	60

a) From the table above, calculate the Total Revenue and Marginal revenue values.

b)         Plot the demand and marginal revenue schedules.

c)         Using the price elasticity method, calculate MR when

i)          P = $50            ii) P = $35            iii) P = 20

Answer 1

Solution :

Total reveune = Price * quantity

Marginal Reveune =( TRn-TRn-1)/Qn-Qn-1

b) The diagram is plotted below:

C.) The relationship between AR MR and elasticity of demand goes like this:

MR =AR (1 - 1/e)

when P=50 Demand = 10

Qd= 60 - P

   = -1

- Ed = * P/Q = -1 * 50/10 = -5

so Ed = 5

Put all these in the above relationship :

AR = 50 Ed = 5

MR = 50(1 -1/5)

MR= 40

MR = 50/0.8=62.5

II) IF PRICE = 35  

AR =35 QD=25

NOW ELASTICITY - Ed = * P/Q = -1 * 35/25 = -1.4

So Ed = 1.4

Now put all these in the above relationship :

mr = AR(1- 1/ed) = 35 ( 1- 1/1.4) = 10

III) IF PRICE = 20

MR =AR( 1- 1/Ed)

Ed = *P/Q = -1 * 20/40 =-0.5 So Ed = 0.5

MR = 20 (1-1/0.5) = -20