If the MR curve of a monopoly firm is given by the equation MR=20-2q, what is the maximum value of TR? (Prices and revenues are in rupees)
Rs 100
Given that the MR curve is given by the equation
MR=20−2q
The slope of the MR curve is -2. Since the MR curve is twice as steep as the demand curve, the slope of the demand curve is -1.
Also, MR and demand curves start from the same point. Hence the equation of the demand curve is
p=20−q
TR is maximum when MR=0 i.e when 20-2q =0.
Hence, TR is maximized at an output level of 10.
At q=10, the maximum price that the firm can set can be obtained from the demand curve
p=20−10=Rs 10
TR=p×q=10×10=Rs 100