Question

The city of Windhoek has a more or less free market in taxi services. Suppose that the
marginal cost per trip of a taxi ride is constant, MC = N$5, and that each taxi has a
capacity of 20 trips per day. Let the demand function for taxi rides be given by: D = 1200
– 20P, where demand is measured in rides per day. Assume that the industry is perfectly
competitive.

What is the competitive equilibrium price?           (5)
(ii) What is the equilibrium number of rides per day and how many taxicabs will be in
the equilibrium?                  (5)
(iii) Provide a clear argument explaining why under a monopoly MR(y) < AR(y) for y
>0, assuming the same price must be charged.

Answer 1

Given Demand Curve: D=1200 - 20P

Or, 20P = 1200 - D

Or, P = 60 - (D/20)

Hence the inverse demand curve can be written as: P = 60 - (D/20)

Marginal cost : MC =N$5

i) The competitive equilibrium is given by -

P=MC

Or, 60 - (D/20) = 5

Or, (D/20) = 60 - 5 = 55

Or, D = 55×20 = 1100

Hence competitive equilibrium price :

P= 60 - (1100/20)

Or, P = 60 - 55

Or, P = 5

Hence the competitive equilibrium price is P=N$5.

[It is quite obvious because, under competitive equilibrium P=MC and we have MC=N$5, so we must have P=MC=N$5].

ii) Equilibrium numbers of rides per day is: D=1100.

Since each taxicabs has the capacity to make 20 trips per day, the equilibrium numbers of taxicabs = (no. of rides per day/20) = 1100/20 = 55.

iii) Let us denoted,

P= Price and Y=output.

Now suppose, the inverse demand function = P(Y).

Hence total revenue:

TR=P(Y)×Y

Average Revenue: AR=(TR/Y)

Or, AR = {P(Y)×Y}/Y

OR, AR = P(Y)

Marginal Revenue:

MR = dTR/dY

Where 'e' is the elasticity of demand and we know that monopolist never produces inelastic portion of demand. So we must have e<-1 [negative sign denotes the price elasticity of demand is negative].

Now, P(Y) = AR.

Thus from above it can be stated that, AR>MR

Since AR and MR are both function of Y, it can be stated as -

AR(Y) > MR(Y) for all Y>0.