Question

Question 4 [20] (a) 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. (i) 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. (10)

Answer 1

TR = P*D = D * ( 60 - 0.05D) = 60D - 0.05D²

In case of perfectly competitive market P = MR = AR and at equilibrium MR = MC = N$5.

MR = 60 - 0.1D (by differentiating the TR equation wrt to D)

or, 5 = 60 - 0.1D

or, D = 550

The equilibrium number of rides per day is 550 and the number of cabs is = 550 / 20 = 27.5

given D = 1200 – 20P

So at equilibrium 550 = 1200 - 20P

or, P = N$32.5

The equilibrium price is N$32.5

In case of a monopolist, the demand curve and the marginal revenue curve both are downward sloping. The demand curve is downward sloping because it can sell additional number of units only if it lowers the price. The marginal revenue is the private benefit that the monopolist derives from selling an additional unit of the product. Since, the monopolist has to lower its price (=AR) in order to sell another unit of the product, MR < AR for a monopolist.

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