Question

A monopolist operates at a constant marginal cost MC 2 zloty, and the market demand function for the good it produces is Q 7000/p. If as a result of the fact that the govemment imposed a unit tax, the sale price in equilibrium increased to the level p 6 zloty, what was the level of this tax?

Answer 1

Answer

Suppose government induced per unit tax t. You can say that in order to produced one more unit of good the monopolist must incur Previous marginal cost + t = 2 + t

Now MC = 2 + t

Profit maximizing Condition of a Monopolist a monopolist produces that quantity at which MR(Marginal Revenue) = MC.

MR = d(TR) / dQ = d(pQ)/dQ . Here, p = (7000/Q)^1/3 => pQ = 7000^1/3Q^2/3

Hence MR = (2/3)*(7000/Q)^1/3

Now,

MR = MC => (2/3)*(7000/Q)^1/3 = 2 + t => t = (2/3)*(7000/Q)^1/3 - 2 ----------------(1)

It is given that new price is 6. Hence Q = 7000/6³

Putting this value of Q in (1) we get :

=> t =  (2/3)*(7000/(7000/6³))^1/3 - 2

=> t = (2/3)*6 - 2 = 4 - 2 = 2

Hence level of this tax = 2 per unit