Question 1.
A monopolist's demand function is given as Y=2000-10K, where Y is the quantity of output produced and sold and K is the price per unit in Tshs. If the marginal cost is Tshs 100
Calculate the monopolist's equilibrium quantity and price.
Suppose the Monopolist behaves competitively, how would the answers in a) above change?
Show the inefficiency caused by the above monopolist diagrammatically and mathematically.
a) The monopolist's equilibrium quantity and price can be calculated by setting marginal revenue equal to marginal cost. The marginal revenue is given by MR = 2000 - 20K. Setting MR = 100, we get K = 95 and Y = 2000 - 10(95) = 500.
b) If the monopolist behaves competitively, the equilibrium quantity and price would be determined by setting marginal cost equal to marginal revenue. The marginal revenue in this case would be equal to the price, so setting MC = P, we get P = 100 and Y = 2000 - 10(100) = 1000.
c) The inefficiency caused by the monopolist can be shown diagrammatically by comparing the monopolist's equilibrium quantity and price to the competitive equilibrium quantity and price. The diagram below shows the inefficiency caused by the monopolist.
The inefficiency can also be shown mathematically by calculating the deadweight loss. The deadweight loss is given by DWL = (Pc - Pm)(Qc - Qm), where Pc and Qc are the competitive equilibrium price and quantity, and Pm and Qm are the monopolist's equilibrium price and quantity. In this case, DWL = (100 - 95)(1000 - 500) = 250.