Many schemes for price discrimination involve some cost.
Assume that a monopolist faces
production costs that are simply proportional to output so that the average total cost and marginal
cost are constant and equal to each other.
Draw the cost, demand and marginal-revenue curves for the monopolist.
Show the price
the monopolist would charge without price discrimination.
In your diagram mark the
area equal to the monopolist’s profit and call it X.
Mark the area equal to the consumer
surplus and mark it Y.
Mark the area equal to the deadweight loss and call it Z.
Suppose the monopolist can perfectly price discriminate.
What is the monopolist’s profit
in terms of X, Y and Z?
What is the change in welfare?
Now suppose that price discrimination has some cost, C.
Under what condition would
price discrimination increase the social welfare compared to the social welfare under
monopoly without price discrimination?