Question

Suppose that a monopolist faces a linear demand curve having a vertical intercept of (0,a) and a horizontal intercept of (b,0). Denote the midpoint on the segment ab by the letter ‘m’ (i.e., am = bm) and let (Q*, P*) denote the coordinates at point ‘m’. A student in ECON 2010 once provided the following argument:

“A profit-maximizing monopolist who sells all units at a uniform price will never produce

more than Q* (or alternatively, will never charge a price below P*) since doing so will lower

total revenue, and by producing more, increase total cost. Even if the cost of production were

zero, the monopolist’s profits would fall if it produced more than Q*.”

Is the student’s argument correct? If so explain clearly why the student’s argument is correct. If not, explain why the student’s argument is wrong

Answer 1

I think the student's argument is not correct, in the sense that it is possible for the Marginal Profit to either go up or down depending on whether the Marginal Cost is lower than or higher than the Marginal Revenue, for an output more than Q. The argument this student makes is that even if the Marginal Cost for producing beyond this quantity Q is zero, profits will fall since Marginal Revenue for selling beyond this point is negative, which is not necessarily true, as the increase in quantity sold may more than offset the drop in price (between Q+x and Q).