Problem Set 5 -
Imperfect Competition, Increasing Returns
Page 2 of 11
Suppose now that the demand curve becomes everywhere more elastic, but
continues to pass through the same price-quantity point that you found to be
optimal in part (a).
(That is, if the profit-maximizing monopolist was producing
and selling it for
in part (a), quantity
still has price
on the new, more
elastic, demand curve.)
Construct the new equilibrium for the monopolist and
compare it to the old, in terms of quantity, price, and profit.
Becoming more elastic, the demand curve rotates counter-clockwise through
point A. The new marginal revenue curve, being half the distance between the
vertical axis and this new curve, intersects MR
directly to the left of A, since
this point is half way between the axis and both curves.
It therefore must lie to
the right of MR
everywhere below p
, and from this it follows that it crosses the
c line at some Q
From the new demand curve, then, it is also true that
, as shown.
Thus quantity rises and price falls, due to this particular change in the demand
Profit, which was (p
and is now (p
, may seem at first to be
ambiguous in its change, since the markup falls but the quantity rises.
However, the firm could continue to produce Q
and charge p
if it wanted to,
and that would give it the same profit as before.
Since it chooses instead to
increase output, this must be because that yields it a larger profit.
So we can
be sure, after all, that profit rises in this case.
Explain what your answer to part (b) could have to do with international trade.
This exercise is relevant to international trade because in general the opening
to trade causes firms to face more elastic demand, due to the competition from
If competition is great enough, demand elasticity would
become infinite, which is more extreme than shown above.
But even with just a
few additional competitors, switching from a monopoly to a duopoly or
oligopoly, the elasticity faced by the firm will increase.
Now whether it will