Consider the general equilibrium model with two sectors of production using different CRTS technologies as reviewed in class. Instead of assuming that both sectors are perfectly com- petitive, assume that sector X is a monopoly while sector Y is a perfectly competitive sector.
(i) A monopoly creates an inefficiency and thus prevents M RTX,Y = pX = M RSX,Y from pY holding. Explain precisely where the breakdown occurs and why it occurs.
(ii) Represent graphically the autarkic equilibrium in the (X, Y ) space when sector X is a monopoly sector;
(iii) Suppose now that free trade is introduced and that the pattern of trade is such that the country imports good X. Also assume that the country is small with respect to its partner. Show graphically the free-trade equilibrium and explain whether the gains from trade are greater or smaller when, in the absence of international trade, sector X is a monopoly instead of being a perfectly competitive sector.
(iv) Suppose sector X remains an imperfectly competitive sector in free trade and X is still imported. Could it be the case that the country is worse off by signing a free-trade agreement? Explain and show graphically.