Set05a-ICIR - Econ 441 Problem Set 5 - Answers Alan...

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Econ 441 Alan Deardorff Problem Set 5 - Answers Imperfect Competition, Increasing Returns Page 1 of 11 Problem Set 5 - Answers Imperfect Competition, Increasing Returns, etc. 1. Consider a monopolist in partial equilibrium who initially faces the demand curve D 1 shown below, and whose marginal cost is constant at c . a. Construct the profit-maximizing equilibrium for this monopolist. This is found from the marginal revenue curve, MR 1 , drawn as the straight line half the distance between the vertical axis and the demand curve D 1 . Where that MR 1 curve cuts the marginal cost line, c, determines the output Q 1 that the monopolist will produce. Vertically above that on the demand curve is the price, p 1 , that will clear the market at that quantity, and p 1 is therefore the price that the monopolist will charge. p Q D 1 MR 1 Q 1 p 1 c p Q D 1 c
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Alan Deardorff Problem Set 5 - Answers Imperfect Competition, Increasing Returns Page 2 of 11 b. 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 Q 1 and selling it for p 1 in part (a), quantity Q 1 still has price p 1 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 1 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 1 everywhere below p 1 , and from this it follows that it crosses the c line at some Q 2 >Q 1 . From the new demand curve, then, it is also true that p 2 <p 1 , as shown. Thus quantity rises and price falls, due to this particular change in the demand curve. Profit, which was (p 1 –c)Q 1 and is now (p 2 –c)Q 2 , 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 1 and charge p 1 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. c. 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 foreign suppliers. 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
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Set05a-ICIR - Econ 441 Problem Set 5 - Answers Alan...

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