Final Exam - Fall 2009 Answers Explained True-False Questions: 1. A monopoly must sell at the same price to all buyers and faces a downward-sloping demand curve. If it is currently selling at least one unit, then its marginal revenue from selling one more unit will be less than the price at which the additional unit is sold. Answer: True Suppose a monopolist is selling 100 units for a price of $10 per unit. To sell 101 units, it must lower its price to $9.95. Its marginal revenue is $9.95*101-$10*100. This expression can be rewritten as $9.95 + $9.95*100 - $10*100, which equal $9.95 – ($10 - $9.95)*100. This expression reduces to $9.95 – ($0.05)*100 = $4.95. Thus marginal revenue, $4.95, is less than price, $9.95. Marginal revenue is less than price because, while the monopolist gets $9.95 for selling one more unit, it must reduce the price by 5 cents on the 100 units it could have sold for $10.00. 2. If a monopolist is able to practice third-degree price discrimination and it charges a higher price in one market than in another, the demand in the market with the higher price is more elastic than the demand in the market with the lower price. Answer: False In lecture on December 2, I derived the relationship between price, marginal revenue and price elasticity. That relationship is ⎥⎦⎤⎢⎣⎡+=11EPMRwhere MR is marginal revenue, P is price and E is the price elasticity of demand. The price elasticity, E, is a negative number. Furthermore E will be less than negative unity because monopolists always produce in the elastic portion of the demand function. So, 1/E is a negative number between -1 and 0. The more elastic demand, the larger this negative number, and thus the smaller is 1/E. In other words, the more elastic is demand, the closer price is to marginal revenue. Intuitively, the more elastic is demand, the less the monopolist will have to reduce price to sell an additional unit, and thus the less revenue the monopolist will lose by having to reduce price to sell an additional unit. The monopolist will choose a quantity and thus a price in each market such that marginal revenue equals marginal cost. Marginal cost will be the same in each market, so marginal revenue will be the same in each market. If marginal revenue is the same in each market, price will be lower in the market with the more elastic demand.
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