Chapter Twenty-Four 29/10/2014 1 Chapter Twenty-Five Monopoly Behavior How Should a Monopoly Price? So far a monopoly has been thought of as a firm which has to sell its product at the same price to...

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Chapter Twenty-Four 29/10/2014 1 Chapter Twenty-Five Monopoly Behavior How Should a Monopoly Price? So far a monopoly has been thought of as a firm which has to sell its product at the same price to every customer. This is uniform pricing. Can price-discrimination earn a monopoly higher profits? Types of Price Discrimination 1st-degree: Each output unit is sold at a different price. Prices may differ across buyers. 2nd-degree: The price paid by a buyer can vary with the quantity demanded by the buyer. But all customers face the same price schedule. E.g. bulk-buying discounts. Types of Price Discrimination 3rd-degree: Price paid by buyers in a given group is the same for all units purchased. But price may differ across buyer groups. E.g., senior citizen and student discounts vs. no discounts for middle-aged persons. First-degree Price Discrimination Each output unit is sold at a different price. Price may differ across buyers.  It requires that the monopolist can discover the buyer with the highest valuation of its product, the buyer with the next highest valuation, and so on. First-degree Price Discrimination p(y) y $/output unit MC(y) y p y( ) Sell the th unit for $y p y( ). 29/10/2014 2 First-degree Price Discrimination p(y) y $/output unit MC(y) y p y( ) y p y( ) Sell the th unit for $ Later on sell the th unit for $ y p y( ). y p y( ). First-degree Price Discrimination p(y) y $/output unit MC(y) y p y( ) y y p y( ) p y( ) Sell the th unit for $ Later on sell the th unit for $ Finally sell the th unit for marginal cost, $ y p y( ). y p y( ). y p y( ). First-degree Price Discrimination p(y) y $/output unit MC(y) y p y( ) y y p y( ) p y( ) The gains to the monopolist on these trades are: and zero. p y MC y p y MC y( ) ( ), ( ) ( )      The consumers’ gains are zero. First-degree Price Discrimination p(y) y $/output unit MC(y) y So the sum of the gains to the monopolist on all trades is the maximum possible total gains-to-trade. PS First-degree Price Discrimination p(y) y $/output unit MC(y) y The monopolist gets the maximum possible gains from trade. PS First-degree price discrimination is Pareto-efficient. First-degree Price Discrimination First-degree price discrimination gives a monopolist all of the possible gains-to-trade, leaves the buyers with zero surplus, and supplies the efficient amount of output. 29/10/2014 3 Third-degree Price Discrimination Price paid by buyers in a given group is the same for all units purchased. But price may differ across buyer groups. Third-degree Price Discrimination A monopolist manipulates market price by altering the quantity of product supplied to that market. So the question “What discriminatory prices will the monopolist set, one for each group?” is really the question “How many units of product will the monopolist supply to each group?” Third-degree Price Discrimination Two markets, 1 and 2. y1 is the quantity supplied to market 1. Market 1’s inverse demand function is p1(y1). y2 is the quantity supplied to market 2. Market 2’s inverse demand function is p2(y2). Third-degree Price Discrimination For given supply levels y1 and y2 the firm’s profit is What values of y1 and y2 maximize profit? ( , ) ( ) ( ) ( ).y y p y y p y y c y y1 2 1 1 1 2 2 2 1 2    Third-degree Price Discrimination ( , ) ( ) ( ) ( ).y y p y y p y y c y y1 2 1 1 1 2 2 2 1 2    The profit-maximization conditions are            y y p y y c y y y y y y y1 1 1 1 1 1 2 1 2 1 2 1 0        ( ) ( ) ( ) ( ) Third-degree Price Discrimination ( , ) ( ) ( ) ( ).y y p y y p y y c y y1 2 1 1 1 2 2 2 1 2    The profit-maximization conditions are            y y p y y c y y y y y y y1 1 1 1 1 1 2 1 2 1 2 1 0        ( ) ( ) ( ) ( )            y y p y y c y y y y y y y2 2 2 2 2 1 2 1 2 1 2 2 0        ( ) ( ) ( ) ( ) 29/10/2014 4 Third-degree Price Discrimination   ( )y y y 1 2 1 1     ( )y y y 1 2 2 1  and so the profit-maximization conditions are      y p y y c y y y y1 1 1 1 1 2 1 2 ( ) ( ) ( )    and      y p y y c y y y y2 2 2 2 1 2 1 2 ( ) ( ) ( ) .   Third-degree Price Discrimination          y p y y y p y y c y y y y1 1 1 1 2 2 2 2 1 2 1 2 ( ) ( ) ( ) ( )     Third-degree Price Discrimination          y p y y y p y y c y y y y1 1 1 1 2 2 2 2 1 2 1 2 ( ) ( ) ( ) ( )     MR1(y1) = MR2(y2) says that the allocation y1, y2 maximizes the revenue from selling y1 + y2 output units. E.g. if MR1(y1) > MR2(y2) then an output unit should be moved from market 2 to market 1 to increase total revenue.  Third-degree Price Discrimination          y p y y y p y y c y y y y1 1 1 1 2 2 2 2 1 2 1 2 ( ) ( ) ( ) ( )      The marginal revenue common to both markets equals the marginal production cost if profit is to be maximized. Third-degree Price Discrimination MR1(y1) MR2(y2) y1 y2y1* y2* p1(y1*) p2(y2*) MC MC p1(y1) p2(y2) Market 1 Market 2 MR1(y1*) = MR2(y2*) = MC Third-degree Price Discrimination MR1(y1) MR2(y2) y1 y2y1* y2* p1(y1*) p2(y2*) MC MC p1(y1) p2(y2) Market 1 Market 2 MR1(y1*) = MR2(y2*) = MC and p1(y1*)  p2(y2*). 29/10/2014 5 Third-degree Price Discrimination  In which market will the monopolist set the higher price? Third-degree Price Discrimination  In which market will the monopolist cause the higher price? Recall that MR y p y1 1 1 1 1 1 1 ( ) ( )        MR y p y2 2 2 2 2 1 1 ( ) ( ) .        and Third-degree Price Discrimination  In which market will the monopolist cause the higher price? Recall that But, MR y p y1 1 1 1 1 1 1 ( ) ( )        MR y p y2 2 2 2 2 1 1 ( ) ( ) .        and MR y MR y MC y y1 1 2 2 1 2( ) ( ) ( ) * * * *   Third-degree Price Discrimination p y p y1 1 1 2 2 2 1 1 1 1 ( ) ( ) . * *                So Third-degree Price Discrimination p y p y1 1 1 2 2 2 1 1 1 1 ( ) ( ) . * *                So Therefore, only ifp y p y1 1 2 2( ) ( ) * * 1 1 1 1 1 2      Third-degree Price Discrimination p y p y1 1 1 2 2 2 1 1 1 1 ( ) ( ) . * *                So Therefore, only ifp y p y1 1 2 2( ) ( ) * * 1 1 1 1 1 2 1 2         . 29/10/2014 6 Third-degree Price Discrimination p y p y1 1 1 2 2 2 1 1 1 1 ( ) ( ) . * *                So Therefore, only ifp y p y1 1 2 2( ) ( ) * * 1 1 1 1 1 2 1 2         . The monopolist sets the higher price in the market where demand is least own-price elastic. Two-Part Tariffs A two-part tariff is a lump-sum fee, p1, plus a price p2 for each unit of product purchased. Thus the cost of buying x units of product is p1 + p2x. Two-Part Tariffs Should a monopolist prefer a two- part tariff to uniform pricing, or to any of the price-discrimination schemes discussed so far?  If so, how should the monopolist design its two-part tariff? Two-Part Tariffs  p1 + p2x Q: What is the largest that p1 can be? Two-Part Tariffs  p1 + p2x Q: What is the largest that p1 can be? A: p1 is the “entrance fee” so the largest it can be is the surplus the buyer gains from entering the market. Set p1 = CS and now