Second Degree Price Discrimination

Second Degree Price Discrimination - Bergals School of...

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Bergals School of Economics Fall 1997/8 Tel Aviv University Second degree price discrimination Yossi Spiegel 1. Introduction Second degree price discrimination refers to cases where a firm does not have precise information about the preferences of individual customers but it can use non-linear tariffs in order to extract the relevant information from its customers. At the optimum, the firm typically offers a menu of offers and buyers self-select from this menu. Second degree price discrimination is undoubtedly much more complex to analyze than first degree or third degree price discrimination. This is because the combination of non linear tariffs and asymmetric information about buyers requires certain techniques to solve the firm’s problem. These techniques were not available until the early 70’s. The major breakthrough was by Mirrlees in his 1971 paper about non linear taxation under asymmetric information. In 1996 Mirrlees got the Nobel prize for this contribution. The methodology that Mirrlees developed is the basis for the analysis of second degree price discrimination. Since this methodology is so widely used we shall study it in detail. 2. The model A monopoly sells a single product to a continuum of buyers. Buyers differ from one another with respect to their utilities: the utility of a representative buyer if he buys is given by where p is the price and θ is the buyer’s type. If a buyer does not buy his utility is 0. As for (1) q, we can give this parameter at least two interpretations. First we can think of q as a quantity (i.e., the number of units the buyer buys). In that case, p is the price of a bundle that contains q units and V(q, θ ) is the gross consumer surplus (i.e., the area under the inverse demand function). This interpretation corresponds to Maskin and Riley’s (1984) paper. Second we can think of q as a measure of the quality of the product. Under this interpretation, each buyer is
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2 interested in buying only one unit, p is the price of that unit, and V(q, θ ) is the direct utility from consumption, ignoring the loss of income due to the payment to the monopoly. The interpretation of q as quality corresponds to Mussa and Rosen’s (1978) paper. As usual, we will assume that V q > 0 > V qq so the direct utility from consumption increases with q (the number of units the buyer buys or the quality of the good he buys) at a decreasing rate. Since V q is the marginal willingness to pay, then if we interpret q is quantity then V q is simply the inverse demand function so the assumptions that V q > 0 > V qq amount to assuming that the inverse demand function is positive and decreasing. 1 Similarly, if we interpret q is quality, the assumption that V q > 0 > V qq implies that the inverse demand function for quality is positive and decreasing.
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