Unformatted text preview: Vertical Product Differentiation A. Product Quality and Consumer Demand Assuming that consumers can ascertain product quality and prefer higher over lower quality, increasing quality will shift the inverse demand function (i.e., the curve below). If z stands for product quality, the inverse demand function (i.e., the Price Function) will now be given as P = P(Q.z). As shown in the Figure below, we distinguish two different ways how quality improvements can shift the inverse demand curve P(Q,z). Consider Q1 and z1 in both panels (a and b) of the Figure below. At P1 the Q1th consumer is indifferent, his CS equals zero. All consumers to his left, the so
called inframarginal consumers, experience a surplus. All consumers to the right of the Q1th consumer do not buy the good. Panel (a): ΔWTPinf > ΔWTPmar The demand by inframarginal consumers is more responsive to a quality improvement from z1 to z2 than the demand by the marginal consumer. The inverse demand curve rotates around the intercept on the quantity axis and becomes €
steeper. Panel (b): ΔWTPinf < ΔWTPmar The demand by inframarginal consumers is less responsive to a quality improvement from z1 to z2 than the demand by the marginal consumer. The inverse demand curve rotates around the intercept on the price axis and becomes flatter. € € € B. Mathematical Solution Let us refer to an example where the price function of a good is given by P = z(50 – Q). It can easily be shown this corresponds to the case where ΔWTPinf > ΔWTPmar . The demand curve rotates around the point Q=50. Further assume that marginal production cost is equal to zero: MCQ=0. €
However, improving quality is associated with a quantity
independent cost F ( z) = 5 z 2 . Thus, MCz=10z. The firm’s profit function is therefore given by π (Q, z) = P (Q, z)Q − F ( z) = z(50 − Q)Q − 5 z 2 (1) First solve for the optimal quantity by setting MCQ=MRQ Since RQ = z(50
Q)Q = z50Q – zQ2 we conclude MRQ = 50z – 2zQ Setting this equal with MCQ (which is zero) yields 0 = 50z – 2zQ 2zQ=50z 2Q=50 Q*=25 (2) Now solve for z We know that the profit maximizing price P* is a function of quality: P* = z(50
Q*). Plugging in 25 for Q* yields P*=25z Therefore, in contrast to quantity, the price is affected by z (remember that F increases with z as well) We set z
related marginal cost and marginal revenue equal: MRz = MCz Since R * = P * Q * = 25 z(25) = 625 z we know that MRz=625. We also know that MCz=10z. Setting both equal yields 10z=625 € z=62.5 Therefore: profit maximizing quantity is Q*=25 profit maximizing quality is z*=62.5 profit maximizing price is P*=25z=1562.5 Total revenue is 39,062.50, total design cost is 19,531.25. The total profit will then be 19,531.25. ...
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 Spring '11
 Storchmann
 Monopoly, the00, is00

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