1.4 Hidden Information and Price Discrimination 1


 Gordon Hines
 3 years ago
 Views:
Transcription
1 1.4 Hidden Information and Price Discrimination 1 To be included in: Elmar Wolfstetter. Topics in Microeconomics: Industrial Organization, Auctions, and Incentives. Cambridge University Press, new edition, forthcoming. 1.4 Hidden Information and Price Discrimination Seconddegree price discrimination is the most widely observed kind of price discrimination. We now take a closer look at it and elaborate on a model that explains why this kind of discrimination emerges, and how it should be done. 1 Consider a profitmaximizing monopolist who deals with a customer who is one of two possible types, with equal probability. 2 Only the customer knows his true type. In other words, the customer s type is his private information. The monopolist only knows the payoff functions of the two possible types, and the probability with which either type occurs. Therefore, price discrimination requires a somewhat sophisticated screening device. While the following model is best suited to analyze a monopolist who faces one customer of unknown type, it can also be interpreted as a pricing problem with a population of customers. However, in an environment with many customers the monopolist may employ more powerful mechanisms that make price offers conditional on their acceptance by all customers, that are ignored here. Also, with many customers there are issues of arbitrage and repeated purchases that are also ignored. The market game is structured as follows: 1. The monopolist sets a uniform nonlinear price function in the form of a menu of price quantity combinations, (T, x), called the sales plan, from which the customer is free to select one: S := {(T 1, x 1 ), (T 2, x 2 ), (0, 0)}. (1.1) The (0, 0) combination is included because market transactions are voluntary; the customer is free to abstain from buying. Of course, x 1, x The customer observes the sales plan and picks that price quantity combination that maximizes his payoff. Payments are made, and the market game ends. Without loss of generality, the component (T 1, x 1 ) is designated for customer type 1, and (T 2, x 2 ) for customer type 2 (incentive compatibility). For convenience these two types will be referred to as customers 1 and 2. Of course, the monopolist could also live with a sales plan where, for example, customer 2 picks (T 1, x 1 ) and 1 picks (T 2, x 2 ), as long as he makes no error in predicting customers rational choice. But then incentive compatibility can be restored simply by relabelling the components of the sales plan. Moreover, one can show that any other format of sales plan can be replicated by an equivalent sales plan of the kind considered here. Therefore, the restriction to incentivecompatible sales plans is without loss of generality. 3 Assumptions Five assumptions are made: A1 (Cost function). Unit costs are constant and normalized to zero. 1 Here we present a twotype version of the continuoustype model by Maskin and Riley (1984a). 2 Equal probability is invoked only in order to minimize notation. 3 This is the essence of the wellknown revelation principle in mechanism design theory (see the Chapter on Mechanism Design).
2 2 A2 (Payoff functions). The monopolist maximizes profit π := 1 2 (T 1 + T 2 ), (1.2) and customers maximize consumer surplus x U i (x, T ) := P i (y) dy T for i = 1, 2, (1.3) 0 where P i (x) denotes i s marginal willingness to pay for x. A3 (Declining marginal willingness to pay). P i (x) is continuously differentiable with P i (x) < 0; also P i (0) > 0, and P i (x) = 0, for some x, i {1, 2}. A4 (Single crossing). For all x A5 (Concavity). For all x P 2 (x) > P 1 (x). (1.4) 2P 1 (x) < P 2 (x). (1.5) A4 is called the singlecrossing assumption for the following reason: Pick an arbitrary point in (x, T ) space, say x1, T 1, and draw the two types indifference curves that pass through this point. Since the slope of the indifference curves is equal to P i (x), A4 assures that these curves cross only once at this given point, as illustrated in Figure 1.1. And A5 is called concavity because it assures the strict concavity of the objective function, as we show later on. OPTIMAL SALES PLAN The optimal sales plan maximizes π subject to the participation constraints (the outside option of not buying is assumed to yield zero utility), and the nonnegative constraints: and the incentive constraints U 1 (x 1, T 1 ) U 1 (0, 0) = 0, (1.6) U 2 (x 2, T 2 ) U 2 (0, 0) = 0, (1.7) U 1 (x 1, T 1 ) U 1 (x 2, T 2 ), (1.8) U 2 (x 2, T 2 ) U 2 (x 1, T 1 ) (1.9) x 1, x 2 0. (1.10) Conditions (1.6) and (1.8) assure that the component of the sales plan designated for customer 1, (T 1, x 1 ), is dominated neither by the (0, 0) nor by the (T 2, x 2 ) option. Similarly, conditions (1.7) and (1.9) assure that (T 2, x 2 ) is dominated neither by (0, 0) nor by (T 1, x 1 ) An Intuitive Exploration Before dwelling on the formal solution it may be worthwhile to explore the problem with the aid of some graphs assembled in Figure 1.1. Figure 1.1 displays buyers indifference curves in the (T, x) space. The curves labelled 1 resp. 2 are indifference curves of customer type 1 resp. 2. Note, they pass through the origin. Therefore, they display the combinations of (T, x) that keep the customer indifferent between buying and not buying. Curve 1 is below curve 2 because type 1 has a lower valuation at each given x. The slope of
3 1.4 Hidden Information and Price Discrimination 3 T T 2 T 2 2 ˆT 2 T T x 1 x 1 x 2 1 x Figure 1.1: Customers Indifference Curves these indifference curves is equal to the marginal rate of substitution which is also called the marginal willingness to pay P i (x) dt i dx = P i (x i ), i {1, 2}. i Ui (x i,t i )=0 As usual, the marginal willingness to pay is declining. At x i = xi it is equal to marginal cost (which has been normalized to zero). Therefore, the indifference curves reach a maximum at the points x 1 = x1, x 2 = x2 where the marginal willingness to pay is equal to marginal cost. Students are sometimes puzzled by the fact that we allow the marginal willingness to pay to be negative. However, this is a consequence of normalizing marginal cost to be equal to zero. Here, a negative marginal willingness to pay only means that the marginal valuation is below marginal cost. 4 All indifference curves that are shifted below curve 2 (resp. curve 1), such as indifference curves 2 and 2, exhibit higher utility. If the monopolist could observe customers type he would obviously choose (x 1 = x1, T 1 = T1 ) and (x 2 = x2, T 2 = T2 ). However, if customers type is not observable this scheme is not incentive compatible because customer 2 would choose the combination (x1, T 1 ) which gives him a higher utility than the designated combination (x2, T 2 ). While maintaining the combination (T1, x 1 ) one can achieve incentive compatibility and induce participation only by choosing a combination (T 2, x 2 ) from the shaded area in between indifference curves 1 and 2. Therefore, given (T1, x 1 ), the best feasible combination designated for type 2 is ( ˆT 2, x2 ). However, this menu of price quantity combinations can be further improved. Indeed, if one reduces x 1 slightly below x1, say to x 1, one loses very little in revenue from type 1, T 1, since the indifference curve of type 1 is flat at (T1, x 1 ). However, this change permits a substantial increase in the price that one can charge type 2, T 2, from ˆT 2 to T2. These observations suggest the following properties of the optimal solution: 1. Offer type 1 less than the efficient quantity, x 1 < x1 ( distortion at the bottom property). 2. Offer type 2 the efficient quantity, x 2 = x2 ( no distortion at the top property). 4 The normalization requires a transformation of the price variables. Exercise 1.1 offers some guidance on how to explicitly carry out this transformation.
4 4 3. Set T 1 in such a way that type 1 is made indifferent between buying and not buying ( no surplus at the bottom property). 4. Set T 2 in such a way that type 2 is indifferent between (x 1, T 1 ) and (x 2, T 2 ), which entails that type 2 prefers buying to not buying, unless it is optimal to set x 1 = Formal Solution We now turn to the formal characterization of the optimization problem: 1 ( ) max T1 + T 2, s.t. (1.6) (1.10). {T 1,T 2,x 1,x 2 } 2 SOME PRELIMINARIES Luckily, that problem can be simplified by eliminating two constraints. Indeed, among the participation constraints only the lower type s constraint (1.6) binds, and among the incentive constraints only the upper type s constraint (1.9) binds. (A constraint does not bind if eliminating it from the optimization program does not affect the solution.) Therefore it is claimed that one can eliminate constraints (1.7) and (1.8) without loss of generality. What makes us come to this conclusion? Obviously, the above analysis of Figure 1.1 suggests this. Therefore, we take it as a working hypothesis. Of course, this is only justified if the solution of the restricted optimization program turns out to also satisfies the eliminated constraints which we will confirm. SOLUTION OF THE RESTRICTED PROGRAM The restricted program restricted by eliminating constraints (1.7) and (1.8) can be further simplified due to the following results. Lemma 1.1. The optimal sales plan exhibits T 1 = x1 0 T 2 = T 1 + P 1 (y) dy, (1.11) x2 x 1 P 2 (y) dy. (1.12) Proof. We have noted (but not yet proved) that the upper type s incentive constraint and the lower type s participation constraints are binding. If a constraint binds, then it is satisfied with equality at the optimal sales plan. Therefore, (1.6) entails (1.11). Using this result concerning T 1 if (1.9) and (1.6) bind, one has 0 = U 2 (x 2, T 2 ) U 2 (x 1, T 1 ) = which entails (1.12), as asserted. x1 0 P 1 (y) dy + x2 x 1 P 2 (y) dy T 2, (1.13) These price functions have a nice interpretation: 1. The low type is charged his maximum willingness to pay for x 1.
5 1.4 Hidden Information and Price Discrimination 5 2. The high type pays the same as the low type for the first x 1 units plus his own maximum willingness to pay for the additional x 2 x 1 units. Therefore, the high type makes a net gain if x 1 > 0, simply because he obtains the first x 1 units at a bargain price. In view of Lemma 1.1 we can now eliminate the T variables in the monopolist s objective function and state the restricted program in the form of the unconstrained optimization problem (except for nonnegativity) max x 1,x 2 0 The Kuhn Tucker conditions of the restricted program are ( 1 x1 x2 ) 2 P 1 (y) dy + P 2 (y) dy. (1.14) 2 0 x 1 φ(x 1 ) := 2P 1 (x 1 ) P 2 (x 1 ) 0 and φ(x 1 )x 1 = 0, (1.15) P 2 (x 2 ) 0 and P 2 (x 2 )x 2 = 0. (1.16) The T s are obtained by inserting the optimal x s into (1.11), (1.12). As you can confirm easily, A5 assures the strict concavity of the objective function. It also entails that φ(x 1 ) is strict monotone decreasing with φ(x) < 0 for some x. This assures that (1.15) has a unique solution; however, since φ(x) may be negative everywhere, one may get the corner solution x 1 = 0. Also, P 2 is declining, with P 2 (0) > 0. Therefore, (1.16) has the unique solution x 2 > 0, implicitly defined by P 2 (x 2 ) = The Optimal Sales Plan Proposition 1.1. The optimal sales plan exhibits P 2 (x 2 ) = 0, x 2 > 0 (no distortion at top), (i) x 2 > x 1, T 2 > T 1 (monotonicity), (ii) P 1 (x 1 ) > 0 (distortion at bottom), (iii) U 1 (x 1, T 1 ) = 0 (no surplus at bottom), (iv) U 2 (x 2, T 2 ) 0 with > x 1 > 0 (surplus at top unless x 1 = 0). (v) The optimal prices are computed in (1.11) and (1.12). Proof. First we characterize the solution of the restricted program (1.14) and then show that it also solves the unrestricted program. We have already shown that the Kuhn Tucker conditions have a unique solution that exhibits x 2 > 0 and x 1 0. (i): Follows immediately from the fact that P 2 (x 2 ) = 0, x 2 > 0, as already noted above, and the fact that marginal cost is constant and has been normalized to zero. (ii): By Lemma 1.1 the T s have the asserted monotonicity property if and only if it holds for the x s. We first prove weak monotonicity: Suppose x 1 > x 2, contrary to what is asserted. Since x 2 > 0, one has also x 1 > 0. Therefore, the first part of condition (1.15) is satisfied with equality, and one has, using the singlecrossing assumption A4, 0 = 2P 1 (x 1 ) P 2 (x 1 ) 2P 2 (x 1 ) P 2 (x 1 ) = P 2 (x 1 ) < P 2 (x 2 ).
6 6 But this contradicts (i). Therefore, x 2 x 1. Finally, note that if it were possible to have x = x 1 = x 2 > 0, one would need to have P 2 (x) = P 1 (x) = 0 for some x, which contradicts A4. Therefore, the monotonicity is strict. (iii): If x 1 = 0, one has P 1 (x 1 ) > 0, by A3. And if x 1 > 0, condition (1.15) combined with monotonicity (ii) entails, due to x 2 > x 1, P 1 (x 1 ) = 1 2 P 2(x 1 ) > 1 2 P 2(x 2 ) = 0. In either case the low customer gets less than the efficient quantity, P 1 (x 1 ) > 0 (distortion at bottom). (iv): U 1 (x 1, T 1 ) = 0 is obvious from (1.11). (v): U 2 (x 2, T 2 ) 0, with strict inequality if x 1 > 0, follows immediately from (1.12) and monotonicity. Finally, we need to confirm that the restricted program also satisfies the two omitted constraints (1.7) and (1.8). The omitted participation constraint (1.7) is obviously satisfied by (v). And the omitted incentive constraint (1.8) holds for the following reasoning (the last step uses the monotonicity property x 2 > x 1 and the singlecrossing assumption A4): This completes the proof. U 1 (x 2, T 2 ) U 1 (x 1, T 1 ) = = < 0. x2 x 1 P 1 (y) dy (T 2 T 1 ) x2 x 1 (P 1 (y) P 2 (y)) dy Why it Pays to Distort Efficiency Why is it optimal to deviate from efficiency in dealing with the low type but not the high type? The intuition is simple. The high type has to be kept indifferent between (x 2, T 2 ) and (x 1, T 1 ). This is achieved by charging the high type the price T 1 for the first x 1 units and a price equal to his maximum willingness to pay for x 2 x 1 units. From this observation it follows immediately that profit is maximized by expanding x 2 to a level where the marginal willingness to pay equals the marginal cost, P 2 (x 2 ) = 0 (see Figure 1.1). In turn, starting from P 1 (x 1 ) = 0 (see point (x 1, T 1 ) in that figure), a small reduction in x 1 is costless in terms of forgone profits from the low type (the marginal profit is zero at this starting point). But, at the same time it extends the domain where the high type is charged a price equal to his maximum willingness to pay. Altogether, it thus pays to introduce a downward distortion at the bottom, illustrated by the twostar variables in Figure 1.1. Figure 1.2 provides another useful illustration of these considerations (for a particular parameter specification). There, the optimal x 1 is at the point where the function φ(x 1 ) reaches zero. Customer type 1 is charged a price T 1 equal to the area under P 1, from 0 to x 1. Type 2 gets the quantity x 2 at which P 1 (x 2 ) = 0, and he is charged a price T 2 equal to the non shaded area under P 2, from 0 to x 2. This illustrates how type 2 is charged T 1 for the first x 1 units plus the area under his inverse demand function for the additional x 2 x 1 units. Therefore, the shaded area is 2 s consumer surplus. That surplus is lowered if one reduces x 1, and it vanishes altogether if one sets x 1 = Sorting, Bunching, and Exclusion Finally, note that it is not always optimal to serve both types of customers and, if we slightly change the assumptions, it may not even be optimal to discriminate. Altogether, the optimal price discrimination falls into one of three categories:
7 1.4 Hidden Information and Price Discrimination 7 P i (x), φ(x) 1 P P 1 (x) 2 (x) φ(x) x 1 = x 2 = 2 x Figure 1.2: Optimal Sorting with Two Customers and P i (x) := 1 x/i. 1. Sorting, with 0 < x 1 < x 2, T 1 < T Bunching, or no discrimination, with x 1 = x 2 > 0, T 1 = T Exclusion, or extreme discrimination, where only the high type is served at a price equal to its maximum willingness to pay, with 0 = x 1 < x 2, T 2 > T 1 = 0. Note carefully that Proposition 1.1 excludes only case 2. Example 1.1. Here we illustrate these three cases. 1. Suppose P i (x) := 1 x/i, i = 1, 2. Then the optimal price discrimination exhibits sorting with x 1 = 2 3, T 1 = 4 9, x 2 = 2, T 2 = 8 9, and, incidentally, exhibits a declining unit price (quantity discount) T 2 /x 2 = 4 9 < 6 9 = 2 3 = T 1/x Suppose P i (x) := θ i (1 x), i = 1, 2, and 1 = θ 1 < θ 2 < 2. Then it is optimal to abstain from discrimination (bunching). Specifically, x 1 = x 2 = 1, T 1 = T 2 = Suppose P i (x) := i x, i = 1, 2. Then it is optimal to serve only the high type (exclusivity) and take away the entire surplus x 1 = T 1 = 0, x 2 = 2, T 2 = 2. However, bunching is a pure borderline case and cannot occur generically. Why? A necessary condition for bunching is that there exists a quantity ξ > 0 for which P 2 (ξ) = P 1 (ξ) = 0 (which is, incidentally, ruled out by A4). This property cannot survive parameter perturbations; hence, it is irrelevant. Example 1.2. Modify Example 1.1(2) by setting θ 2 > 2. Then φ(x 1 ) = (2 θ 2 )(1 x 1 ) is evidently not decreasing; hence, the monopolist s payoff is not concave. In that case, the Kuhn Tucker conditions have two solutions: 1) x 1 = x 2 = 1 and 2) x 1 = 0, x 2 = 1 (see Figure 1.3). Comparing payoffs shows that the unique maximizer is the corner solution x 1 = 0, x 2 = 1 (exclusion) Generalization* The above analysis of optimal pricequantity combinations generalizes in a straightforward manner to n 2 types with the singlecrossing marginal willingnesstopay functions P 1 (y) < P 2 (y) < < P n (y), y. (1.45)
8 8 P i (x), φ(x) 3 2 P 2 (x) φ(x) P 1 (x) x Figure 1.3: Nonconcavity: P i (x) := θ i (1 x), θ 1 = 1, θ 2 = 3. In particular, if complete sorting is optimal, one can show that the optimal price discrimination exhibits 1. zero consumer surplus for the lowest type only; 2. no distortion at the top only; 3. only local downward incentive constraints bind (customer i 2 is indifferent between (T i, x i ) and (T i 1, x i 1 ); all other price quantity combinations in the optimal sales plan are inferior). Moreover, the optimal sales plan is then completely characterized by the following rules: (n + 1 i)p i (x i ) = (n i)p i+1 (x i ), i {1,..., n 1} P n (x n ) = 0 T 1 = x1 0 T i = T i 1 + P 1 (y) dy, xi x i 1 P i (y)dy, i {2,..., n}. The proof of these assertions is a fairly straightforward extension of the above analysis of the twotypes case. It also generalizes to a continuum of types, as we show in the followup analysis in Chapter 9, Section TwoPart Tariffs A Special Case An alternative pricediscrimination scheme is to offer a menu of twopart tariffs. A twopart tariff is an affine price function T i (x) := t i x + f i with the constant unitprice t i and the lumpsum f i. This pricing scheme is frequently observed for example in public utilities pricing, in the taxi business, in mobile phone contracts, to name just a few.
9 1.4 Hidden Information and Price Discrimination 9 In the present case of two types of customers, the monopolist who employs twopart tariffs offers the sales plan, S := {(t 1, f 1 ), (t 2, f 2 )}, asks each customer to pick one component, and then lets each customer buy as many units as he wishes, unless he chose the nobuy option. Twopart tariffs are generally less profitable than optimal pricequantity combinations. This is due to fact that under twopart tariffs, consumers choose the price combination, and then are free to choose their consumption level, which gives the mechanism designer less control. This reflects in the fact that incentive compatibility requirements are more stringent in this case, as we explain below. Implementing an allocation (x 1, x 2 ) by a menu of twopart tariffs S requires: U 1 (x 1, t 1 x 1 + f 1 ) U 1 (x, t 1 x + f 1 ) U 1 (x 1, t 1 x 1 + f 1 ) U 1 (x, t 2 x + f 2 ) U 2 (x 2, t 2 x 2 + f 2 ) U 2 (x, t 2 x + f 2 ) U 2 (x 2, t 2 x 2 + f 2 ) U 2 (x, t 1 x + f 1 ) x x x x. The presence of several for all x operators indicates that these requirements are far more stringent than the corresponding requirements that apply to pricequantity bundles. We may simplify these conditions by defining the optimal consumption level of consumer i as a function of the unit price t j : x i (t j ) := P 1 i (t j ). Evidently, a menu of twopart tariffs can only implement allocations (x 1 (t 1), x 2 (t 2) that represent an optimal choice of consumption for the designated price package. Therefore, the optimal twopart tariffs, S, solve the following optimization problem: 1 ( max t1 x {t 1,t 2, f 1, f 2 } 2 1 (t 1) + t 2 x2 (t ) 2) + f 1 + f 2, s.t. (1.46) U 1 (x 1 (t 1), t 1 x 1 (t 1) + f 1 ) U 1 (x 1 (t 2), t 2 x 1 (t 2) + f 2 ) (1.47) U 1 (x 1 (t 1), t 1 x 1 (t 1) + f 1 ) U 1 (0, 0) (1.48) U 2 (x 2 (t 2), t 2 x 2 (t 2) + f 2 ) U 2 (x 2 (t 1), t 1 x 2 (t 1) + f 1 ) (1.49) U 2 (x 2 (t 2), t 2 x 2 (t 2) + f 2 ) U 2 (0, 0). (1.50) Similar to our analysis of the optimal sales plan S, there is a simple solution procedure, as follows: Suppose, as a working hypothesis, that only the constraints (1.49) and (1.48) are binding (which we will have to confirm). Then, one can eliminate the variables ( f 1, f 2 ) and one obtains an unconstrained maximization problem with the variables (t 1, t 2 ) that is easy to solve. Of course, at the end, you have to confirm that the working hypothesis that was used to construct the solution is actually satisfied by the solution. Working out the solution is left to the reader as an exercise. We close with an example. This example is also used to illustrate the fact that the optimal menu of pricequantity combinations is generally not implementable by twopart tariffs, although it is, of course, always possible to implement the outcome of every menu of twopart tariffs by a menu of pricequantity combinations. For this purpose consider case 1) in example 1.1, for which the optimal menu of pricequantity combinations has already been shown to be S = {{ 23, 49 }, {2, 89 } }, {0, 0}. (1.51)
10 10 If one wishes to implement the allocation implemented by S by a menu of twopart tariffs, S, one obviously needs to set t 1 = P 1 (2/3) = 1 3, f 1 = 2 9, t 2 = P 2 (2) = 0, f 2 = 8 9. (1.52) This assures that each consumer i who chooses the price package (t i, f i ) will actually consume x i and pay altogether T i, as stated in S. However, implementability also requires that no consumer has an incentive to choose the not designated price package for all possible consumption levels (nor choose no trade ). Specifically, for consumer 2 this requires that condition (1.49) is satisfied. However, x 2 (t 1) = 4/3 and one obtains: U 2 (x 2 (t 1), t 1 x 2 (t 1) + f 1 ) = 2/9 > 1/9 = U 2 (x 2 (t 2), t 2 x 2 (t 2) + f 2 ). (1.53) Hence, one cannot find a twopart tariff, S, that implements the allocation that is implemented by S. You may also wish to confirm that, for this example, the optimal menu of twopart tariffs is S = { (t 1 = 1/2, f 1 = 1/8), (t 2 = 0, f 2 = 7/8) }. (1.54) The optimal menu of pricequantity combinations, S, yields a profit equal to 5/4, whereas the optimal menu of twopart tariffs yields a lower profit equal to 4/3 < 4+1/3+1 = 5/4. These results beg the question: why are twopart tariffs so popular? Do firms overlook the fact that pricequantity combinations are the more powerful tool of profit extraction? The answer is that, in many applications pricequantity combinations are too complex, especially if one would need to offer a large number of pricequantity combinations, or not practical for other reasons. One reason is that customers demand is often subject to randomness, and customers cannot predict exactly how much they plan to consume. The demand for mobile phone services is a case in point. Under such circumstance customers do not like to commit to a particular pricequantity combination which may explain why, in these cases, twopart tariffs are the preferred means of seconddegree price discrimination Other Screening Devices Instead of combining price and quantity, one can and frequently does use other screening devices. Their analysis is similar. The important point is that unit price alone cannot screen, although, as we showed, unit price bundled with a lump sum can. We now briefly elaborate on one such variation, taken from airline pricing. Airlines serve a blend of customers with dispersed willingness to pay, such as business travelers and tourists. Typically, their planes cannot be filled with business customers alone. Therefore, some form of price discrimination is an essential ingredient of airline pricing. 5 Typically, if someone makes a reservation, the airline cannot directly tell who is a highprice and who is a lowprice customer. Therefore, price discrimination requires a screening device. Typically, screening is achieved by requiring advance booking on tourist class tickets, combined with rationing in the form of offering a limited number of tourist class tickets. 6 Nobody likes to commit in advance to traveling at a particular day and time. However, customers differ in their willingness to pay to avoid having to commit in advance. Therefore, bundling price and the amount of time the ticket has to be bought prior to the flight may induce screening and boost the airline s profit. 5 This touches on the public good problem; for more on price discrimination and the public good problem see Section??. 6 In addition, business travelers are offered more space, better service, food and drinks, and priority checkin, which we ignore here.
11 1.4 Hidden Information and Price Discrimination 11 As a simple illustration, assume the following utility functions of business b and tourist t travelers for a given trip as a function of price, T, and waiting time W, with γ (0, 1) and δ > 1. U b (T b, W b ) = 1 γ T b δw b, U t (T t, W t ) = 1 T t W t (1.55) Suppose the plane seats k customers. There are 0 < n b < k business customers and n t tourist class customers, with n b + n t > k. For simplicity, the operating cost per customer is normalized to zero. In order to understand the basics of optimal price discrimination in this case, it is useful to draw the indifference curves of the two kinds of customers in the (W, T )space. These are plotted in Figure 1.4 for γ = 1/2, δ = 2. The solid lines represent the indifference curves that yield zeroutility, and the dotted line represents the indifference curve of a business customer whose utility is kept the same as that of choosing the touristclass package (W t, T t ). Special attention will be paid to the pricewaiting time menu {A, B}, and to the uniform (nondiscriminating) price represented by point C. T 1/γ A b s C T t B t s W t 1 W Figure 1.4: Airline pricing: customers indifference curves The optimal pricing scheme can be sketched as follows: If the number of business customers n b is sufficiently large, the optimal menu of twopart tariffs is {A, B}. In other words, business customers pay the maximum possible price T b = 1/γ and are not subject to waiting time, W b = 0. And tourist customers are subject to that combination of price and waiting time, represented by point B, that keeps business customers indifferent between the two tariffs and yet extracts all surplus. Whereas, if business customers are sufficiently rare, it is most profitable to pool and offer the uniform tariff T = 1, W = 0, represented by point C. Altogether, business customers are never subjected to waiting time, W b = 0, and discrimination, if it pays, extracts all surplus. We close this digression with a word of caution concerning the relevance of that model. The key assumption we made was that customers have an aversion against advance booking. While this may be true for some customers, the applied literature on airline pricing generally rejects this assumption and instead stipulates that tourists typically have a preference for early booking whereas business customers have a preference for late booking. Tourists typically wish to book in advance because they must coordinate their vacation schedule with other employees at their workplace or with their spouse, and they must find a dog sitter etc. Whereas business customers prefer late booking because their travel plans typically occur on short notice. An immediate consequence is that if the airline
12 12 would sell all tickets either early or late, it would most likely lose either business or tourist customers. This creates an incentive to sell at different points in time to the two groups of customers that tend to be separated in time. Of course, this calls for a different model. FOLLOWUP READING If you want to know more about seconddegree price discrimination under incomplete information, take a look at our followup analysis in Chapter 9, Section 9.6, where a continuum of types is assumed and more advanced techniques are employed. If you want to learn more about the revenue management techniques employed by airlines, take a look at BELOBABA (1987) and DANA (1998). Unlike in the above model, that literature assumes that tourists have a preference for advance booking and business customers have a preference for late booking. Recently, VULCANO ET AL. (2002) have married that literature with dynamic auctions that determine endogenously how many seats are allocated over time, who is served at each time, and which prices are paid by those who are served. EXERCISES Exercise 1.1 (Explicit Normalization). In the analysis of second degree price discrimination under incomplete information the assumed constant marginal cost was normalized to zero. Here you are asked to explicitly carry out that normalization. Normalization involves a transformation of the price variable. As a result, the transformed marginal rate of substitution dt/dx is equal to the difference between customers marginal willingness to pay and marginal cost. The answer to that exercise is sketched as follows. Suppose marginal cost is equal to c/2 > 0. Prior to the change of variables, the optimization problem is (note: the t instead of T and the p i instead of the P i functions) 1 ( max t1 + t 2 c(x 1 + x 2 ) ), {x,t} 2 s.t. the constraints, U i (x i, t i ) 0, U i (x i, t i ) U i (x j, t j ), i, j = 1, 2, U i (x, t) := x 0 p i (y)dy t. Now define T i := t i cx i, P i (y) := p i (y) c. Inserting these, one obtains s.t. the above constraints, where x j U i (x j, T j ) = 0 1 max {x,t } 2 (T 1 + T 2 ), x j (p i (y) c) dy T j = P i (y)dy T j 0 as in the main text. Note, the slope of the indifference curve is equal to P i (x i ) = p i (x i ) c. Therefore, the negative slope of the indifference curves displayed in parts of Figure 1.1 means that there the marginal cost parameter c exceeds the marginal willingness to pay. Exercise 1.2 (Airline Pricing and Sorting I). Consider the airline price discrimination example. Suppose k = 50, γ = 1/2, δ = 2. Show that price discrimination with the menu { ( S 2 = {(T b, W b ), (T t, W t )} = (2, 0), 3, 1 )} (1.56) 3 is optimal iff n b 13. Whereas a uniform tariff (no discrimination) with T b = T t = 1 and W b = W t = 0 is optimal iff n b 12.
13 1.4 Hidden Information and Price Discrimination 13 Exercise 1.3 (Airline Pricing and Sorting II). Consider the airline price discrimination example. How can one change the utility function of tourist customers so that it exhibits aversion to rationing? Can rationing serve as a screening device in that case?
14 14
15 Bibliography BELOBABA, P. [1987], Airline yield management: An overview of seat inventory control, Transportation Science, 21, DANA, J. D. [1998], Advancepurchase discounts and price discrimination in competitive markets, Journal of Political Economy, 106, MASKIN, E. AND J. G. RILEY [1984], Monopoly with incomplete information, RAND Journal of Economics, 15, PIGOU, A. C. [1920], The Economics of Welfare, Cambridge University Press. VULCANO, G., G. VAN RYZIN, AND C. MAGLARAS [2002], Optimal dynamic auctions for revenue management, Management Science, 48,
ADVANCED MICROECONOMICS (TUTORIAL)
ELMAR G. WOLFSTETTER, MAY 12, 214 ADVANCED MICROECONOMICS (TUTORIAL) EXERCISE SHEET 4  ANSWERS AND HINTS We appreciate any comments and suggestions that may help to improve these solution sets. Exercise
More informationPrice Discrimination: Part 2. Sotiris Georganas
Price Discrimination: Part 2 Sotiris Georganas 1 More pricing techniques We will look at some further pricing techniques... 1. Nonlinear pricing (2nd degree price discrimination) 2. Bundling 2 Nonlinear
More informationSecond degree price discrimination
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
More informationSECONDDEGREE PRICE DISCRIMINATION
SECONDDEGREE PRICE DISCRIMINATION FIRST Degree: The firm knows that it faces different individuals with different demand functions and furthermore the firm can tell who is who. In this case the firm extracts
More informationConditions for Efficiency in Package Pricing
Conditions for Efficiency in Package Pricing Babu Nahata Department of Economics University of Louisville Louisville, Kentucky 40292, USA. email: nahata@louisville.edu and Serguei Kokovin and Evgeny Zhelobodko
More informationUnraveling versus Unraveling: A Memo on Competitive Equilibriums and Trade in Insurance Markets
Unraveling versus Unraveling: A Memo on Competitive Equilibriums and Trade in Insurance Markets Nathaniel Hendren January, 2014 Abstract Both Akerlof (1970) and Rothschild and Stiglitz (1976) show that
More informationLecture 6: Price discrimination II (Nonlinear Pricing)
Lecture 6: Price discrimination II (Nonlinear Pricing) EC 105. Industrial Organization. Fall 2011 Matt Shum HSS, California Institute of Technology November 14, 2012 EC 105. Industrial Organization. Fall
More information3 Price Discrimination
Joe Chen 26 3 Price Discrimination There is no universally accepted definition for price discrimination (PD). In most cases, you may consider PD as: producers sell two units of the same physical good at
More informationProblem Set 9 Solutions
Problem Set 9 s 1. A monopoly insurance company provides accident insurance to two types of customers: low risk customers, for whom the probability of an accident is 0.25, and high risk customers, for
More informationChapter 7. Sealedbid Auctions
Chapter 7 Sealedbid Auctions An auction is a procedure used for selling and buying items by offering them up for bid. Auctions are often used to sell objects that have a variable price (for example oil)
More informationMoral Hazard. Itay Goldstein. Wharton School, University of Pennsylvania
Moral Hazard Itay Goldstein Wharton School, University of Pennsylvania 1 PrincipalAgent Problem Basic problem in corporate finance: separation of ownership and control: o The owners of the firm are typically
More informationMarket Power and Efficiency in Card Payment Systems: A Comment on Rochet and Tirole
Market Power and Efficiency in Card Payment Systems: A Comment on Rochet and Tirole Luís M. B. Cabral New York University and CEPR November 2005 1 Introduction Beginning with their seminal 2002 paper,
More informationLecture 9: Price Discrimination
Lecture 9: Price Discrimination EC 105. Industrial Organization. Fall 2011 Matt Shum HSS, California Institute of Technology September 9, 2011 September 9, 2011 1 / 23 Outline Outline 1 Perfect price discrimination
More informationI. The Monopolist, Market Size and Price Discrimination
Economics 335 February 16, 1999 Notes 5: Monopoly and Price Discrimination I. The Monopolist, Market Size and Price Discrimination A. Definition of a monopoly A firm is a monopoly if it is the only supplier
More informationMonopoly. John Asker Econ 170 Industrial Organization March 27, / 26
Monopoly John Asker Econ 170 Industrial Organization March 27, 2016 1 / 26 Monopoly Overview Definition: A firm is a monopoly if it is the only supplier of a product in a market. A monopolist s demand
More informationChapter 12. Introduction. 2 nd Degree Price Discrimination. 2nd Degree Price Discrimination. This presentation covers 2 nd degree price discrimination
Chapter 12 2nd Degree Price Discrimination Introduction This presentation covers 2 nd degree price discrimination Block pricing Twopart tariffs Menu pricing and versioning 2 nd Degree Price Discrimination
More informationTHIS IS NOT A REQUIRED READING. Chapter 11B. Nonlinear Pricing. 11B.2 Perfect price discrimination, revisited
THIS IS NOT A REQUIRED READING. Chapter 11B Nonlinear Pricing 11B.1 Motivation and objectives In Chapter 11 we looked at sophisticated pricing strategies that implicitly differentiate among customers.
More informationWorking Paper Does retailer power lead to exclusion?
econstor www.econstor.eu Der OpenAccessPublikationsserver der ZBW LeibnizInformationszentrum Wirtschaft The Open Access Publication Server of the ZBW Leibniz Information Centre for Economics Rey, Patrick;
More informationPrice Discrimination 1
Price Discrimination 1 Introduction Price Discrimination describes strategies used by firms to extract surplus from customers Examples of price discrimination presumably profitable should affect market
More informationK 1 < K 2 = P (K 1 ) P (K 2 ) (6) This holds for both American and European Options.
Slope and Convexity Restrictions and How to implement Arbitrage Opportunities 1 These notes will show how to implement arbitrage opportunities when either the slope or the convexity restriction is violated.
More informationFigure 1, A Monopolistically Competitive Firm
The Digital Economist Lecture 9 Pricing Power and Price Discrimination Many firms have the ability to charge prices for their products consistent with their best interests even thought they may not be
More informationEconomics of Insurance
Economics of Insurance In this last lecture, we cover most topics of Economics of Information within a single application. Through this, you will see how the differential informational assumptions allow
More informationOligopoly: How do firms behave when there are only a few competitors? These firms produce all or most of their industry s output.
Topic 8 Chapter 13 Oligopoly and Monopolistic Competition Econ 203 Topic 8 page 1 Oligopoly: How do firms behave when there are only a few competitors? These firms produce all or most of their industry
More information17.6.1 Introduction to Auction Design
CS787: Advanced Algorithms Topic: Sponsored Search Auction Design Presenter(s): Nilay, Srikrishna, Taedong 17.6.1 Introduction to Auction Design The Internet, which started of as a research project in
More informationKEELE UNIVERSITY MIDTERM TEST, 2007 BA BUSINESS ECONOMICS BA FINANCE AND ECONOMICS BA MANAGEMENT SCIENCE ECO 20015 MANAGERIAL ECONOMICS II
KEELE UNIVERSITY MIDTERM TEST, 2007 Thursday 22nd NOVEMBER, 12.0512.55 BA BUSINESS ECONOMICS BA FINANCE AND ECONOMICS BA MANAGEMENT SCIENCE ECO 20015 MANAGERIAL ECONOMICS II Candidates should attempt
More informationWhy do merchants accept payment cards?
Why do merchants accept payment cards? Julian Wright National University of Singapore Abstract This note explains why merchants accept expensive payment cards when merchants are Cournot competitors. The
More informationChapter 21: The Discounted Utility Model
Chapter 21: The Discounted Utility Model 21.1: Introduction This is an important chapter in that it introduces, and explores the implications of, an empirically relevant utility function representing intertemporal
More informationPrice Discrimination and Monopoly: Nonlinear Pricing
Discrimination and Monopoly: 1 Introduction Annual subscriptions generally cost less in total than oneoff purchases Buying in bulk usually offers a price discount these are price discrimination reflecting
More informationNonExclusive Competition in the Market for Lemons
NonExclusive Competition in the Market for Lemons Andrea Attar Thomas Mariotti François Salanié October 2007 Abstract In order to check the impact of the exclusivity regime on equilibrium allocations,
More informationANOTHER PERVERSE EFFECT OF MONOPOLY POWER
ANOTHER PERVERSE EFFECT OF MONOPOLY POWER Jean J. Gabszewicz and Xavier Y. Wauthy November 2000 Abstract We show that the simple fact that a monopolist sells a good in units which are indivisible may well
More informationWeek 7  Game Theory and Industrial Organisation
Week 7  Game Theory and Industrial Organisation The Cournot and Bertrand models are the two basic templates for models of oligopoly; industry structures with a small number of firms. There are a number
More informationPRICE DISCRIMINATION Industrial Organization B
PRICE DISCRIMINATION Industrial Organization B THIBAUD VERGÉ Autorité de la Concurrence and CRESTLEI Master of Science in Economics  HEC Lausanne (20092010) THIBAUD VERGÉ (AdlC, CRESTLEI) Price Discrimination
More informationPrice Discrimination: Case of Monopoly
Price Discrimination: Case of Monopoly The firm charges different prices to different consumers, or different prices for different units purchased. Prevelent in reality. Examples: 1. tickets (airline,
More informationPrice Discrimination
Price Discrimination Economics 302  Microeconomic Theory II: Strategic Behavior Shih En Lu Simon Fraser University (with thanks to Anke Kessler) ECON 302 (SFU) Price Discrimination 1 / 17 Most Important
More information12.1 Why and How Firms Price Discriminate
Chapter 12 Pricing and Advertising 12.1 Why and How Firms Price Why does Disneyworld charge local residents $369 for an annual pass and outoftowners $489? Why are airline fares less if you book in advance?
More informationPrice discrimination by a monopolist
Review Imperfect Competition: Monopoly Reasons for monopolies Monopolies problem: Choses quantity such that marginal costs equal to marginal revenue The social deadweight loss of a monopoly Price discrimination
More informationPart IV. Pricing strategies and market segmentation
Part IV. Pricing strategies and market segmentation Chapter 9. Menu pricing Slides Industrial Organization: Markets and Strategies Paul Belleflamme and Martin Peitz Cambridge University Press 2010 Chapter
More information2. Information Economics
2. Information Economics In General Equilibrium Theory all agents had full information regarding any variable of interest (prices, commodities, state of nature, cost function, preferences, etc.) In many
More informationFrequent flyer programs and dynamic contracting with limited commitment
Frequent flyer programs and dynamic contracting with limited commitment Emil Temnyalov March 14, 2015 Abstract I present a novel contract theoretic explanation of the profitability and management of loyalty
More informationPrice Dispersion. Ed Hopkins Economics University of Edinburgh Edinburgh EH8 9JY, UK. November, 2006. Abstract
Price Dispersion Ed Hopkins Economics University of Edinburgh Edinburgh EH8 9JY, UK November, 2006 Abstract A brief survey of the economics of price dispersion, written for the New Palgrave Dictionary
More information1 Worked Solutions 5. Lectures 9 and 10. Question Lecture 1. L9 2. L9 3. L9 4. L9 5. L9 6. L9 7. L9 8. L9 9. L9 10. L9 11. L9 12.
1 Worked Solutions 5 Lectures 9 and 10. Question Lecture 1. L9 2. L9 3. L9 4. L9 5. L9 6. L9 7. L9 8. L9 9. L9 10. L9 11. L9 12. L10 Unit 5 solutions Exercise 1 There may be practical difficulties in
More information2. Price Discrimination
The theory of Industrial Organization Ph. D. Program in Law and Economics Session 5: Price Discrimination J. L. Moraga 2. Price Discrimination Practise of selling the same product to distinct consumers
More informationIntermediate Microeconomics. Chapter 13 Monopoly
Intermediate Microeconomics Chapter 13 Monopoly Noncompetitive market Price maker = economic decision maker that recognizes that its quantity choice has an influence on the price at which it buys or sells
More informationImperfect information Up to now, consider only firms and consumers who are perfectly informed about market conditions: 1. prices, range of products
Imperfect information Up to now, consider only firms and consumers who are perfectly informed about market conditions: 1. prices, range of products available 2. characteristics or relative qualities of
More informationTHE FUNDAMENTAL THEOREM OF ARBITRAGE PRICING
THE FUNDAMENTAL THEOREM OF ARBITRAGE PRICING 1. Introduction The BlackScholes theory, which is the main subject of this course and its sequel, is based on the Efficient Market Hypothesis, that arbitrages
More informationFirst degree price discrimination ECON 171
First degree price discrimination Introduction Annual subscriptions generally cost less in total than oneoff purchases Buying in bulk usually offers a price discount these are price discrimination reflecting
More informationScreening. Sandeep Baliga. March 29. Sandeep Baliga () Screening March 29 1 / 26
Screening Sandeep Baliga March 29 Sandeep Baliga () Screening March 29 1 / 26 Screening So far we studied competitive equilibrium and benevolent government intervention when there is asymmetric information.
More informationChapter 11 Pricing Strategies for Firms with Market Power
Managerial Economics & Business Strategy Chapter 11 Pricing Strategies for Firms with Market Power McGrawHill/Irwin Copyright 2010 by the McGrawHill Companies, Inc. All rights reserved. Overview I. Basic
More informationTHE UNIVERSITY OF MELBOURNE MELBOURNE BUSINESS SCHOOL. MANAGERIAL ECONOMICS Term 1 1999 First MidTerm Solutions DR.
THE UNIVERSITY OF MELBOURNE MELBOURNE BUSINESS SCHOOL MANAGERIAL ECONOMICS Term 1 1999 First MidTerm Solutions DR. VIVEK CHAUDHRI Part A: Multiple Choice Questions Answer all of the following 10 questions
More informationCommon in European countries government runs telephone, water, electric companies.
Public ownership Common in European countries government runs telephone, water, electric companies. US: Postal service. Because delivery of mail seems to be natural monopoly. Private ownership incentive
More informationMonopoly Behavior or Price Discrimination Chapter 25
Monopoly Behavior or Price Discrimination Chapter 25 monoply.gif (GIF Image, 289x289 pixels) http://i4.photobucket.com/albums/y144/alwayswondering1/monoply.gif?... Monopoly Pricing Uniform pricing: charging
More informationPrinciples of demand management Airline yield management Determining the booking limits. » A simple problem» Stochastic gradients for general problems
Demand Management Principles of demand management Airline yield management Determining the booking limits» A simple problem» Stochastic gradients for general problems Principles of demand management Issues:»
More informationOptimal Auctions. Jonathan Levin 1. Winter 2009. Economics 285 Market Design. 1 These slides are based on Paul Milgrom s.
Optimal Auctions Jonathan Levin 1 Economics 285 Market Design Winter 29 1 These slides are based on Paul Milgrom s. onathan Levin Optimal Auctions Winter 29 1 / 25 Optimal Auctions What auction rules lead
More informationMatching E Multiple Choice d. a & b a. Identifying different types of customers and avoiding arbitrage by customers c.
ECON115 Industrial Organization Midterm 01 Key Version 2k14 PART I: Matching. Match the terms on the left with the definitions on the right. (1/2 point each) 1 Arbitrage E a. When the seller charges a
More informationLecture 4: Monopoly. Daniel Zhiyun LI. September Durham University Business School (DUBS)
Lecture 4: Monopoly Daniel Zhiyun LI Durham University Business School (DUBS) September 2014 Plan of the Lecture Introduction The Problem of Monopoly Price Discriminations Introduction the other extreme
More informationp, we suppress the wealth arguments in the aggregate demand function. We can thus state the monopolist s problem as follows: max pq (p) c (q (p)).
Chapter 9 Monopoly As you will recall from intermediate micro, monopoly is the situation where there is a single seller of a good. Because of this, it has the power to set both the price and quantity of
More informationThe Limits of Price Discrimination
The Limits of Price Discrimination Dirk Bergemann, Ben Brooks and Stephen Morris University of Zurich May 204 Introduction: A classic economic issue... a classic issue in the analysis of monpoly is the
More informationBundling in Cable Television: A Pedagogical Note With a Policy Option. Keith Brown and Peter J. Alexander Federal Communications Commission, USA
K. Bundling Brown and in Cable P. J. Alexander Television Bundling in Cable Television: A Pedagogical Note With a Policy Option Keith Brown and Peter J. Alexander Federal Communications Commission, USA
More informationSecondDegree Price Discrimination
SecondDegree Price Discrimination Lecture 4 Goal: Separating buyers into di erent categories by o ering suitable deals: Screening. Monopolist knows that buyers come in di erent types. Maybe some buyers
More informationUsing yield management to shift demand when the peak time is unknown
RAND Journal of Economics Vol. 30, No. 3, Autumn 1999 pp. 456 474 Using yield management to shift demand when the peak time is unknown James D. Dana, Jr.* Traditional peakload and stochastic peakload
More informationScreening by the Company You Keep: Joint Liability Lending and the Peer Selection Maitreesh Ghatak presented by Chi Wan
Screening by the Company You Keep: Joint Liability Lending and the Peer Selection Maitreesh Ghatak presented by Chi Wan 1. Introduction The paper looks at an economic environment where borrowers have some
More informationA dynamic auction for multiobject procurement under a hard budget constraint
A dynamic auction for multiobject procurement under a hard budget constraint Ludwig Ensthaler Humboldt University at Berlin DIW Berlin Thomas Giebe Humboldt University at Berlin March 3, 2010 Abstract
More informationIndifference Curves and the Marginal Rate of Substitution
Introduction Introduction to Microeconomics Indifference Curves and the Marginal Rate of Substitution In microeconomics we study the decisions and allocative outcomes of firms, consumers, households and
More informationOligopoly: Cournot/Bertrand/Stackelberg
Outline Alternative Market Models Wirtschaftswissenschaften Humboldt Universität zu Berlin March 5, 2006 Outline 1 Introduction Introduction Alternative Market Models 2 Game, Reaction Functions, Solution
More informationINDIAN INSTITUTE OF MANAGEMENT CALCUTTA WORKING PAPER SERIES. WPS No. 681/ September 2011
INDIAN INSTITUTE OF MANAGEMENT CALCUTTA WORKING PAPER SERIES WPS No. 681/ September 2011 Pricing InfrastructureasaService for Online Two Sided Platform Providers by Soumyakanti Chakraborty Assistant
More information1. Suppose demand for a monopolist s product is given by P = 300 6Q
Solution for June, Micro Part A Each of the following questions is worth 5 marks. 1. Suppose demand for a monopolist s product is given by P = 300 6Q while the monopolist s marginal cost is given by MC
More informationSoftware piracy and social welfare: an analysis of protection mechanisms and. pricing strategies
Software piracy and social welfare: an analysis of protection mechanisms and pricing strategies aris Cevik, Gokhan Ozertan* Department of Economics, ogazici University, ebek, 34342 Istanbul, Turkey bstract
More informationLabor Economics, 14.661. Lecture 3: Education, Selection, and Signaling
Labor Economics, 14.661. Lecture 3: Education, Selection, and Signaling Daron Acemoglu MIT November 3, 2011. Daron Acemoglu (MIT) Education, Selection, and Signaling November 3, 2011. 1 / 31 Introduction
More informationWorking Paper Series
RGEA Universidade de Vigo http://webs.uvigo.es/rgea Working Paper Series A Market Game Approach to Differential Information Economies Guadalupe Fugarolas, Carlos HervésBeloso, Emma Moreno García and
More informationBusiness Ethics Concepts & Cases
Business Ethics Concepts & Cases Manuel G. Velasquez Chapter Four Ethics in the Marketplace Definition of Market A forum in which people come together to exchange ownership of goods; a place where goods
More informationInsurance. Michael Peters. December 27, 2013
Insurance Michael Peters December 27, 2013 1 Introduction In this chapter, we study a very simple model of insurance using the ideas and concepts developed in the chapter on risk aversion. You may recall
More informationReadings. D Chapter 1. Lecture 2: Constrained Optimization. Cecilia Fieler. Example: Input Demand Functions. Consumer Problem
Economics 245 January 17, 2012 : Example Readings D Chapter 1 : Example The FOCs are max p ( x 1 + x 2 ) w 1 x 1 w 2 x 2. x 1,x 2 0 p 2 x i w i = 0 for i = 1, 2. These are two equations in two unknowns,
More informationChapter 15: Monopoly WHY MONOPOLIES ARISE HOW MONOPOLIES MAKE PRODUCTION AND PRICING DECISIONS
Chapter 15: While a competitive firm is a taker, a monopoly firm is a maker. A firm is considered a monopoly if... it is the sole seller of its product. its product does not have close substitutes. The
More informationRegret and Rejoicing Effects on Mixed Insurance *
Regret and Rejoicing Effects on Mixed Insurance * Yoichiro Fujii, Osaka Sangyo University Mahito Okura, Doshisha Women s College of Liberal Arts Yusuke Osaki, Osaka Sangyo University + Abstract This papers
More informationOptimal Auctions Continued
Lecture 6 Optimal Auctions Continued 1 Recap Last week, we... Set up the Myerson auction environment: n riskneutral bidders independent types t i F i with support [, b i ] residual valuation of t 0 for
More information12 MONOPOLY. Chapter. Key Concepts
Chapter 12 MONOPOLY Key Concepts Market Power Monopolies have market power, the ability to affect the market price by changing the total quantity offered for sale. A monopoly is a firm that produces a
More informationBuyer Search Costs and Endogenous Product Design
Buyer Search Costs and Endogenous Product Design Dmitri Kuksov kuksov@haas.berkeley.edu University of California, Berkeley August, 2002 Abstract In many cases, buyers must incur search costs to find the
More informationOn the Existence of Nash Equilibrium in General Imperfectly Competitive Insurance Markets with Asymmetric Information
analysing existence in general insurance environments that go beyond the canonical insurance paradigm. More recently, theoretical and empirical work has attempted to identify selection in insurance markets
More informationChoice under Uncertainty
Choice under Uncertainty Part 1: Expected Utility Function, Attitudes towards Risk, Demand for Insurance Slide 1 Choice under Uncertainty We ll analyze the underlying assumptions of expected utility theory
More informationECON 312: Oligopolisitic Competition 1. Industrial Organization Oligopolistic Competition
ECON 312: Oligopolisitic Competition 1 Industrial Organization Oligopolistic Competition Both the monopoly and the perfectly competitive market structure has in common is that neither has to concern itself
More informationA.2 The Prevalence of Transfer Pricing in International Trade
19. Transfer Prices A. The Transfer Price Problem A.1 What is a Transfer Price? 19.1 When there is a international transaction between say two divisions of a multinational enterprise that has establishments
More informationarxiv:1112.0829v1 [math.pr] 5 Dec 2011
How Not to Win a Million Dollars: A Counterexample to a Conjecture of L. Breiman Thomas P. Hayes arxiv:1112.0829v1 [math.pr] 5 Dec 2011 Abstract Consider a gambling game in which we are allowed to repeatedly
More informationThe Effect of ThirdParty Funding of Plaintiffs on Settlement. Andrew F. Daughety and Jennifer F. Reinganum. Online Appendix
1 The Effect of ThirdParty Funding of Plaintiffs on Settlement Andrew F. Daughety and Jennifer F. Reinganum Online Appendix See the main paper for a description of the notation, payoffs, and game form
More informationDecision Theory. 36.1 Rational prospecting
36 Decision Theory Decision theory is trivial, apart from computational details (just like playing chess!). You have a choice of various actions, a. The world may be in one of many states x; which one
More informationLecture Note 7: Revealed Preference and Consumer Welfare
Lecture Note 7: Revealed Preference and Consumer Welfare David Autor, Massachusetts Institute of Technology 14.03/14.003 Microeconomic Theory and Public Policy, Fall 2010 1 1 Revealed Preference and Consumer
More informationPerfect Competition and Pure Monopoly
In the Name of God Sharif University of Technology Graduate School of Management and Economics Microeconomics (for MBA students) 44111 (139394 1 st term)  Group 2 Dr. S. Farshad Fatemi Perfect Competition
More informationSharing Online Advertising Revenue with Consumers
Sharing Online Advertising Revenue with Consumers Yiling Chen 2,, Arpita Ghosh 1, Preston McAfee 1, and David Pennock 1 1 Yahoo! Research. Email: arpita, mcafee, pennockd@yahooinc.com 2 Harvard University.
More informationMicroeconomic Analysis
Microeconomic Analysis Seminar 4 Marco Pelliccia (mp63@soas.ac.uk, Room 474) SOAS, 2014 Price Discrimination A firm with market power faces a downward sloping demand curve. In the standard case of nondiscriminatory
More informationProblem Set #3 Answer Key
Problem Set #3 Answer Key Economics 305: Macroeconomic Theory Spring 2007 1 Chapter 4, Problem #2 a) To specify an indifference curve, we hold utility constant at ū. Next, rearrange in the form: C = ū
More informationA Simple Model of Price Dispersion *
Federal Reserve Bank of Dallas Globalization and Monetary Policy Institute Working Paper No. 112 http://www.dallasfed.org/assets/documents/institute/wpapers/2012/0112.pdf A Simple Model of Price Dispersion
More informationA Detailed Price Discrimination Example
A Detailed Price Discrimination Example Suppose that there are two different types of customers for a monopolist s product. Customers of type 1 have demand curves as follows. These demand curves include
More information2.2 Price Discrimination
2.2 Price Discrimination Matilde Machado Download the slides from: http://www.eco.uc3m.es/~mmachado/teaching/oiimei/index.html 1 2.2 Price Discrimination Everyday situations where price discrimination
More informationCHAPTER 8 PROFIT MAXIMIZATION AND COMPETITIVE SUPPLY
CHAPTER 8 PROFIT MAXIMIZATION AND COMPETITIVE SUPPLY TEACHING NOTES This chapter begins by explaining what we mean by a competitive market and why it makes sense to assume that firms try to maximize profit.
More informationCHAPTER 18 MARKETS WITH MARKET POWER Principles of Economics in Context (Goodwin et al.)
CHAPTER 18 MARKETS WITH MARKET POWER Principles of Economics in Context (Goodwin et al.) Chapter Summary Now that you understand the model of a perfectly competitive market, this chapter complicates the
More information1 Portfolio mean and variance
Copyright c 2005 by Karl Sigman Portfolio mean and variance Here we study the performance of a oneperiod investment X 0 > 0 (dollars) shared among several different assets. Our criterion for measuring
More informationUnit 7. Firm behaviour and market structure: monopoly
Unit 7. Firm behaviour and market structure: monopoly Learning objectives: to identify and examine the sources of monopoly power; to understand the relationship between a monopolist s demand curve and
More informationPricing information goods. The economics of ICT. The Economics of Information Technology Varian Farrel and Shapiro (2004); Comino and Manenti ch.
3/04/06 The Economics of Information Technology Varian Farrel and Shapiro (004); Comino and Manenti ch. ICT is a general purpose technology; it refers to the set of technologies used to manage information.
More informationDefn. Market power the abiliby of a single economic actor (or small group of actors) to have a substantial influence on market prices.
Notes for Chapter 15 Monopoly Firms in perfect competition face the most competition. (They have no market power.) Monopolies face the least competition. (They have the most market power.) Defn. Market
More informationCournot s model of oligopoly
Cournot s model of oligopoly Single good produced by n firms Cost to firm i of producing q i units: C i (q i ), where C i is nonnegative and increasing If firms total output is Q then market price is P(Q),
More information