Regulation Under Asymmetric Information

Transcription

1 Regulation Under Asymmetric Information Lecture 5: Course 608 Sugata Bag Delhi School of Economics February 2013 Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 1 / 50

2 Basic Concepts The Environment Regulatory Context One product to be produced and consumed Two players: Principal (Regulator) and Agent (Firm) Firm is a profit maximizing monopolist; e.g., water, power suppliers, road, airport service providers Benevolent Regulator wants to maximize social welfare Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 2 / 50

3 Basic Concepts The Environment Information Asymmetry Environment Firm s private info on cost/s can take two states a low (L) with probablity φ [0, 1] a high (H) with probablity (1 φ) 3 possible cases of AI faced by regulator related to firm s info on costs unknown but exgenous MC, fixed cost is known - regulator makes a transfer itself for firm - regulator collects the transfer from consumer to pay firm both MC and F unknown to Regulator MC of firm is endogenous and observable by regulator, but he is not fully informed about F In the 3 situations above demand function is common knowledge. Regulator in all cases above sets a unit price p and a tranfer T Another case, when there s asymmetric demand Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 3 / 50

4 The Model-I Set-up Hidden Information Model -I Model-I: Implementation of a menu of contract {q,t} and its issues. Regulator does not charge the consumers, makes the transfer to the firm itself which is necessary to carry on the production, and sets a quantity target for the firm Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 4 / 50

5 The Model-I Set-up The Assumptions Consumer Suplus & Cost V (q) denotes the consumer surplus from (or the (money) value of) q units of output to the Regulator, where V (q) > 0 and V (q) < 0 Cost of production C (q, θ) = θq + F where θ i {θ L, θ H } with θ L < θ H Note that regulator being uninformed about MC attaches a probability to each type - Pr(θ = θ L ) = φ and Pr(θ = θ H ) = 1 φ Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 5 / 50

6 The Model-I Set-up Full Information Bench mark The First Best Let the social welfare in state i be: W i (q) = {V (q) C (q, θ i } Therefore, for given θ i {θ L, θ H }, the FB is a solution to the following problem for the regulator when he is aware of the realised state i for the monopoly firm - max q W i (q) = {V (q) C (q, θ i )} i.e. max q {V (q) θ i.q F } The unique (interior) solution is provided by the following FoC: V (q) = θ i for each i Let qi be the solution for the previous equation. Clearly ql > q H > 0 Indeed you can verify the following: V (q L ) θ L.q L F > V (q H ) θ H.q H F W (q L ) > W (q H ) 0 Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 6 / 50

7 The Model-I Set-up The First Best Implementing the FB Let the transfer to the firm from the regulator be t i such that t i = θ i.q i + F. When there is no informational asymmetry about θ, the Regulator will make the following take it or leave it offers:- If θ = θ L, firm is offered (q L ; t L ), i.e., t L for production level q L ; and If θ = θ H, firm is offered (q H ; t H ), i.e., t H for production level q H ; Since each type of firm gets non-negative utility from the offer, it accepts the offer. Note that this transfer is not collected from the consumers. The first best payoff for the Regulator is - V (q L ) t L, if θ = θ L V (q H ) t H, if θ = θ H Ex-ante pay-off to the regulator is - W = φ{v (q L ) t L } + (1 φ){v (q H ) t H } the Regulator is able to appropriate the entire surplus from the trade. Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 7 / 50

8 Hidden Information -I: The Model-I Set-up The Second Best Assumption: The Regulator does not observe θ. However, knows the distribution - Pr(θ = θ L ) = φ and Pr(θ = θ H ) = 1 φ Let θ = θ H θ L > 0 be a measure of the spread of uncertainty of firm type. Only Contractible variables are q and monetary transfers from principle to the Firm t. Definition Contracts: A contract is a feasible, observable and verifiable allocation (q; t). The set of contracts is - A= {(q; t) : q R +, t R} Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 8 / 50

9 The Model-I Set-up The Second Best Hidden Information-II: Implementing issue Proposition: When Regulator does not observe θ, contract ((ql ; t L ); (q H ; t H )) cannot be implemented. Note under contract {(q L ; t L ), (q H ; t H )}, π L = t L θ L.q L F = 0 and π H = t H θ H.q H F = 0 i.e. truth telling means that each firm type s profit is equal to zero, i.e., the outside (reservation) profit. However, since θ H > θ L t H θ L.q H F t H θ H.q H F = 0 Therefore, t H θ L.q H F > t L θ L.q L F = 0 i.e. type L Firm is better off mimicking as type H. Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 9 / 50

10 The Model-I Set-up The Second Best Hidden Information-III : Incentive Compatibility Definition A menu of contracts {(q L ; t L ); (q H ; t H )} is incentive compatible if - t L θ L.q L F t H θ L.q H F = {t H θ H.q H F } + {θ H.q H θ L.q H } i.e. π L π H + θ.q H (1) t H θ H.q H F t L θ H.q L F = {t L θ L.q L F } {θ H.q L θ H.q L } i.e. π H π L θ.q L (2) Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 10 / 50

11 The Model-I Set-up The Second Best Hidden Information-IV : A Feasible Contract Definition A menu of contracts {(q L ; t L ); (q H ; t H )} is incentive compatible [given (1) and (2)] and rationality feasible if it satisfies the following individual rationality constraints - t L θ L.q L F 0 i.e. π L 0 (3) t H θ H.q H F 0 i.e. π H 0 (4) Example 1. Consider {(qh ; t H ); (q H ; t H )}This contract results in pooling of types. 2. Consider {(ql ; t L ); (0; 0)}. This contract results in shutting down of ineffi cient types. Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 11 / 50

12 Hidden Information-V The Model-I Set-up The Second Best Remarks Monotonicity of Output: Adding (1) and (2) gives us - (θ H θ L ).q L (θ H θ L ).q H i.e. q L q H. In fact, any pair (q L ; q H ) is implementable iff q L q H (1) and (4) imply that as long as q H > 0, t L θ L.q L > 0; i:e:; if ineffi cient type is required to produce, the profit of the effi cient type will be positive. Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 12 / 50

13 The Model-I Set-up The Second Best Hidden Information-VI The Regulator s optimization problem is - max (q L,t L ),(q H,t H ) W = φ{v (q L) t L } + (1 φ){v (q H ) t H } subject to (1)-(4) As π L = t L θ L.q L F and π H = t H θ H.q H F, we rewrite (1) to (4) - π L π H + θ.q H (5) π H π L θ.q L (6) π L 0 (7) π H 0 (8) Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 13 / 50

14 The Model-I Set-up The Second Best Hidden Information-VII Now regulator s optimisation problem can be further rewritten as - max φ{v (q L) θ L q L } + (1 φ){v (q H ) θ H q H } (q L,π L ),(q H,π H ) subject to (5) to (8). - Note that - {φπ L + (1 φ)π H } Allocative Effi ciency: φ{v (q L ) θ L.q L } + (1 φ){v (q H ) θ H.q H } Information Rent: {φ.π L + (1 φ).π H } Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 14 / 50

15 The Model-I Set-up The Second Best Hidden Information-IX: Remarks Remark: (5) and (8) together imply (7). That is, [π L π H + θ.q H ] and [π H 0] π L 0 under optimum contract (5) and (8) will both bind, i.e., π H = 0 and (9) π L = θ.q H (10) Ignoring (6) for the time being, the Regulator s optimization problem becomes - max [φ{v (q L) θ L.q L F } + (1 φ){v (q H ) θ H.q H F } φ. θ.q H ] (q L,q H ) Note that we have effectively substituted all the constraints in the objective function above by now. Now we can derive the FoC s... but pause for a moment to consider... Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 15 / 50

16 The Model-I Set-up The Second Best Hidden Information-VIII: Consider following - Consider a menu of contract like the following - {(F + θ L.q L + θ.q H ); q L}, {(F + θ H.q H ); q H } i.e.{(π L = θ.q H ); q L}, {(π H = 0); q H }. It is incentive feasible and implements the FB. But, will Regulator offer this contract? Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 16 / 50

17 The Model-I Set-up The Second Best Hidden info - Optimisation Results: V (q L ) = θ L (11) V (q H ) = θ H + φ 1 φ. θ (12) That is, ql SB = ql but qsb H < q H. Verify that at the SB values (6) is satisfied. The SB transfers are given by (9) and (10), i.e., π SB H = π H = 0 and πsb L > πl. i.e. - th SB = θ H.qH SB and tsb H = θ L.qL + θ.qh SB Fact (Remark) k 1. Allocative ineffi ciency increases with θ. 2. The (information) rent yielded to the effi cient type increases with θ. Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 17 / 50

18 The Model-I Set-up Optimisation Result: Remarks The Second Best Moreover, (12) can be expressed as (1 φ){v (qh SB ) θ H } = φ. θ i.e. at the SB marginal benefit (LHS) from increasing q H is equal to the marginal cost (RHS) of doing so. Clearly, if V (.) is finite, shutdown takes place for φ close to 1. More generally, shutting down of ineffi cient type is optimal for the Regulator if φ[v (ql) θ L.qL] φ[v (ql SB ) θ L.qL SB θ.q SB φ. θ.q SB H (1 φ)[v (q SB H ) θ H.q SB H ] (1 φ)[v (qh SB ) θ H.qH SB ] H ] + Market failure Ex: Show that shutdown becomes more likely as the outside profit (status quo utility level) goes up. Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 18 / 50

19 The Model-II Set-up Hidden Information Model -II Model-II: Implementation of a menu of contract {p,t}, and its issues Benevolent Regulator wants to maximize social welfare [S + αr] Regulator tries to implement two part paricing, collects transfers from consumers to pay to firm Regulator values CS (S) more highly than the Rents (R) or net profits to firm. Thus attaches a weight α [0, 1] to R when α = 1, regulator treats S and R equally when α < 1, firm s rent R is socially costly Regulator wishes to limit the the transfer from consumers to firm and tries to limit R to a miminimum Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 19 / 50

20 The Model-II Set-up The Assumptions Demand & Consumer Suplus Monopoly supplies single product at a regulated price p 0 The demand curve for the regulated product: Q(p) Consumer suplus at price p is v(p) where v(.) is a convex function of p Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 20 / 50

21 Cost of production The Model-II Set-up The Assumptions C (Q, c i ) = c i.q + F, where c i {c L, c H } and Note that regulator being uninformed about MC attaches a probability to each type - Pr(c = c L ) = φ and Pr(c = c H ) = 1 φ c = c H c L > 0, a measure of spread of uncetainty of firm type. For MC type i (:= L, H) at price p i - firm profit : π i = Q(p i ).(p i c i ) F and firm rent: R i = π i (p i ) + T i = Q(p i ).(p i c i ) F + T i Let us now make an important assumption on the difference in firm s operating profit at price p in states H and L - π (p) = π H (p) π L (p) and d dp π > 0 (13) This "increasing difference" property reflects the standard single crossing property which holds when the firm s MRS of price for transfer payment varies monotonically with underlying state. Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 21 / 50

22 The Model-II Set-up The Assumptions Regulator s Optimisation - I Regulator seeks to maximise S + αr Welfare in state i (i.e. eigheted average of of CS & Rent) when p i price is charged and T i transfer is made - W i = S i + αr i = [v i (p i ) T i ] + α[π i (p i ) + T i ] = [v i (p i ) + π i (p i )] (1 α)[π i (p i ) + T i ] Or, W i = w i (p i ) (1 α)r i, where i = L, H (14) where w i (p i ) = v i (p i ) + π i (p i ) : total unweighted surplus (the sum of consumer surplus and profit) in state i when price p i is charged Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 22 / 50

23 The Model-II Set-up The First Best Regulator s Optimisation - II : Full Information set-up Fact Will Marginal cost pricing be allowed? That is will p i = c i hold? If Regulator can observe firm s realised MC (i.e. either c L or c H ) then he would implement the (Ramsey) price that maximise w i (.) when MC is c i in the previous expression (2) for i = L, H. These full information prices would be MC prices (i.e. p i = c i ) and In effect R i = 0 => T i = F Clearly, p L = c L < p H = c H and, w L (p L ) > w H (p H ) > 0 Definition Contracts: A contract is a feasible, observable and verifiable allocation (p; T), where p is the per-unit price the firm can charge and T is the payment it receives from the regulator. The set of contracts is A= {(p; T ) : p R +, T R} Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 23 / 50

24 The Model-II Set-up The First Best Implementing the first best in full info set up Note that we already have, T i = T = F and p i = c i When there is no informational asymmetry about, the Regulator will make the following take it or leave it offers: - If c = c L, the Firm is offered (p L, T ) and If c = c H, the Firm is offered (p H, T ) Since each Firm gets non-negative utility from the offer, it accepts the offer. The first best payoff for the Regulator is - w L (pl ) (1 α)r L w H (ph ) (1 α)r H if c = c L if c = c H Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 24 / 50

25 The Model-II Set-up The Second Best: Hidden Information Case Issue of implementing the first best in Hidden info set up Why? Let s see... Suppose the regulator announces that he will implement unit price p i and transfer payment T i when the firm claims to have marginal cost c i ; for i = L; H. When the firm in i th state with cost c i chooses the (p i ; T i ) option, its rent will be R i = Q(p i ).(p i c i ) F + T i In contrast, if when the firm in i th state with cost c i chooses the (p j ; T j ) option, its rent will be Q(p j ).(p j c i ) F + T j = R j + Q(p j ).(c j c i ) From expression above, low cost firm may have an incentive to over-state its MC!!! What about high cost firm s temptation? Low-cost firm will choose (p L ; T L ) option, if following be true R L R H + c.q(p H ) (15) Therefore, the full-information outcome is not feasible, since inequality (15) cannot hold when both R H = 0 and R L = 0. Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 25 / 50

26 The Model-II Set-up The Second Best: Hidden Information Case Menu of contract Regulator has offer a different menu of contract than FB and follow a constrined optimisation procedure as follows - The regulator seeks to maximize the expected value of a weighted average of consumer surplus and rent in two states [of expression (14) above]. Therefore, ex ante expected welfare is - W = φ{w L (p L ) (1 α)r L } + (1 φ){w H (p H ) (1 α)r H } (16). To implement a menu of contracts {(p L ; T L ); (p H ; T H )}, Regulator would optimise expression above under following constrints - [IR] Individual rationality or participation constraint,and [IC] Incentive compatibility constrint Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 26 / 50

27 The Model-II Set-up The Second Best: Hidden Information Case Menu of contract II Definition A menu of contracts is individually rational when type i firm agrees to produce only if she receives a non-negative rent i.e. R H 0 and R L 0 (17) If the state of world unkown to the regulator, he must ensure that contracts are such that each type of firm finds it in its interest to choose the correct contract i.e. IC. Definition A menu of contracts {(p L ; T L ); (p H ; T H )} is IC if - Q(p L ).(p L c L ) F + T L Q(p H ).(p H c L ) F + T H (18) Q(p H ).(p H c H ) F + T H Q(p L ).(p L c H ) F + T L (19) Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 27 / 50

28 Menu of contract III The Model-II Set-up The Second Best: Hidden Information Case IC s can be re-written respectively as follows - R L R H π (p H ) (20) R H R L + π (p L ) (21) Adding the expressions (20) and (21) we get - π (p H ) π (p L ) (22) Note that increasing difference expression (13) together with inequality (22) just above ensure that eqlm prices must be higher in state H than in state L in any incentivecompatible regulatory policy, i.e., - p H p L (23) Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 28 / 50

29 The Model-II Set-up The Second Best: Hidden Information Case Regulator s Optimisation Let s now re-write Regulator s optimisation problem as follows - max [φ{w L(p L ) (1 α)r L } + (1 φ){w H (p H ) (1 α)r H }] (p L,T L ),(p H,T H ) Or, max [φ{w L(p L ) (1 α)r L } + (1 φ){w H (p H ) (1 α)r H }] (p L,R L ),(p H,R H ) Subject to R L 0 and (24) R H 0 (25) R L R H π (p H ) (26) R H R L + π (p L ) (27) The expression (25) and (26) bind the solution. which means... next page... Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 29 / 50

30 The Model-II Set-up Regulator s Optimisation II The Second Best: Hidden Information Case The expression (25) and (26) bind the solution. which means - R H 0 (28) R L = π (p H ) (29) will hold. Using (28) and (29), optimisation problem becomes max W = φ{w L(p L ) + (1 α) π (p H )} + (1 φ){w H (p H )} (30) (p L,p H ) Since w i (p i ) = v i (p i ) + π i (p i ), we re-write above expression as - max φ{v L(p L ) + π L (p L ) + (1 α) π (p H )} + (1 φ){v H (p H ) + π H (p H )} (p L,p H ) where, recall that, π i = Q(p i ).(p i c i ) F. We derive the foc as follows - Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 30 / 50

31 The Model-II Set-up Regulator s Optimisation III : FoC result The Second Best: Hidden Information Case Proposition 1: When the firm is privately informed about its MC of production, optimal regulatory policy has following features: - Fact pl SB = c L = pl (31) ph SB = c H + φ 1 φ (1 α) c > ph (32) R L = c.q(p H ); and R H = 0 (33) 1. For all α < 1, ph SB > p H i.e. Q(pSB H ) < Q(p H ); increase in p H above c H reduces the rent of the low-cost firm which increases welfare it reduces the total surplus available when the firm is high cost type. 2. α = 1, ph SB = p H i.e. Q(pSB H ) = Q(p H ), Note here that this coincides with Loeb-Magat case dealt earlier 3. α > 1, ph SB < p H i.e. Q(pSB H ) > Q(p H ) Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 31 / 50

32 The Model-III Endogenous MC & FC Hidden Information Model -III Model-III: Endogenous costs (fixed cost and MC are inversely related) Implementation of a menu of contract {p,t}, and its issues First Best menu is possible but conditional Benevolent Regulator wants to maximize social welfare [S + αr] where α [0, 1] Regulator tries to implement two part paricing, collects transfers from consumers to pay to firm Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 32 / 50

33 The Model-III Endogenous MC & FC The Hidden Information Case Counterveiling Incentives: The environment The firm is privately informed about both its F & MC It is common knowledge that F is inversely relate MC Fixed Cost c L F L c H F H where c L < c H = F L > F H with c = c H c L > 0 and F = F L F H > 0 Monopoly supplies single product at a regulated price p 0 The demand curve for the regulated product: Q(p) Consumer suplus at price p is v(p) where v(.) is a convex in p. Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 33 / 50

34 The Model-III Endogenous MC & FC The Hidden Information Case Social Welfare, firm profit & rent Note that regulator being uninformed about MC attaches a probability to each type - Pr(c = c L ) = φ and Pr(c = c H ) = 1 φ For MC type i (:= L, H) at price p i - firm profit : π i = Q(p i ).(p i c i ) F i and (34) firm rent : R i = π i (p i ) + T i = Q(p i ).(p i c i ) F i + T i (35) Welfare in state i when p i price is charged and T i transfer is made - W i = S i + αr i = [v i (p i ) T i ] + α[π i (p i ) + T i ]Or, W i = w i (p i ) (1 α)r i, where i = L, H where w i (p i ) = v i (p i ) + π i (p i ) is total unweighted surplus. Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 34 / 50

35 The Model-III Endogenous MC & FC First Best menu in full info state The Hidden Information Case If Regulator can observe firm s realised MC (i.e. either c L or c H ), so that it can indirectly infer about the respective fixed cost; then he would implement the (Ramsey) price that maximise w i (.) when MC is c i in the previous expression ( ) for i = L, H. These full information prices would be MC prices (i.e. pi In effect Ri = 0 => Ti = F i Clearly, pl = c L < ph = c H and, TL = F L > TH = F H further, w L (p L ) > w H (p H ) > 0 = c i ) and Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 35 / 50

36 The Model-III Endogenous MC & FC The First Best Implementing the first best in full info set up Note that we already have, T i = F i and p i = c i When there is no informational asymmetry about, the Regulator will make the following take it or leave it offers: - If c = c L, the Firm is offered (p L, T L = F L) and If c = c H, the Firm is offered (p H, T H = F H ) Since each Firm gets non-negative utility from the offer, it accepts the offer. The first best payoff for the Regulator is - w L (pl ) (1 α)r L w H (ph ) (1 α)r H if c = c L if c = c H Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 36 / 50

37 The Model-III Endogenous MC & FC The Hidden Info and issue FB implementation problem: which type wants deviate? Note that if when the firm in i th state firm claims to be j th state and chooses the (p j ; T j ) option, its rent will be - Q(p j ).(p j c i ) F i + T j = R j + Q(p j ).(c j c i ) i.e. when L state claims to be H, gets a rent - Q(p H ).(p H c L ) F L + T H = R H F + c Q(p H ) (36) From expression above, low cost firm may have an incentive to over-state its MC!!! What about high cost firm s temptation? when H state firm claims L, gets a rent - Q(p L ).(p L c H ) F H + T L = R L + F c Q(p L ) (37) From expression above, high cost firm may also have an incentive to under-state its MC!!! Something suprising here?!! Incentive to each type depends on the interaction of the magnitude of F and c Q(p i ) Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 37 / 50

38 The Model-III Endogenous MC & FC The Hidden Info and issue Regulator s Optimisation - I Regulator might have to offer a different menu of contract than FB The regulator to implement a menu of contracts {(p L ; T L ); (p H ; T H )}, follows a constrined optimisation procedure to maximise ex ante expected welfare as follows - Max W = φ{w L (p L ) (1 α)r L } + (1 φ){w H (p H ) (1 α)r H } (38) under following constrints - R L 0 [IR L ] (39) R H 0 [IR H ] (40) R L R H F + c Q(p H ) [IC L ] (41) R H R L + F c Q(p L ) [IC H ] (42) Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 38 / 50

39 The Model-III Endogenous MC & FC The Hidden Info and issue Regulator s Optimisation - II Since π i (p) = Q(p).(p c i ) F i, it then follows that - Therefore we can rewrite IC s as follows - π (p) = F c Q(p) (43) R L R H π (p H ) [IC L ] (44) R H R L + π (p L ) [IC H ] (45) Adding the expressions above, we get - π (p H ) π (p L ) Note that increasing difference expression (13) together with inequality just above just above ensure that eqlm prices must be higher in state H than in state L in any incentive compatible regulatory policy, i.e., - p H p L Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 39 / 50

40 The Model-III Endogenous MC & FC First Proposition of the model The Hidden Info and issue Proposition 2: When the firm is privately informed about both its F & MC: (i) If F [ c Q(c H ); c Q(c L )] then the full-information outcome is feasible (and optimal); (ii) If F < c Q(c H ) then p H > c H and p L = c L ; (iii) If F > c Q(c L ) then p L < c L and p H = c H Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 40 / 50

41 Pair of inequalities in (46) if the full-info outcome is to be attainable, profit functions π H (.) and π L (.) must cross: operating profit must be higher in state H than in L at full-info price p H, & same must be lower in state H than in L at full-info price p L.Full-info outcome won t be feasible if firm s operating profit is systematically higher in one state than the other (e.g. as when firm is privately Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 41 / 50 The Model-III Endogenous MC & FC Proof of Proposition 2: Part i The Hidden Info and issue If F [ c Q(c H ); c Q(c L )] then full-info outcome is feasible & optimal Recall that in the full-information outcome, the type-i firm sets price pi and receives zero rent. when the regulator does not observe the state, the IC s (44) and (45) imply that this full-info outcome is attainable iff π (ph ) }{{} (R H R L ) }{{}}{{} π (pl ) ICL =0 ICH i.e. F c Q(p H ) 0 F c Q(p L ) Or, c Q(p H ) F c Q(p L ) (46)

42 The Model-III Endogenous MC & FC The Hidden Info and issue Proof of Proposition 2: Part iii (iii) If F > c Q(c L ) then p H = c H and p L < c L ; In this case, the first-best contract given above violates (ICH) only, which implies (ICH) must be binding at the optimum. p L < p H is necessary and suffi cient for (ICL) to be satisfied, given that (ICH) is binding. the binding incentive problem for the regulator is to prevent the firm from exaggerating its F via understating its mc. To mitigate the firm s incentive to understate c, the regulator sets p L < c L. Doing so increases beyond its full-info level the output the firm must produce at a rate of compensation that is unprofitable when the firm s mc is high. Similarly, part ii can be proved. When the potential variation in F is either more pronounced or less pronounced than in part (i) of Proposition 2, the full-information outcome is no longer feasible. Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 42 / 50

43 The Model-III Endogenous MC & FC The Hidden Info and issue Proof of Proposition 2: Solution for Part ii, FoCs (ii) If F < c Q(c H ) then p H > c H and p L = c L ; The expression (41) and (42) bind the solution. which means - R H 0 (47) R L = π (p H ) (48) will hold. Using (47) and (48) above, optimisation problem becomes - max (p L,p H ) W = φ{w L(p L ) + (1 α) π (p H )} + (1 φ){w H (p H )} Since w i (p i ) = v i (p i ) + π i (p i ), we re-write above expression as - max φ{v L(p L ) + π L (p L ) + (1 α) π (p H )} + (1 φ){v H (p H ) + π H (p H )} (p L,p H ) where, recall that, π i = Q(p i ).(p i c i ) F. We derive the foc as in proposition 1. Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 43 / 50

44 The Model-III Endogenous MC & FC The Hidden Info and issue Regulator s Optimisation III : FoC result When F < c Q(c H ) then p H > c H and p L = c L When the firm is privately informed about its MC of production, optimal regulatory policy has following features: - pl SB = c L = pl (49) ph SB = c H + φ 1 φ (1 α) c > ph (50) R L = c.q(p H ); and R H = 0 (51) Can you deduce the results for the other case?? Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 44 / 50

45 The Model-III Endogenous MC & FC Implications of Proposition 2 The Hidden Info and issue The regulator may gain by creating countervailing incentives for the regulated firm. For instance, the regulator may mandate the adoption of technologies in which fixed costs vary inversely with variable costs. Alternatively, he may authorize expanded participation in unregulated markets the more lucrative the firm reports such participation to be (and thus the lower the firm admits its operating cost in the regulated market to be) Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 45 / 50

46 The Model-IV Endogenous MC & FC Hidden Information Model -IV The regulator can observe firm s mc but cannot ascertain how this mc is realised (i.e. whether exogenously chosen by nature or, endogenously chosen through effort, which is modelled via fixed cost) Two types of firms - type-l: has to spend relatively low F to achive low mc type-h: has to spend relatively greater F to achive low mc Let F i (c) denote the fixed cost for type-i where F i (.) is decreasing and convex with F H (c) > F L (c) and d dc [F H (c) F L (c)] < 0 Regulator cannot observe firm type (i.e its F H (c)) but attaches probability φ F L (c) Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 46 / 50

47 The Model-IV Endogenous MC & FC What happens in this setting? The regulator has 3 policy instuments in this situation viz. p, T and c. The regulator s limited info allows the firm with low F to get a rent Towards limiting this rent, regulator may restrict reward to to type-l firm Distortion happens, firm type-l may not reduce its mc to the full-info level Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 47 / 50

48 The Model-IV Endogenous MC & FC What happens in this setting?... 2 The regulator announces that he will authorise p i, T i when the firm claims to be type-i, provided mc=c i is observed. Similar to earlier cases, eqlm rent for type-i firm R i is given by - R i = Q(p i ).(p i c i ) F i (c i ) + T i (52) Again low cost firm won t claim to have high F iff - R L R H + F H (c H ) F L (c H ) (53) Note that high-cost firm does not have any incentive to mimick type-l - Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 48 / 50

49 The Model-IV Endogenous MC & FC The First Best The net consumer surplus in state-i is - v i (p i ) T i Using expression (52) above, we can rewrite this as follows - v i (p i ) + Q(p i ).(p i c i ) F i (c i ) R i (54) Regulator s choice of prices {p L, p H } does not affect the binding incentive constraint (53) above, given the coice of rents {R L, R H }. Thus prices do not affect the the rents. This is the Laffont-Tirole s "Incentive-pricing Dichotomy" i.e. - prices (generally) should be used solely to attain allocative effi ciency, while rents should be used to motivate the firm to produce at low cost. Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 49 / 50

50 The Proposition The Model-IV Endogenous MC & FC If regulator knew firm s type, he would also require the effi cient level of mc, which is the cost that maximizes total surplus {v(c) F i (c)}. As usual, though, the full-info outcome is not feasible when the regulator does not share the firm s knowledge of its technology. To limit the low-cost firm s rent, the regulator inflates the high-cost firm s mc above the full-info level, as reported in Proposition next. Proposition 3: When the firm s mc is observable but endogenous, the optimal regulatory policy has the following features: p L = c L ; p H = c H ; (55) Q(c L ) + F L(c L ) = 0; (56) Q(c H ) + F H (c H ) = φ 1 φ [F H (c H ) F L(c H )] > 0 (57) R L = F H (c H ) F L (c H ) > 0; R H = 0 (58) Sugata Bag (DSE) Regulation Under Asymmetric Information 08/02 50 / 50