Department of Economics and Institute for Policy Analysis University of Toronto 150 St. George Street Toronto, Ontario M5S 3G7 Canada

Transcription

1 Deartment of Economics and Institute for Policy Analysis University of Toronto 150 St. George Street Toronto, Ontario M5S 3G7 Canada WORKING PAPER NUMBER UT-ECIPA-ECPAP CORPORATION TAX ASYMMETRIES: AN OLIGOPOLISTIC SUPERGAME ANALYSIS by Pierre-Pascal Gendron June 24, 1996 Latest Version: July 8, 1996 Coyright 1996 by Pierre-Pascal Gendron Deartment of Economics University of Toronto ISSN On-line Version: htt:// Author's

2 Cororation Tax Asymmetries: An Oligoolistic Suergame Analysis * Pierre-Pascal Gendron June 24, 1996 Abstract Cororation tax systems around the world treat gains and losses asymmetrically. This aer examines the imact of changing the refundability of tax losses in a cash flow tax system. A dynamic game of comlete information is used to analyse refund olicies in an imerfectly cometitive setting. In this suergame, firms roduce a homogeneous good and sustain tacit collusion by using credible and severe unishments of deviations. The analysis of the most collusive equilibrium with losses indicates that a tax olicy which increases refundability has the following imacts: it reduces collusive industry outut, increases market rice, and therefore enhances tacit collusion. This olicy also reduces social welfare even though refunds are never given in equilibrium. JEL classification: C72 and H25. * I am grateful to Jack Mintz, Michael Peters, and Michael Smart for useful discussions and suggestions. Their invaluable comments on the revious drafts of this aer are greatly areciated. My thanks also go to Frank Mathewson for suggesting examles. The usual disclaimer alies. Mailing address is Deartment of Economics, University of Toronto, 150 St. George Street, Toronto, Ontario, Canada M5S 3G7; address is gendron@chass.utoronto.ca

3 1.0 INTRODUCTION The accumulation of cororate tax losses in many countries in recent history has raised a number of imortant issues concerning the economic imact of cororate tax olicies. The study of tax losses entails imortant dynamic asects that are emhasized in theoretical studies such as Edwards and Keen (1985) and Auerbach (1986), and in emirical work such as that of Auerbach and Poterba (1987), Mintz (1988) and Altshuler and Auerbach (1990). This emirical work also underscores the economic significance of tax losses. The aroriate modelling strategy to study the imact of tax losses and their non-refundability must be dynamic in nature. A common feature of tax systems around the world is the non-refundability of tax losses. Those systems, however, generally allow tax losses to be carried back against taxes aid in the ast or carried forward to reduce future tax liabilities. For examle, cororate tax systems in Canada, the U.K. and the U.S. allow firms to carry back losses for a limited number of years, thereby claiming a refund of ast taxes aid. They also allow firms to carry such losses forward at no interest but for longer eriods. The cororate tax system in Canada includes limited instances of refundability such as carrybacks, the refundable scientific research and develoment tax credit, and the refundable small business tax credit. Those measures constitute an attemt to move towards a neutral tax system. Mintz (1991) oints out that tax losses and their lack of refundability raise imortant issues with resect to market structure. In site of that, he notes that the toic has received virtually no attention. The entire body of literature he surveys does indeed embody the assumtion of erfect cometition in roduct markets. 1

4 The resent aer exlores a different justification for the non- refundability of tax losses. The framework is one in which oligoolistic firms interact reeatedly and collusive behaviour may be suorted by non-cooerative equilibria. In contrast to the traditional suergame literature, this model allows for unishments that are more severe than the Cournot-Nash reversion in order to suort tacit collusion. The Cournot-Nash reversion is a unishment mechanism which secifies that all industry members revert to Cournot cometition once any individual firm deviates from its collusive outut share. The most collusive equilibrium can generate short-run losses during the unishment hase. Such losses can be artially recoued in the future; hence, the availability of tax loss refunds can affect the most collusive outcome. 1 In this aer, tax loss refund rovisions diminish the imact of any loss incurred during the unishment hase. It is shown that a olicy that increases tax loss refundability reduces the most collusive outut and raises rices. More generally, in the symmetric information environment studied here, refunding losses in any way can have this collusion-enhancing effect. The work of Abreu (1986) is now the standard view on tacit collusion. This emerged from his wish "to study the maximal degree of collusion sustainable by credible threats for arbitrary values of the discount factor" (192, italics in original). His 1986 and 1988 aers focus on strategy rofiles that yield the most severe unishments or outcome aths. Those unishments constitute subgameerfect equilibrium strategies which can be severe enough under certain conditions so as to make negative rofits ossible during the unishment hase. Although Abreu is interested in characterizing the most collusive equilibrium, the idea I wish to convey can be made in a very simle way by restricting attention to symmetric unishments. Such unishments require all firms to roduce identical outut streams, whether the oligooly is in a 2

5 collusive or unishment hase. It is imortant to note that such unishments are a generalization of unishments based on Cournot reversions as in Friedman (1971). In articular, symmetric unishments can suort lower oututs and higher rices than a simle Cournot reversion by invoking the unishment hase in which firms can make short-run losses. It is recisely those short-run losses that constitute the focal oint of the aer. The aer is organized as follows. Section 2.0 resents the basic model. Section 3.0 resents a descrition of the tax treatment of losses and characterizes the outcome aths and equilibria with a cash flow tax. Section 4.0 analyses the effects of changes in refundability on rofits, outut and welfare. Finally, Section 5.0 concludes the aer by a summary and a discussion of interesting extensions to the resent work. 3

6 2.0 THE MODEL Suose an oligoolistic industry consists of n firms which lay an infinitely reeated Cournot game with discounting. In each eriod, all firms simultaneously choose outut quantities and maximize rofits. Firms wish to maximize the resent value of their rofits. For the moment, let any taxes be subsumed in the rofit functions. Uncertainty is ignored throughout. 2 Each firm makes its quantity decision in eriod t knowing what every other firm has roduced in all revious eriods. Firms are identical, quantity-setting and roduce a homogeneous outut. Let C(x) denote the total cost of roducing x units of outut. Let P(X) denote the industry's inverse demand function, where X = nx is total industry outut. The rofit er firm, when each roduces outut x, is then given by B(x) = P(nx)x - C(x). Let d B (x) = max y P(y + (n-1)x)y - C(y) be the maximal rofit that firm i, i = 1,...,n, can earn in a single eriod while deviating, given that all other firms are each roducing x. The value of y that maximizes the above exression is the firm's best-resonse or deviation outut, which deends on the outut roduced by the remaining (n-1) firms. What follows summarizes the assumtions needed to roceed. d Assumtion 1. The functions B(x) and B (x) satisfy: (a) B(x) is strictly concave; d d (b) B (x) is nonnegative, continuous, convex, nonincreasing, and satisfies B (0) > 0; n n d n (c) there exists a unique x such that B(x ) = B (x ). 4

7 s Denote the action set of firm i by S i = [0,x (*)], where * 0 (0,1) is the discount factor common to all firms. Let * / 1/(1+r) where r is the firms' fixed one-eriod discount rate. Outut s s x(*) satisfies -B(x (*),0,...,0) > */(1-*)su B(x,0,...,0). The above inequality says that it is never in x s a firm's interest to roduce outut beyond x (*). If a firm did, even with all other firms roducing nothing, then it would not be able to recou the ensuing one-eriod loss even by roducing monooly outut forever after. Attention is thus restricted to bounded strategy sets S. Since B(x) is strictly i m concave, argmax{b(x)*x 0 S i} is a singleton whose unique element is x. Let G = (S,B;i=1,...,n) denote the one-shot Cournot game. Assumtion 1 imlies that G has i L L a unique symmetric ure-strategy Nash equilibrium. Let x 0 S be the outut er firm such that B(x ) = 0. The suergame with discounting is obtained by reeating G infinitely often and evaluating rofits using the discount factor *. The definitions that follow rovide the notation necessary to study the outcome aths from this game. It is imortant to note that the collusive industry does not simly behave like a monoolist here: the industry enforces tacit collusion using a scheme that unishes deviations from collusive behaviour. In the general case where firms are not extremely atient or do not necessarily exect collusive interaction to last forever, the resence of incentive constraints rules out the monooly outcome as a constrained joint rofit maximum. i 5

8 The following Proosition summarizes the model's structure thus far. Proosition 1. Under Assumtion 1: s L n m (a) x > x > x > x ; m n s (b) B(x ) > B(x ) > 0 > B(x ); n d n (c) B(x ) = B (x ) > 0; d d (d) if x > x $ 0, then B (x ) $ B (x ) Proof. See Abreu (1986). The contents of Proosition 1 are illustrated in Figure 1. For instance, Part (c) imlies that d n the best-resonse rofit function B (C) is just tangent to the rofit function B(C) at outut x since static Cournot-Nash rofit-maximization by each firm is itself a best-resonse. Part (d) underscores the key feature of the model with resect to best-resonse rofit functions: the more all other firms attemt to restrict joint outut, the higher is the one-eriod gain from deviating for a single firm. I further characterize the suergame environment as follows. A tacitly collusive agreement 3 is one in which individual firms jointly maximize rofits by restricting industry outut. Each individual firm within the cartel can, however, increase its one-eriod rofits by roducing a higher outut than the share secified by the joint rofit-maximization rogram. A deviator who lays his best-resonse obtains strictly higher one-eriod rofits than any other firm, given that all other firms d abide by their collusive outut shares. This can be shown using Figure 1 and noting that B (C) > B(C) n n away from x. For examle, a best-resonse in a collusive hase (x is to the left of x ) is to roduce 6

9 m n more than x, given that all other firms lay an outut x such that x 0 (x,x ). Given the incentive to cheat at the individual firm level, the industry must choose a unishment outut that makes it otimal for firms to tacitly collude rather than defect if higher rofits than the Cournot-Nash level are to be reaed. Similarly, subgame-erfection requires that firms refer to cooerate in their own unishment in anticiation of future rofits that such behaviour would rovide. To simlify matters, I will assume that the unishment is symmetric in the sense of Abreu 4 (1986). A symmetric carrot-stick strategy rofile (x,x ) is defined as follows: if all firms roduce x or x in the revious eriod, each firm roduces x this eriod; for any other rofile of outut, each firm roduces x this eriod. The key result from Abreu (1986) is summarized in the Proosition that follows. Proosition 2. Under Assumtion 1, a symmetric carrot-stick strategy rofile (x,x ) is a subgame- erfect equilibrium if and only if : B d (x) % *B(x ) # (1% *) B(x). (1) B d (x ) % *B(x ) # B(x )%*B(x). (2) Proof. See Abreu (1986). 7

10 The rofit-maximization rogram available to the industry is characterized by the two firmsecific incentive constraints (1) and (2). The first constraint is a no-defection condition. It requires that an individual firm weakly refer collusion forever to a sequence of deviation, unishment, and collusion forever after. In other words, the firm must weakly refer collusion to deviation in a collusive hase. The second constraint is a unishment-accetance condition. It requires that a deviator weakly refer to articiate to the unishment, and collude forever after to a sequence of best-resonse to the unishment (which is itself a deviation), unishment, and collusion forever after. This constraint says that the firm refers to cooerate in its own unishment rather than deviate. In summary, the two constraints ensure that the discounted rofits from deviation do not exceed the discounted rofits from collusion. 5 The key issue at this oint is whether the unishment can be severe enough so as to generate a loss for each firm in the unishment hase. (Taxes are ignored until the next Section since their resence does not affect the qualitative conclusions to be drawn below.) Abreu (1986) shows that there exist games in which the most severe unishment involves losses during the unishment hase. Proosition 3. Under Assumtion 1, there exists a * and a subgame-erfect equilibrium ath (x,x ) such that B(x ) < 0. Proof. See Abreu (1986). 8

11 Proosition 4. Under Assumtion 1, joint rofits are maximized for the smallest value of x such that (x,x ) is a symmetric carrot-stick strategy rofile and both (1) and (2) hold with equality. Proof. Let the no-defection locus (NDL) be the set of outut airs such that (1) holds with equality, and let the unishment-accetance locus (PAL) be the set of outut airs such that (2) holds with r equality. Let x be the most rofitable collusive outut that can be suorted by a Cournot reversion. m r n Without loss of generality, one can restrict attention to discount factors such that x < x < x. Think of NDL as being drawn as in Figure 2, with unishment outut on the vertical axis. Then: m r Result 1. NDL is downward-sloing when the collusive outut is between x and x, and is n uward-sloing when collusive outut is near x. m r n Proof. Let x 0 [x,x ]. I shall show that there exists an x such that x > x and (x,x ) is on r n n n NDL. Point (x,x ) is on NDL by definition, and so is oint (x,x ). Thus, the following two equations hold: B d (x r ) & B(x r ) ' *[B(x r )& B(x n )]. (3) B d (x n ) & B(x n ) ' *[B(x n )& B(x n )]. (4) 9

12 r n Following the definitions of x and x, subtracting (4) from (3) yields: x & n n [B m d) (x) & B ) x (x)]dx '&* B m ) (x)dx. x r x r (5) r Now, take any x < x. The change in the left-hand side of NDL that takes lace when outut is n reduced from x to x is given by: x & n r [B m d) (x) & B ) x (x)]dx & [B m d) (x) & B ) (x)]dx. x r x (6) The corresonding change in the right-hand side of NDL is given by: x & n r * B m ) x (x) dx & * B m ) (x)dx. x r x (7) d By Assumtion 1, the function [B (x)-b(x)] is convex while B(x) is concave. It follows that the second integral in (6) is ositive and strictly larger than the second integral in (7). In turn, this means n that the left-hand side of NDL rises by more than its right-hand side when outut falls from x to x, n if the unishment outut is held constant at x. To restore the equality in NDL, x must be increased. m r I conclude that NDL must be downward-sloing when x is between x and x. 10

13 m n Result 2. PAL is has a downward-sloing segment between x and x. Furthermore, PAL m reaches its eak at x. n n m n Proof. Point (x,x ) is on PAL by definition. Take any outut x such that x < x < x and d n write PAL as B (x ) - (1-*)B(x ) = *B(x). When x = x, the left-hand side of the exression is strictly smaller than the right-hand side. On the other hand, if x is very large, the left-hand side becomes d very large because of the concavity of B(x) and the non-negativity of B (x ). Thus, by the mean-value theorem, there exists an x such that the exression holds with equality. This shows that there is a m n m downward-sloing segment in PAL between x and x. To show that the segment eaks at x, take m a oint (x,x ) on PAL such that x is close to x. Reducing x will cause the right-hand side of PAL to rise initially, and then fall back to its original level as x falls below the joint rofit-maximizing m outut x. Now, to finish the roof of Proosition 4, note that Results 1 and 2 guarantee that NDL is steeer than PAL (as in Figure 2) at its leftmost intersection. Take any oint (x,x ) that lies on the m r downward-sloing segment of NDL between x and x. If x increases slightly while x is held constant, then (1) must hold with strict inequality because the unishment is more severe. Thus, erfect equilibrium oints must lie to the right of NDL. On the other hand, if (x,x ) is a oint on the m n downward-sloing segment of PAL between x and x, then cutting x slightly while holding x constant will ensure that (2) holds with strict inequality since the reward for adhering to the unishment is increased. Thus, erfect equilibrium oints must lie to the left of PAL. If (x,x ) is a symmetric carrot-stick strategy rofile that does not lie on NDL, then it must lie to the right of NDL by the argument of the revious aragrah. Since that oint cannot lie to the right of PAL, there will be a smaller outut y such that (y,x ) is a symmetric carrot-stick strategy 11

14 rofile. Since collusive outut is smaller, rofits will be higher. If (x,x ) is a symmetric carrot-stick strategy rofile that lies on NDL but not on PAL, then it must lie to the left of PAL by the argument of the revious aragrah. Then, there is a symmetric carrot-stick strategy rofile (y,y ) such that y < x and y > x because of the fact that NDL is downward-sloing. Again, collusive rofits will be higher in this new equilibrium. * * air (x,x ). The contents of Proosition 4 are shown in Figure 2. The most collusive equilibrium is the 12

15 3.0 PATHS AND EQUILIBRIA WITH CASH FLOW TAXATION The first art of this Section resents a characterization of the tax treatment of losses. In order to kee the cororation tax system simle, I ignore the issues of investment and financial olicy. Losses arise in the model due to severe unishments of deviations. I therefore ignore losses caused by tax 6 incentives such as generous investment tax credits and caital cost allowances. Taxation is initially asymmetric since gains are not treated in the same way as losses. Positive rofits are taxed at a constant rate J but strictly negative rofits (losses) do not entitle the firm to an immediate refund of -JB(C). Instead, losses are carried forward at a zero rate of interest. In ractice, tax losses can be claimed against future rofits in ways that deend on the articular tax code. To simlify matters, I assume that the firm making a loss of B in eriod t simly t receives a lum-sum refund of DJB in eriod t + 1. Let factor D be included to account for the t ossibility that the firm face restrictions or enhancements to its ability to utilize the refund in t + 1. For instance, the government may wish to ay interest on loss carryforwards, which can be catured by setting D > 1. Recall that the firms' discount rate is r and that * / 1/(1+r). Now assume that the government ays interest on carryforwards. Then, D is equal to one lus the interest rate aid on such carryforwards. It is straightforward to show the following using (1) and (2). First, allowing carryforwards to earn interest at rate r (so that D = 1 + r) is equivalent to a full immediate refund in resent value. The tax system is symmetric (i.e. neutral) in that case. On the other hand, if carryforwards earn no interest (so that D = 1) then the tax system is characterized by the asymmetry 7 described earlier. I assume in what follows that D is included in the interval [1,1+r]. 13

16 Aart from my treatment of investment, the resent exosition closely follows Auerbach (1986). He finds that asymmetries in the cash flow tax have comlicated imacts on firm behaviour. While there are economic arguments in favour of cash flow taxes, their main advantage for the resent uroses is that they can be fit into Abreu s (1986) framework. 8 I now introduce some definitions and resent a heuristic discussion on how losses are generated. Let L reresent the accumulated loss carried forward from eriod t - 1 to eriod t where t L t $ 0 for all t. For a firm which is not taxable at the margin, current after-tax rofits are B t and the accumulated loss carried forward to the next eriod is given by L = L - B. For a firm that is t+1 t t taxable at the margin, B > L and the corresonding after-tax rofits are equal to (1-J)B + JL. t t t t In articular, if B(C) is the re-tax rofit function satisfying Assumtion 1, then the after-tax rofit function is: B(C) ' (1& J) B(C) if B(C) $ 0, (1& *DJ)B(C) if B(C) <0. (8) d d d Let after-tax best-resonse rofit function simly be B (C) = (1-J)B (C) since B (C) $ 0 for oututs in S. i Two comments are in order. Firstly, it is straightforward to show that the after-tax rofit d functions B (C) and B (C) satisfy Assumtion 1 by using the fact that retention rates in (8) are constant. Secondly, (8) is constructed under the assumtion that losses must be written off in the eriod that immediately follows the loss. Underlying this assumtion is the requirement that collusive rofits following the unishment be sufficient to absorb the tax loss. Thus, the resent value of the refund 14

17 taking lace in the next eriod must be equal to a lum-sum equivalent given in the eriod in which the loss occurs. This equivalence ensures that the one-eriod (static) game remains the same over time and hence that the suergame aroach is an aroriate one. The after-tax incentive constraints that embody two-hase unishments are characterized in the following Proosition, which immediately follows from Proosition 2 and the fact that both B (C) d and B (C) satisfy Assumtion 1. Proosition 5. A symmetric carrot-stick strategy rofile (x,x ) is a subgame-erfect equilibrium for the game with taxes if and only if: B d (x) % * B(x ) # (1% *) B(x). (9) B d (x ) % * B(x ) # B(x )% * B(x). (10) 15

18 4.0 EFFECTS OF CHANGING REFUNDABILITY In this Section, I examine the imact of changes to the extent of refundability on the most collusive equilibrium. Following Proosition 5 and the fact that the equivalent of Proosition 4 holds for the game with taxes as well, the most collusive equilibrium is the air (x,x ) such that (9) and (10) both hold with equality. Recall that arameter D is an increasing index of refundability. The direct aroach, which consists in solving for comarative static imacts of changing D 9 on x and x, is not informative. The difficulty is that the change in D shifts both NDL and PAL in the same direction in outut sace. This makes it imossible to determine what haens to collusive outut. One aroach to resolve this ambiguity is to move the analysis from outut sace to after-tax c rofit sace. Naturally, this requires a slight notational change. Let B^ and B^ denote realized after- tax rofits er firm in collusive and unishment hases, resectively. Define the function b(b^) = d {B (C):B (C) = B^}. The value b(b^) describes after-tax rofits obtained by deviating from a situation where all firms after-tax rofits are B^. 16

19 Alying the equivalent of Proosition 4 to the after-tax case imlies that the most collusive c equilibrium will involve a air of after-tax rofit levels (B^,B^ ) satisfying: b( B c ) % * B # (1% *) B c. (11) b( B,D) % * B # B % * B c. (12) In order to find deviation rofits b(b^), simly determine the level of outut for each firm that generates a level of after-tax rofit of B^, and then calculate the rofit that a firm could earn by unilaterally deviating. There are two ways in which D might affect this calculation. Firstly, the deviation rofit might be negative so that changing D will change after-tax rofits directly. To kee the analysis simle, I assume that fixed costs are zero. In that case, deviation rofits cannot be negative since the firm can always roduce nothing during that eriod. Hence, D cannot have any direct effect on deviation rofits. Secondly, there is a more comlicated ossibility that D might affect deviation rofits indirectly by changing the level of outut that suorts rofits er firm of B^. In that case, changing D will affect the rofit that the firm can obtain from deviating away from that outut. A collusive hase is rofitable by definition so refunds are never made in such a hase. Thus, c changing D has no effect on b(b^ ). In a unishment hase with losses, however, changing D will reduce losses associated with any level of outut. Hence, to suort any given after-tax rofit level in the unishment hase, firms will have to roduce a higher outut, which will reduce rofits that can be obtained by deviating. In short, b(b^,d) is a nonincreasing function of D. The foregoing analysis is illustrated in Figure 3. The equilibrium outut air rior to the change in D is (x 1,x 1 ). 17

20 When D is increased from D to D, after-tax rofits in the unishment hase rise for any level of 1 2 outut. The unishment outut necessary to suort B^ must then increase from x 1 to x 2. Deviation rofits are such that b(b^,d) < b(b^,d). 2 1 The main result of this Section is summarized in what follows. Proosition 6. If the most collusive equilibrium involves losses in the unishment hase, then an increase in refundability will enhance collusion and reduce the most collusive outut. Remark. Increasing D makes it less rofitable for firms to deviate in the unishment hase. This makes it ossible to enforce a more severe unishment. It is that fact that enhances the firms ability to collude. Proof. By Proosition 4, the most collusive equilibrium must satisfy the following equations: b( B c ) % * B ' (1% *) B c. (13) b( B,D) % * B ' B % * B c. (14) The first term on the left-hand side of (14) is the only one that is affected by a change in D. For any given unishment outut, increasing D reduces the loss in a unishment hase. The severity of the initial unishment, which is measured by B^, can only be maintained by increasing the unishment outut. This means that the associated best-resonse rofits b(b^,d) must fall. Then, holding B^ 18

21 constant, collusive rofits must fall in order to maintain the equality in (14). The overall effect just described can be seen by redrawing NDL and PAL in after-tax rofit sace. With after-tax rofit in a unishment hase on the vertical axis, these loci resemble the ones drawn in Figure 4. c I shall show that NDL cuts PAL from above in after-tax rofit sace. Pick a oint (B^,B^ ) on c c c NDL near the most collusive equilibrium (B^ 1,B^ 1 ) satisfying B^ < B^ 1 as well as B^ > 1 B^. The existence of such a oint can be established by icking a symmetric carrot-stick strategy rofile (x,x ) that lies on the downward-sloing segment of NDL in outut sace. By Results 1 and 2 in the Proof of Proosition 4, PAL must lie to the right of this oint in outut sace. Holding unishment outut constant at x, PAL can satisfied by raising collusive outut. In after-tax rofit sace, holding x constant amounts to holding B^ constant. Increasing c c collusive outut amounts to reducing B^. Thus, PAL lies to the left of the above oint (B^,B^) in after-tax rofit sace. The result in Proosition 6 is then shown in Figure 4. c The initial most collusive equilibrium in Figure 4 consists of the air of rofits (B^,B^ ). At that oint, NDL and PAL intersect. Increasing refundability rotates the segment of PAL in the loss region; the rotation takes lace on the horizontal axis and in a southwesterly direction. The new segment is labelled PALN. Since NDL does not move, the new most collusive equilibrium is c determined by the osition of PALN and is thus given by the air (B^,B^ ). This oint is characterized by lower (more negative) unishment rofits and higher collusive rofits. For ease of comarison n with Figure 2, B^ denote after-tax Cournot rofits. Proosition 6 goes against the intuition according to which increasing refundability makes the unishment easier to bear. In conclusion, the olicy serves to enhance collusion in the industry. As

22 ointed out earlier, there exists a literature based uon static models which usually favours increasing 10 the symmetry of tax systems. The model resented above shows that such a conclusion is reversed once imerfect cometition in a dynamic context is taken into account. An imortant feature of the foregoing analysis is that losses do not occur in equilibrium. This results from the fact that (13) and (14) intersect at the most collusive equilibrium, and therefore that both incentive constraints (11) and (12) hold with equality at that oint. In that case, firms do not deviate and hence unishments never have to be used in equilibrium. The imacts of changing refundability are thus deduced from behaviour off the equilibrium ath. For the uroses of welfare analysis, it follows immediately that collusive outut is the only measure of roduction that matters. By reducing that outut, the refundability olicy increases industry rice. If the firms marginal costs are nondecreasing, the olicy has the unambiguous effect 11 of widening the ga between rice and marginal cost. The artial equilibrium welfare imact of the olicy is obvious in this case: its outut reression effect reduces welfare. 20

23 5.0 SUMMARY AND CONCLUSIONS This aer alies a suergame oligooly model of an industry to study cororate cash flow taxes with different tax loss regimes. The after-tax incentive constraints facing the firms embody all the imortant timing features of unishments, reversions to collusion, taxes and refunds. Unlike most of the literature in which loss offsets are analysed in the context of risk-taking, tax losses result from collusive enforcement in the resent model. The analysis of changes in refundability on the most collusive equilibrium with losses finds that enhancing tax loss refundability reduces collusive outut along the equilibrium ath. The olicy roduces such an effect by weakening the incentive to deviate in a unishment hase. Refundability thus hels to sustain tacit collusion and hence hinders cometition in the industry. From a artial equilibrium standoint, the olicy also reduces welfare. This new framework to analyse taxes could be made more realistic by allowing for uncertainty. Subject to some conditions, uncertainty will do away with the counterfactual result that losses are not observed in equilibrium. The welfare conclusions in the uncertainty case aear to be much less clear-cut since the behaviour of outut in actual unishment hases must be taken into account in that case. The aroriate framework for this analysis would be insired by the work of Abreu et al. (1986 and 1990). 21

24 Figure 1 Pre-Tax and Best-Resonse Profit Functions 22

25 Figure 2 Most Collusive Equilibrium in Outut Sace 23

26 Figure 3 Effects of Increasing Refundability I: Oututs and After-Tax Profits 24

27 Figure 4 Effects of Increasing Refundability II: After-Tax Profits 25

28 NOTES 1. See Abreu (1986). 2. In that resect, this aer must be contrasted with the literature on loss offsets which tyically focuses on the imact of refundability on risk and risk-taking. Key aers in that vein include Domar and Musgrave (1944), Mossin (1968), Stiglitz (1969), and Mintz (1981). See also the brief summary in Myles (1995). As will be shown below, refundability matters, even without uncertainty. To anticiate Section 3.0 below, the fact that refundability matters under erfect certainty may also be used to justify a cash flow tax. 3. Recent examles of industries that have been studied using the suergame aroach include retail-gasoline in Canada (Slade [1992]) and salt in the U.K. (Rees [1993]). Furthermore, antitrust action in the form of consiracy charges has been undertaken against sellers of comressed gas to hositals (Canada), Southern road contractors (U.S.), and ready-mix cement (world-wide). In her survey, Slade (1995) reorts emirical results which suggest that outcomes are generally more collusive than the Nash equilibria of their associated one-shot games. 4. As shown by Abreu (1986), asymmetric unishments generally yield more collusive outcomes. Such unishments, however, are not as neatly characterized as symmetric ones Constraints (1) and (2) could also be written with an extra term on each side, * B(x)/(1-*), which reresents an infinite series of collusive rofits. The constraints in the text have been simlified by subtracting that term from each side. 6. See Glenday and Mintz (1991) for a discussion of losses that arise from tax incentives. One cannot strictly talk about economic rofit losses in the resent model unless there is a full loss offset (full refundability). 7. Of course, intermediate situations characterized by D < 1 + r also reflect a tax asymmetry. 8. For a thorough discussion of cash flow taxation, see Boadway et al. (1987 and 1989); for a real-world alication, see Stangeland (1995). 9. Those derivations are available from the author uon request. 10. See Myles (1995) for a brief summary, and Boadway et al. (1989) for secific roosals. 11. This result may still be obtained in the decreasing cost case if marginal cost does not decline too raidly as outut exands. 26

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