ALBERT

Notes: Summary and implications We have analyzed long-run behavior in rent-seeking under several conditions and behavioral hypotheses. The question of interest is whether or not the long-run expenditures will exactly equal the value of the rents. Our results depend on the type of competitive response which is assumed to exist in the long-run and on the r-value governing the probability of winning. For the case where the r-value is less than or equal to one, Tullock has pointed out that aggregate expenditures will always be less than the value of the game. The long-run solution, however, results in each firm submitting an infinitesimal bid — not a very realistic solution. We showed that when a minium bet requirement is imposed, the number of players is determined in the long-run, and all rents will be dissipated if the minimum bet is integer divisible into the payoff. If not, aggregate expenditures depend upon the size of the minimum bet relative to the total payoff; however, the tendency towards complete dissipation of expected profits still exists. For r-values greater than one we looked at entry under hit and run and hardball competition. Under hit and run competition entry occurs if the potential entrant can make positive expected profit. In the long-run this suggests that incumbents make their bets to pre-empt potential competition. We found a range of possible pre-emptory bets. Using this range we considered the Cournot-Nash and the collusion solutions. For both cases the hit and run entry assumption allows various numbers of incumbents to be a stable equilibrium. For high r-values, however, only one player can exist. Aggregate expenditures under both kinds of solutions dissipate the greater part but not all of the available rents. As the number of players is increased greater dissipation of the rents results. Hardball competition was defined as entry occurring so long as accommodation could be forced by imposing expected losses on the incumbents if accommodation and resulting expected profits for the entrant are not obtained. This would require the potential entrant to be willing to absorb a short-run loss. If this type of entry is carried out, the number of players increases to the point where the minimum pre-emptory bid yields a negative expected profit for the players. The number of players will thus depend upon the r-value. The rents will always be very nearly dissipated in hardball competition whether the incumbents collude or settle at the C-N solution initially. These results assume the payoff is known with certainty and is treated as if the game is continually replayed. Since all players were assumed identical, the long-run results could also be considered the solution where each possible player has timeto consider alternatives and signal ‘precommittal’ behavior. It is perhaps interesting that the results concerning hardball competition are similar in nature to those obtained in the monopoly analysis of Baumol, Panzar and Willig (1982) on potential competition. They find that the presence of potential competition dissipates monopoly profits under certainty and non-increasing average costs. This is very similar to our findings that rents are nearly dissipated with the potential for entry if the entrant would be willing to accept short-run losses. Given the social objective to minimize the expenditure of resources in rent-seeking the following are implied by our results: 1. Dissallowing any type of entry and minimizing the number of players will hold down the aggregate expenditure of resources. Further reductions will be obtained if collusion is encouraged allowing players to place the minimum bet to maximize expected profits. 2. If entry cannot be disallowed then regulate against hardball competition whereby entrants incur short-run expected losses to gain accommodation by incumbents. Here again collusion is preferable, not only because it results in minimum expenditures by each incumbent but also because the C-N solution is unstable at low numbers of players for certain r-values and hit and run entry will result. 3. If hardball entry cannot be prevented then encouraging competition among the incumbents with a likely C-N solution appears to be marginally preferable to allowing collusion. 4. Application of a lump sum cost as a condition for participating in the rent-seeking process, e.g., a license, will reduce the total expenditure in rent-seeking by an equal amount.

Notes: Implications and summary The objective of this paper is to investigate the assertion that a given rent payoff gives rise to an equal value of total expenditure. An analogy with perfect competition suggests a long-run perspective, which would allow the number of players to vary. Accordingly, a game theoretic model of the competitive process where competitors anticipate rival reactions and expend resources to increase their probability of winning is extended to include entry. Long-run quilibrium occurs when the incentive for entry is dissipated, i.e., expected profits equal 0 or the expected rate of return equals the opportunity cost discount rate. When this occurs total expenditure in rent-seeking is found to equal the payoff as in the standard competitive case. How does this result affect Tullock's policy recommendations? His first finding that total expenditures in rent-seeking can be minimized by holding the number of players down remains intact. Essentially, this requirement restricts entry and as a result maintains the short-run conditions indicated by equations (2) and (3) for a given number of firms. His second recommendation, that of increasing the marginal cost of improving a player's probability of winning must, however, be qualified. If the long-run equilibrium is attained total expenditures will equal the payoff regardless of the marginal cost. If the marginal cost is such that the long-run equilibrium is unbounded, there exists a continuous incentive for new entry. It is possible that total expenditures will increase as entry mounts, but this cannot be determined. A policy of increasing the marginal cost will work, however, if carried out in conjunction with a restriction on entry. In this case the short-run results still apply. Finally, an additional policy recommendation can be deduced. From equation (10) total rent-seeking expenditures will be reduced if the opportunity cost discount rate of return is increased. This may be achieved by such actions as increasing the lag between rent-seeking expenditures and the associated payoff, or unfettering alternative productive investments (reduced taxes, deregulation, etc.). Both result in a larger discount of the payoff. The results support the concern with rent-seeking behavior. It indicates that in the long-run each opportunity for rent — a transfer of wealth — displaces an opportunity for the creation of value which will be equal to or greater than the rent payoff. It will be greater, of course, where the investment alternative cannot capture the full social gain.