رشد اقتصادی تعاونی

We comparatively study optimal economic growth in a simple endogenous growth model and under two different games, i.e., dynamic sequential game and cooperative stochastic differential game, between a representative household and a typical self-interested politician. Sequential equilibrium solution is derived by applying Backward Induction Principle and corresponding optimal economic growth rate is endogenously determined. Moreover, cooperative equilibrium solution is established with group rationality, individual rationality and sub-game consistency requirements fulfilled, and it is further confirmed that the representative household will save more, and the self-interested politician will tax less, thereby leading to much faster economic growth, when compared to those of the sequential equilibrium solution.

It is widely argued that institutional difference is one of the major differences between the developing economies and the developed economies. Usually, different institutional arrangements will induce different economic behaviors of the individuals, different fiscal policies of the government, and hence different speeds of economic growth. On the one hand, game structure as a product is endogenously embedded into institutions (see, Amable, 2003, Hurwicz, 1996, North, 1990 and Williamson, 2000). On the other hand, institutions themselves can be regarded as the equilibrium outcomes of some given games (e.g., Aoki, 2001, Greif, 2006, Schotter, 1981, Schotter and Sopher, 2003, Sugden, 1989, Young, 1993 and Young, 1998). That is, different game structures lead to different institutional arrangements, hence producing different speeds of economic growth. The major goal of the current exploration is to comparatively study optimal economic growth under different game structures, i.e., dynamic sequential game and cooperative stochastic differential game. In a simple model of endogenous economic growth (e.g., Aghion, 2004, Barro, 1990, Dai, 2012, Rebelo, 1991 and Turnovsky, 2000), competitive assumption is employed for the firm, endogenous savings rate is determined by the representative household and the goal of the self-interested politician is to choose a tax policy such that the utility from tax revenue, which can be viewed as the rent, is maximized. Leong and Huang (2010) confirm that uncertainty will produce more realistic solution than that of the deterministic case (see, Kaitala and Pohjola, 1990). We also consider a stochastic environment as in Merton (1975), i.e., the source of uncertainty is the population size. Indeed, the present study reveals that different game structures imply different investment choices of the representative household, different fiscal policies of the self-interested politician, and hence different speeds of optimal economic growth. In particular, it is demonstrated that cooperative stochastic differential game corresponds to much more savings of the representative household, much lower tax rate of the self-interested politician, and hence much faster speed of optimal economic growth, when compared to those of the dynamic sequential game. Accordingly, as a byproduct, it is reasonably argued that the widely employed sequential-equilibrium tax scheme may definitely result in dynamic inefficiency from the perspectives of both economic welfare and economic growth in some cases. Noting that, as in North (1971), the game structures or rules of the game can be interpreted as the fundamental institutional arrangements while the fiscal policies can be viewed as secondary institutional arrangements in the present case, we indeed have proved the following North's (1971) proposition, Proposition. The failure to devise and enforce such basic decision rules, i.e., fundamental institutional arrangements, is the source of the poor performance of economies in the past and in the present. That is, for the present model economy, the failure to shift from the rules of the dynamic sequential game to the rules of the cooperative stochastic differential game will result in dynamic inefficiency, and hence poor performance of optimal economic growth. Moreover, noting the uniqueness of the game equilibrium of the games discussed here, i.e., there exists a one-to-one correspondence between the fundamental institutional arrangement and the secondary institutional arrangement, it is reasonably argued that the rules of cooperative stochastic differential game will produce much more efficient secondary institutional arrangements, and hence providing much more appropriate incentives for capital accumulation and economic growth than that of the rules of the dynamic sequential game. Last but not least, the present framework can be easily extended to include more than two different game structures, for example, through introducing different informational constraints on the games.

In the paper, we comparatively study optimal economic growth under two different game situations, i.e., cooperative stochastic differential game and dynamic sequential game. There are two players, a representative household and a typical self-interested politician, who are assumed to share the same discount factor (in Kaitala and Pohjola (1990), the workers and the capitalists are assumed to share the same discount factor, and also in Leong and Huang (2010), the government and the firm are assumed to share the same discount factor. Hence, to make things easier, we are in line with Kaitala and Pohjola (1990) and Leong and Huang (2010) and supposing that the representative household and the self-interested politician will share the same discount factor. Indeed, one can employ heterogeneous discount factors in the model at the cost of making the corresponding computations more complicated) and the same type of preferences (indeed, as the reviewer points out that the preferences between the households and the self-interested politician are significantly different in reality. Nevertheless, one can reasonably interpret the present assumption as follows: in reality, there generally are many households while only one major politician (or government in the present sense); noting that the households generally exhibit different types of preference, i.e., heterogeneous households, and also that there is only one representative household in the present model economy, we conjecture that one can choose an appropriate sample of the heterogeneous households such that the average preference (by using certain version of the law of large numbers) is just equal to the politician's preference. And this also makes the corresponding computations much easier. Needless to say, one can also consider different types of preferences between the representative household and the self-interested politician by using the basic framework developed here, and we leave it to the interested reader). The optimal control problem facing the representative household is maximizing the utility from consumption by choosing an optimal savings rate while the self-interested politician determining a critical value of capital income tax rate such that the utility from taxation revenue is maximized. Sequential equilibrium solution is derived by applying Backward Induction Principle and the corresponding optimal economic growth rate is endogenously determined. In the cooperative game, the cooperative equilibrium solution is established and it is shown that the representative household will save more, the typical politician will tax less, thereby leading to much faster economic growth, when compared to those of the sequential equilibrium solution. Moreover, group rationality, which is the necessary condition of cooperation, is proved to be satisfied, sub-game consistent imputation scheme is well-defined and derived, and corresponding individual-rationality requirement is demonstrated to be fulfilled when the players agree to divide the total cooperative payoff satisfying the Nash bargaining outcome. All in all, we show in a simple endogenous growth model with a competitive firm, a representative household and a self-interested politician that cooperation leads to much faster economic growth than sequential-game structure in some cases and under relatively weak conditions. Finally, we admit that we are concerned with the issue about cooperative economic growth with the representative household and the self-interested politician as two rational economic agents with equal social status, and this limited exploration is only encouraged to provide us with the positive possibility that cooperation is better than sequential action from the viewpoint of economic growth. That is to say, there is a far-away distance between our theory and its application to reality. Indeed, the reality is highly complicated and our theories derived from these abstract mathematical models can just provide us with some inspirations from different and also limited perspectives.