The Economics of Animal Farm.

William A. Hamlen, Jr. [*]

This paper uses George Orwell's fictional story Animal Farm to make a comparison between Orwell's predictions and the Chinese experience with communism. An analogy is made between two characters from his novel, Napoleon the Boar, who attains power, and Boxer the horse, who does not. These are analogous to members and nonmembers of the Communist party, respectively. Readily available data by Griffen and Renwei (1988) are then used to compare the economic conditions of approximately 22,000 individuals. The empirical results strongly support many of Orwell's predictions. A theoretical predatory growth model that potentially explains the results is also introduced.

All animals are equal but some animals are more equal than others.

George Orwell (1946)

1. Introduction

Economic theory readily supports the existence of a public sector. Adam Smith recognized the need for centralization of the national defense and the judicial and monetary systems. The contemporary theory of public goods extends the justification of centralization to those areas where the optimal output of some goods and services cannot be attained without coordinated action, usually through the public sector. Communism, on the other hand, represents, at least in theory, the extreme extension of the public sector.

Communist economic philosophies and systems rose to power through revolutions over the past century motivated by the Marxian promises of reduced income inequality and improvement in the general welfare of the population relative to the competing free market paradigm espoused earlier by Adam Smith. However, in recent years most of these communist systems have initiated reforms favoring reductions in economic centralization and encouragement of free markets. A common view of this transition, prominent in the press, is that while communist governments originally implemented extensive socialist policies that initially reduced income inequalities, the average standard of living of the peoples within communist systems has subsequently fallen below those living within countries that permit greater amounts of market freedom. Therefore, in order to improve the well-being of its citizens, those in power within the communist countries have wisely chosen to seek a reduction in the degree of economic centralization.

An alternative perspective on this recent transition is to attribute it more to realization of economic self-interest of those in power (or at least of those supporting them) and less to their benevolence toward the rest of society. In this alternative view, the Communist party in each country represents just another form of a predatory power group that tends to exclude members and seeks to maintain power and to reap the maximum benefits from those excluded from the group. While such groups often voice demands for economic equality, that is, "from each according to his ability, to each according to his need," because of human nature and the gravity of self-interest they eventually and inevitably undertake policies that result in new income inequalities favoring themselves, that is, "from each according to his ability, to each according to his membership."

This description of communism as a self-serving and predatory power group is conveniently portrayed in George Orwell's fictional classic Animal Farm (1946), hence the title of this paper. In the second section, the main economic predictions of Orwell's novel are reviewed and used as a reference for the rest of the paper. In the third section, several regressions, using empirical data from China, are presented that support Orwell's predictions. Unconventionally, the model follows the empirical results, as the latter stand on their own in support of Orwell's predictions. The fourth section presents a simple growth model that embodies the assumptions underlying Orwell's economics of Animal Farm. In the fifth section, the simulations of the growth model produce some of the specific peculiarities obtained in the empirical results and provide a potential explanation, based on self-interest, for the willingness of the communist leaders to reduce the degree of centralization.

With respect to the current literature, the reader will find throughout the paper that it spans a number of different areas of research. On the empirical side, the study makes use of a data set on households in China, originally obtained by Griffen and Renwei (1988) and recently used by Khan et al. (1992), Knight and Shi (1993), and Liu (1998) to estimate the returns on human capital in China. In this paper, the data are used to show that Chinese elite, as indicated by membership in the Communist party, were able to maintain their elite economic status after the transition to a more market-oriented economy. This result agrees with a similar study by Bird, Frick, and Wagner (1998) for the case of the East German transition.

On the theoretical side, this paper draws on the ideas of Becker (1983) by modeling a situation where one dominant political group in power designs economic policies to benefit itself but not without being influenced by the behavior and response of another group. Unlike Becker's model, which is placed in a democratic setting and allows the dominated group to nevertheless have active political influence, here the setting is a constrained dictatorship where the influence of dominated group on the dominant group is purely economic, not political. Specifically, the dominant party uses a Stackelberg-type (leader-follower) approach to optimization. Also, unlike Becker's model, this paper makes use of a growth model. The primary theoretical result obtained from the model is that certain peculiarities of the empirical results are explained by the theoretical growth model. However, also within this growth context, the model produces convergent growth rates of disposable income for Napoleon and Boxer, but Napoleon's l evel of disposable income ultimately exceeds Boxer's. Also, the growth rates are lower for higher tax rates, conclusions that are supported by Baumol's (1986) study of growth rates. The growth model presented in this paper results in economic inequality decreasing in the initial stages of growth but then increasing in the later stages of growth. Kuznets (1955, 1963) predicted the opposite situation for growth in a democratic, free market situation.

2. Analogy to Animal Farm

The two main characters in Orwell's Animal Farm are taken here to be representative of two groups: Napoleon, the boar who lacks productive skills but is able to grasp power and subsequently becomes the net beneficiary of the socialized system, and Boxer, the horse who is endowed with highly productive skills but does not acquire power and gradually depletes his resources as the net loser in the system. Napoleon holds power in a self-serving manner. This is in contrast to the espoused rhetoric of communism and also to that of a purely competitive economy, which, as Negishi (1960) proved, acts as if to maximize the weighted sum of the utilities of all individuals. However, Napoleon does not have absolute authority and must earn the tolerance of his policies by the other members of the society, in this example Boxer. He does this in the Machiavellian tradition by implementing uniform, egalitarian principles in those areas that are more observable while reserving his self-enhancing preferential policies for less observable areas. This is illustrated in Orwell's narrative when Napoleon initially abolishes private ownership and seeks to establish a total socialist state. However, at some point in the growth process following the revolution, Napoleon is found to have reestablished the market system, and in fact Napoleon himself has quietly become a leader of the new entrepreneurial class. Napoleon's motives for reintroducing the market system are clearly those of self-interest and growth of the system that he now controls, not that of basic reform of the political economy.

Before the revolution, Mr. Jones, the original overseer of the farm, is regarded as a useless and wasteful parasite within the community. After the revolution, Napoleon reconsiders this view and determines that it is indeed essential to devote a significant proportion of the farm's total resources toward assisting him in his new and important position as the farm's overseer. There is, of course, some change in status for some animals in the transition from Mr. Jones to Mr. Napoleon. Some who were less essential within the original system are now highly rewarded by Napoleon. Others find their relative position diminished. From Boxer's perspective, the passage of time, as well as the change of overseer, brings few lasting benefits, and in fact he finds himself clearly worse off as his daily allocation decreases and his productive capital stock depreciates without replacement.

In Napoleon's initial leadership of the animal farm, investment in human (animal) capital stock, such as education, is deemed wasteful. Again, somewhere into the growth process, Napoleon is found to have reconsidered this decision and devoted considerable resources to education, along with appropriate remunerations for the attainment of the proper education. However, Napoleon's policies toward education are found to have a disproportional benefit to himself and his own offspring. In contrast, Boxer depletes his productive capital stock. In the end, Napoleon the boar's self-serving leadership seems hardly different from that of the man, Mr. Jones. In fact, to quote Orwell, "The creatures outside looked from pig to man, and from man to pig, and from pig to man again; but already it was impossible to say which was which" (p. 155).

3. Empirical Evidence

A microdata set on Chinese households, made available by Griffen and Renwei (1988), conveniently provides an opportunity to test Orwell's analogy of the transition from a communist economy to a market-oriented economy. An essential feature of the panel data is that individuals describe both their economic condition and whether they are members of the Communist party. Thus, in the current context, Napoleon is taken to be representative of those who are official members of the Communist party and Boxer to be representative of those who are not official members. This data set is well documented, including SAS files, and is readily available through Inter-university Consortium for Political and Social Research (1993-1994). The data have been used by Khan et al. (1992), Knight and Shi (1993), and Liu (1998) to estimate the returns on human capital in China. Here, a subset of the data consisting of approximately 22,000 urban households is examined.

There have been a number of recent studies on China's transition to a less centralized market place that indicate that it represents a reasonable example of the economics of Animal Farm. Pomfret (1997) concludes that China's transition is oriented toward growth rather than reform per se. This reminds us that Napoleon's main goal for reintroducing the free market was to increase productivity for his own needs, not to improve the condition of those outside his inner group. Meng and Kidd (1997) note that wage rates for human capital lag behind comparable levels in more free market economies. Again, as described previously, the economic well-being of Boxer (representing the nonelite majority) gradually diminished under the communist system. Lin, Cai, and Li (1996) describe China's transition as an "evolution" as opposed to a single shift from centralization to decentralization. This is analogous to Napoleon's quiet reintroduction of the market system following the revolution. The use of an evolutionary transitio n as opposed to a "bang-bang" solution will play an important part in the growth model developed and simulated in the fourth and fifth sections. The empirical finding that the elite class in China (Communist party members) continue to out-prosper the nonelite class (nonparty members) is consistent with the findings by Bird, Frick, and Wagner for East Germany's transition. In their study, however, they chose the household's ownership of a telephone as the measure of being elite rather than membership in the Communist party.

Napoleon is taken to be representative of those who are official members of the Communist party and Boxer to be representative of those who are not official members. The disposable income (after direct taxes and subsidies) of each individual has been calculated. Individuals are also identified by their respective provinces. In each province, Zheng (1995) has calculated the approximate proportion of the province's income that is in public control. Based on Orwell's predictions, Napoleon's economic well-being is expected to be considerably above that of Boxer's. In addition, this difference is predicted to be an increasing function of the degree of centralization because, with more of the wealth controlled by the government, there are more opportunities for Napoleon to obtain a disproportional share. Nevertheless, despite the increasing disparity between the two classes as centralization increases, it is also predicted that, ceteris paribus, increases in centralization decrease the absolute level of income to Napoleon as well as Boxer. In addition, as Napoleon becomes the relatively wealthier class, he begins to bear an increasingly greater share of the cost of centralization. Thus, Napoleon begins to see that it is in his own self-interest to reestablish the free market system.

Table 1 contains the results for three regression equations for each individual type, Boxer and Napoleon. These include simultaneous regressions on the factors expected to determine DISPOSABLE INCOME (in yuan) and levels of human capital stock as measured by YEARS OF EDUCATION, along with coefficients and standard errors of the coefficients and a single equation estimation showing the NET TAX function (taxes minus subsidies in yuan) facing each group (Napoleon and Boxer) in the sample.

Consider first the single-stage NET TAX equations. The empirically estimated net tax rate as a direct function of GROSS INCOME is extremely close for Napoleon (0.24) and Boxer (0.22). Because Napoleon is, on average, wealthier than Boxer, the tax rate suggests a slightly progressive tax. However, inclusion of a quadratic income term did not make a significant improvement in the regression. Thus, we might conclude that the national income tax seems quite egalitarian. The CONSTANTs, on the other hand, represent the net tax "levels" and are quite different for Napoleon and Boxer. For both Napoleon and Boxer, these are negative, as expected in most economies. However, Napoleon's (-665 yuan) is significantly lower than Boxer's (-481 yuan), suggesting that there is a lower base tax for Napoleon. In addition, there is the differential province taxes for individuals living in provinces with substantially different degrees of public control. PUBLIC SECTOR represents the degree of centralization within the province an d is measured as the ratio of a province's output controlled by the public sector to the total output (in yuan). For Boxer, NET TAX increases significantly when PUBLIC SECTOR increases with a coefficient of 130.32. The coefficient is substantially lower for Napoleon (9.154) and is not significantly different from zero. In essence, after initial redistributions there is still a net cost of government that must be paid primarily by Boxer. This supports Orwell's prediction that Napoleon's net benefits from the centralized system are much higher than Boxer's.

The equations for Napoleon's DISPOSABLE INCOME and YEARS OF EDUCATION are estimated simultaneously (two-stage least squares), as are the same equations for Boxer. We consider first the results for the DISPOSABLE INCOME regressions. Possibly the most important result is the finding that increases in PUBLIC SECTOR, again representing the cross-sectional degree of centralization, are both negative and significant for Napoleon and Boxer. This presents a primary motive for Napoleon to seek to reduce the degree of centralization. In addition, the negative effect of a greater degree of centralization is worse for Napoleon (coefficient = -690.2) than for Boxer (-173.51). Thus, we might even expect to find less enthusiasm by Boxer for reducing the degree of centralization than by Napoleon.

Another interesting result of the DISPOSABLE INCOME regressions is that Napoleon seems to gain more (coefficient = 956.51) than Boxer (741.69) when it comes to earning disposable income through the PRIVATE ENTERPRISE. Here PRIVATE ENTERPRISE is just a zero-one variable, with the value of one if the individual responds affirmatively to making some income from the private sector. This result agrees with Orwell's depiction of Napoleon as becoming the leader of the new entrepreneurial class.

Also from Table 1 we find that Napoleon obtains approximately three times the increment in DISPOSABLE INCOME of Boxer for every year of education. Unfortunately, we cannot determine whether this is due to the type of schooling available to Napoleon and Boxer or to political capital in obtaining the best positions on graduation. Along with this is the fact that for every year of age, Napoleon increments his disposable income (coefficient = 55.81) at about twice the rate as Boxer (27.23).

The variable SEX is a zero-one variable that takes on the value of one when the individual is a male and zero when a female. It is interesting that being a female has a positive benefit to incrementing DISPOSABLE INCOME for Napoleon, while being male has a positive benefit for Boxer. In most societies, males still tend to receive greater disposable incomes than females, even when controlling for training and experience. It is not as clear why females in the Communist Chinese party receive greater disposable incomes than males. It might be that this can be attributable to the combination of a self-selection process and a sample size problem. Those females who broke with the traditional roles held by women and sought achievement through the avenues open to them as members of the Communist party might be, on average, higher in achievement motivation than the average male member in the Communist party. Possibly, if we considered only the most highly remunerated male members of the Chinese Communist party and too k a sample size that just matched the sample size of all female members of the party, we would find that being female does not statistically result in higher compensation and might very likely result in a lower disposable income.

JOB SECURITY in the regressions is also a zero-one variable, where one is given to any respondent who described his job as having permanent job security. For both Napoleon and Boxer, JOB SECURITY has a negative effect on DISPOSABLE INCOME. This is not unexpected. There is typically a trade-off between income and job security in all economies, for example, tenured finance professors. It is somewhat interesting that JOB SECURITY costs Napoleon (coefficient = -- 1408.81) many more times that of Boxer (--53.35). One possible explanation is that job security is often associated with public sector jobs, and Napoleon is more likely than Boxer to have public sector position, which includes prestige and status. These can be strong substitutes for disposable income. An analogy could be made with an attorney in the U.S. Congress. The opportunity cost of an attorney remaining in Congress is likely to be much higher than that of other public servants.

The effect of greater centralization (more PUBLIC SECTOR) on human capital accumulation (YEARS OF EDUCATION) is different from its effect on DISPOSABLE INCOME. Whereas an increase in PUBLIC SECTOR decreased both Boxer's and Napoleon's disposable income, an increase in the PUBLIC SECTOR is associated with an increase in Napoleon's YEARS OF EDUCATION but with a decrease in Boxer's YEARS OF EDUCATION. As demonstrated in the predatory growth model presented in the following, the negative effect that excessive centralization has on Napoleon's disposable income occurs at a lower degree of centralization than that at which it occurs on his (human) capital stock accumulation. Thus, if Napoleon seeks to reduce the degree of centralization at the marginal tax rate where it first produces negative effects on his disposable income, this will be at a rate that is still positively related to his capital accumulation. Of course, as expected in a predatory growth model, there is a negative effect of increased centralization on both Boxer's disposable income and his capital accumulation.

Increased per capita investment of the province has a positive and significant effect on the YEARS OF EDUCATION for both Napoleon and Boxer. In essence, the accumulation of human capital stock is generally associated with the accumulation of physical capital stock. The incentive to obtain additional years of education increases if there are opportunities to use the education. It is seen that either the incentives or the opportunities are greater for Napoleon (coefficient = 0.00678) than for Boxer (0.0023).

AGE and earning some income in PRIVATE ENTERPRISE are negatively related to YEARS OF EDUCATION for both Napoleon and Boxer. In both cases, the negative effect is stronger for Napoleon than for Boxer, but the difference is significant only in the case of AGE. China is like most emerging markets, where the push for more education has been fairly recent, explaining why older citizens are likely to have obtained less education. Greater education can also be a direct function of the lack of alternative employment opportunities. Thus, in a ceteris paribus context, Boxer would possibly have more available time to continue education. With respect to the negative coefficient of PRIVATE ENTERPRISE, it is usually one of self-selection and would be found to be negative in almost any economy. Those with less education tend to choose or find positions in the private sector, while the public sector often allocates its positions on the basis of the extent of one's education.

Finally, being male increases the YEARS OF EDUCATION for both Napoleon and Boxer. However, it is significantly more positive for Boxer. This result is easy to explain. As pointed out in the discussion of the effect of gender on disposable income, female Napoleons are more likely to be self-selected achievers than female Boxers. In addition, female Napoleons are more likely to have broken with the traditional roles assigned to men and women.

In summary, the empirical results support Orwell's view that while Napoleon might initially gain by more centralization that can be used to shift wealth from Boxer to himself, eventually he finds that the cost of a high degree of centralization outweighs the gain from his perspective. When this occurs, he has an incentive to reduce the degree of centralization. In particular, an observed inverse relationship between Napoleon's disposable income and the degree of centralization at the margin would provide Napoleon with both the signal and the motivation to seek a shift toward more free markets.

4. A Simple Predatory Growth Model

The purpose of the predatory growth model proposed in the following is to capture the essence of the transitions in the Orwellian economy of Animal Farm and simultaneously to offer a reasonable description for some of the empirical results described already. The empirical results demonstrated that Boxer was forced to pay a disproportionately high share of the net cost (after transfers) of government because of a greater degree of centralization. Or, equivalently stated, the share of the net revenues collected (after the cost of government) allocated to Napoleon exceeded the share allocated to Boxer. At the same time, the disposable income of both Boxer and Napoleon were inversely related to the degree of centralization, while only Boxer's capital stock was inversely related to the degree of centralization. Thus, one of the criteria of the model must be that we obtained this observed phenomenon.

The literature on economic models where one political party is assumed to be in power and acts in a self-serving manner is summarized by Becker (1983). These, including Becker's contribution, are static equilibrium models, whereas the current model is a dynamic growth model. In addition, the existing models are generally couched in the context of democratic systems where "losers need not passively accept their fate, but can trim their losses and gains to winners by lobbying, threats, disobedience, migration, and other kinds of political pressure to raise their influence" (Becker 1983, p. 377). The results in such cases are that the political influence by those in power and those out of power will shift efficiently so as to equalize the marginal benefits and costs of altering the existing policies while still maintaining the bias in favor of the group in power. Under nondemocratic systems, the political influence of those out of power, that is, Boxer, is rather limited unless there is a revolution. Most of th e time their influence is solely economic, as they allow the economy to naturally take a degenerative turn caused by the disincentive effects on effort and capital accumulation. Those in power, however, are not unaware of the disincentive effects and recognize that it is in their own best interest to eventually alter the policies. In the model developed here, Napoleon is assumed to be intellegent enough to include Boxer's behavior functions in his own optimal plans. Thus, Boxer's influence function lies in his choice of leisure and consumption in response to Napoleon's chosen tax rate.

The following assumptions are made:

ASSUMPTION 1. There are two representative types of individuals, Napoleon (N) and Boxer (B), fulfilling the roles of the Communist party members and nonmembers, respectively.

ASSUMPTION 2. Boxer begins with a greater endowment of productive capital stock than Napoleon, [H.sub.ON] [less than] [H.sub.OB].

ASSUMPTION 3. Both Napoleon and Boxer choose their own levels of effort, [E.sub.i], i = N, B and consumption, C, i = N, B. However, Napoleon is assumed to take into account Boxer's optimal choice functions in making his own optimal decisions (the Stackelberg solution).

ASSUMPTION 4. The difference between disposable income, [YD.sub.i], i = N, B, and consumption, [c.sub.i], i = N, B, is used to accumulate personal capital stock, [dH.sub.i]/dt, i = N, B, which in this context and for simplicity is assumed to be in the form of a single homogeneous human capital stock.

ASSUMPTION 5. The degree of centralization is represented by a single, proportional and uniform income tax, e. This tax, representing the degree of centralization, is selected by Napoleon, who takes Boxer's choice functions into account.

ASSUMPTION 6. Government is inefficient, and thus of all the revenues collected, only a fraction, 0 [less than] [theta] [less than] 1, is returned in the form of true spending power to Napoleon and Boxer.

ASSUMPTION 7. Napoleon's share of the net subsidies paid out is always greater than Boxer's, or [S.sub.N] [greater than] [S.sub.B].

As in all models, these assumptions somewhat oversimplify the actual conditions. For example, in both Orwell's book and the real events in China, there are many individuals of varying endowments represented here by Boxer and Napoleon. Nevertheless, the goal here is to maintain simplicity while, it is hoped, capturing the most important aspects of Orwell's scenario.

A simple production function relating total output, Y, to inputs of effort, [E.sub.N], [E.sub.B], by Napoleon and Boxer, respectively, and to their respective capital stocks, [H.sub.N], [H.sub.B], is given by

Y = ([H.sub.N] + [H.sub.B] + [E.sub.N] + [E.sub.B]). (1)

It should be noted here that capital stock could represent the traditional classical definition of physical capital stock, for example, plant and equipment, or it could represent the contemporary definitions of human capital stock implying innate intelligence, training, and education. In both cases, there is a common element in that this stock of something allows the owner to obtain an additional earnings (economic rent) per unit of time and effort allocated to the workforce. In Orwell's story, Boxer's capital stock is in his above-average endowment of strength, which allows him to accomplish more work per unit of time than the other animals. Much of that strength is innate. However, the original owner and overseer of the farm, Mr. Jones, at least had the insight to invest a sufficient amount of feed and rest to maintain Boxer's physical capital stock. Napoleon, on the other hand, lacks the incentive to make such a commitment, and Boxer's physical stock is swiftly depreciated until he is sold for scrap value to the local glue factory. Despite the fact that the capital stock could be of the physical or human variety, the reader will note that it is generally used here in the sense of human capital stock. The primary reason for this is that the empirical data on China had very good data on the level of the head of household's education, that is, the proxy for human capital stock. However, the data did not include the level of physical capital stock owned by each head of household.

Because of the assumption of constant returns to scale embodied in Equation 1, remuneration based on marginal productivity would completely exhaust the output. In the communist system, personal wages are based on something less than the marginal productivity, but they still represent a reasonable proxy for wages (Meng and Kidd 1997). In addition, the additive form of Equation 1 implies that there is no interactive effect between labor and capital. Alternatively stated in contemporary terms, there is no "trickle down" effect wherein labor's effort is made more valuable by being able to work with additional capital stock. This sacrifice of the interactive effect is once again made at the gain of mathematical simplicity.

The marginal productivity evaluations are

[partial]Y/[partial][H.sub.i] = 1 and [partial]Y/[partial][E.sub.i] = 1, i = N, B. (2)

Based on Assumption 5, a single uniform tax, e, is chosen by Napoleon at each stage of the growth process. Baumol and Fischer (1979) have shown that with a single uniform tax it is sometimes impossible to achieve predetermined and nontrvial income redistribution objectives. However, Hamlen (1982) showed that the Baumol-Fischer dilemma can be avoided if differential subsidies can be used along with the uniform tax. Thus, it is assumed that Napoleon wisely combines a uniform tax, with its egalitarian appearance, with a set of less observable differential subsidies that favor himself. Of the tax revenues collected, only the fraction [theta] (0 [less than] [theta] [less than] 1) is returned to Napoleon and Boxer, while the rest is assumed lost in the inefficiencies of the public sector. Napoleon distributes the available tax revenues, e[theta]([Y.sub.N] + [Y.sub.B]), through subsidies based on relative shares to Napoleon, [S.sub.N], and Boxer, [S.sub.B]. Following Assumption 7, it is assumed that [S.sub.N] + [S.sub.B] = 1 and [S.sub.N] [greater than] [S.sub.B]. There is no attempt here to model the determination of these specific shares, only that Napoleon always captures a higher share, but political restraints force [S.sub.N] [less than] 1. The empirical results described previously indicate that [S.sub.N] was quite high for China.

The respective disposable incomes for Boxer and Napoleon are

Y[D.sub.i] = ([H.sub.i] + [E.sub.i])[1 - e(1 - [theta][s.sub.i])] + (e[theta][s.sub.i])([H.sub.j] + [E.sub.j]), i = B, N; j = B, N; i [neq] j (3)

Based on Assumption 4, it is assumed that both Napoleon and Boxer use whatever they do not consume, [c.sub.i], i = B, N, to add to their own personal capital stocks. Thus, including depreciation at the rate [delta], the dynamic capital accumulation equations are

d[H.sub.i]/dt = Y[D.sub.i] - [c.sub.i] - [delta][H.sub.i], i = B, N. (4)

The utility functions for Napoleon and Boxer are taken to be the familiar simple negative exponential utility functions with parameters, [a.sub.N], [a.sub.B], [b.sub.N] and [b.sub.B], and personal discount rates, [[rho].sub.N] and [[rho].sub.B]. These are written as

[U.sub.i]([c.sub.i], [E.sub.i]) = {-exp(-[a.sub.i][c.sub.i]) - exp[-[b.sub.i]([[bar{E}].sub.i] - [E.sub.i])]}exp(-[[rho].sub.i]t), i = B, N. (5)

Napoleon and Boxer each solve a fixed-time optimal control problem. The Hamiltonian for this optimal control problem facing both Boxer and Napoleon is

[H.sub.i] = [U.sub.i]([c.sub.i], [E.sub.i]) + [p.sub.i](t)[Y[d.sub.i] - [c.sub.i] - [delta][H.sub.i]], i = B, N (6)

where [p.sub.i](t), i = B, N, is the costate variable.

The necessary conditions for the optimal solution for both Napoleon and Boxer are

[partial][H.sub.i]/[partial][c.sub.i] = [a.sub.i]exp(-[a.sub.i][c.sub.i] - [[rho].sub.i]t) - [p.sub.i](t) = 0, i = B, N (7)

[partial][H.sub.i]/[partial][E.sub.i] = [b.sub.i]exp[-[b.sub.i]([[bar{E}].sub.i] - [E.sub.i]) - [[rho].sub.i]t] - [p.sub.i](t)[1 - e(1 - [theta][s.sub.i])] = 0 i = B, N (8)

d[p.sub.i](t)/dt = -[p.sub.i](t)[1 - e(1 - [theta][s.sub.i]) - [delta]], i = B, N (9)

Integration of Equation 9 yields

[p.sub.i](t) = exp{-t[1 - e(1 - [theta][s.sub.i]) - [delta]]}, i = B, N. (10)

Combining this with equation 7 produces the optimal consumption equations: [c.sub.i] = {t[1 - e(1 - [theta][s.sub.i]) - [[rho].sub.i]] + In([a.sub.i])}/[a.sub.i], i = B, N. (11)

Likewise, combining Equations 8 and 10, the optimal solution for effort is given by

[E.sub.i] = [[bar{E}].sub.i] - {[In([b.sub.i]/[1 - e(1 - [theta][s.sub.i])]) - (1 - e(1 - [theta][s.sub.i]) - [delta] - [[rho].sub.i])t]/[b.sub.i]}, i = B, N. (12)

The optimal solutions for consumption and effort are functionally the same for Napoleon and Boxer even though, based on Assumption 3, Napoleon is assumed to take Boxer's decision functions into consideration but Boxer is assumed to act naively. It is in Napoleon's choice of the optimal tax, e, that is, the optimal degree of centralization, that Assumption 3 makes a difference. The assumption that Napoleon takes Boxer's decision functions into consideration when choosing the optimal tax rate not only agrees with the intelligent character portrait of Napoleon given by Orwell but, in the current model, also prevents Napoleon's solution from being one of the bang-bang variety. It can be shown that if Napoleon naively chose the tax rate without considering its effects on Boxer's optimal decisions, then he would choose a 100% tax in the early stages of the growth problem with a single shift to a zero tax rate in the later stages of growth. However, as is well known in these types of problems, this naive approach by Napoleon can never provide him with a higher utility than one in which he takes Boxer's reactions into consideration. It is also useful to note that while some of the heralded transitional moves of communist systems to free market economies may seem like they are of the bang-bang variety (e.g., Russia's transition), a more in-depth study finds that large portions of these systems had previously been allowed to move toward free markets, and even after the proclaimed shift, large portions of the economy remain centralized. Thus, the bang-bang type of solutions are not the norm for these real-world transitions.

It is easy to see in the current model that optimizing the Hamiltonian with respect to the control variable, e, is equivalent to maximizing Napoleon's disposable income over time with respect to the optimal tax, e. Substituting Boxer's optimal effort function from Equation 12 for [E.sub.B] in the disposable income equation 3, and solving Napoleon's optimal control problem given by Equation 6 yields the following optimal tax condition for each moment of continuous time, t:

([H.sub.N] + [E.sub.N])(1 - [theta][s.sub.N]) + [theta][s.sub.N]([H.sub.B] + [E.sub.B] + e[theta][s.sub.N]([partial][H.sub.B]/[partial]e + [partial][E.sub.B]/[partial]e) = 0. (13)

In Equation 13, [E.sub.B] and [partial][E.sub.B]/[partial]e can be obtained analytically from Equation 18 for Boxer, but [partial][H.sub.B]/[partial]e does not yield a direct analytical solution, and insight to its effect must be obtained through simulations. In the simulations, the solution is simple and requires only determining the tax that minimizes Napoleon's disposable income, given that Boxer's optimal effort function is included in the calculation of the disposable income. The optimal tax, e, changes over time, as in Equation 13 both [H.sub.N] and [H.sub.B] are continuously changing, as is time, t, in Boxer's decision function, [E.sub.B]. The transversality condition for both Napoleon and Boxer in this type of problem is quite simple and given by [P.sub.B](T) = [k.sub.B], where [k.sub.B] is some constant (Takayama 1974, p. 611).

5. Simulations

The two dynamic equations corresponding to Equation 4 can now be calculated and simulated using the optimal solutions for [c.sub.i], [E.sub.i], i = B, N, from Equations 11, 12 and the implicit solution for e in Equation 13. The results of the simulations are quite robust for any reasonable parameter changes within the current context, and thus a stylized relationship can be described with use of a specific example. Napoleon and Boxer are assumed to have the same preferences and discount factors with parameters arbitrarily set at [a.sub.i] = 1, [b.sub.i] = 1, and [[rho].sub.i] = 0.1, i = N, B. From Assumption 2, Napoleon begins with less endowment than Boxer: [H.sub.N](0) = 1, [H.sub.B](0) = 100,000. Both are assumed to have the same limitations on potential use of time with [[bar{E}].sub.N] = 1 and [[bar{E}].sub.B] = 1. The efficiency rate of government is arbitrarily set at [theta] = 0.8, and the fixed shares of the net tax revenue are set at [s.sub.N] = 0.8 and [s.sub.B] = 0.2. The existing capital stock is assumed to decay at a 10% rate of depreciation, [delta], per period. The parameter values are purposely exaggerated in order to allow the simulations to present clear distinct graphs of the desired results and to force the model to converge fairly rapidly.

Figure 1 shows the simulation for the second period of growth in this simple economy. The diagram shows the disposable incomes and capital accumulations for both Napoleon and Boxer for different tax rates in the second period. The optimal tax rate, given by Equation 13 and as stated previously, maximizes Napoleon's disposable income and takes on a boundary solution of a 100% tax representing a totally centralized system. At that rate, both Napoleon's disposable income and capital stock are marginally increasing with the tax rate (in a ceteris paribus sense), while both of Boxer's are decreasing with increases in the tax rate. In this second period, representing the initial stage of economic growth, Napoleon is receiving a large net subsidy from Boxer.

Figure 2 illustrates the situation in the fourth period of growth, which, because of the rapid growth in capital stock within the model, represents a much later period in the growth process. The extreme left portion of region "A" in Figure 2 indicates the tax rate that maximizes Napoleon's disposable income. This would be approximately a 60% tax rate. Assuming that the shift from centralization (the 100% tax rate in period 2) to less centralization (the 60% tax rate in period 4) experiences some rigidities and lags that prevent Napoleon from obtaining instantaneous optimality, the tax rates marked by the segment "A"' would be the set of rates likely to prevail in period 4. Throughout that region, Napoleon's disposable income is inversely related to the tax rate, while his capital stock is directly related to the tax rate. Boxer's disposable income and capital stock continue to be inversely related to the tax rate. What is taking place in this situation is that at any higher tax rate, Napoleon will become a n et subsidizer of Boxer. This is true even though the subsidy "rate" favors Napoleon. One could envision an extreme case, for example, where Boxer obtains a zero level of income and Napoleon's income is equal to the national income. Then, at any positive subsidy rate for Boxer, Napoleon would end up subsidizing Boxer. Furthermore, the subsidization would increase with increases in the tax rate. At later periods in the growth process, the results are similar to those in Figure 2 except that the optimal tax rate continues to decrease. However, under the usual assumptions of equal tastes and preferences, it should never quite go to a zero tax rate. At a zero tax rate, Boxer's capital stock would begin to grow at a faster rate than Napoleon's. This would occur because, under the assumption of equal tastes and preferences, Napoleon, being now wealthier than Boxer, would tend to work less and consume more. As Boxer's share of the total wealth began to catch up to Napoleon's, it would induce Napoleon to reestablish t he tax subsidy system. In fact, it is easy to show that Napoleon will always gain with the tax-subsidy system if ([H.sub.N] + [E.sub.N])/([H.sub.T] + [E.sub.T]) [less than] [theta][s.sub.N], where [H.sub.T] = [H.sub.N] + [H.sub.B] and [E.sub.T] = [E.sub.N] + [E.sub.B], that is, if his share of total income, which is almost equivalent to his share of total wealth, is less than the fraction [theta][s.sub.N].

This simulation result matches the empirical results of the Chinese data analyzed in the third section of this paper, where the disposable income and human capital of Boxer and the disposable income of Napoleon are inversely related to the degree of centralization but Napoleon's human capital stock is positively related to the degree of centralization. Sensitivity analysis has also provided insight into workings of the model. The results of the model are not dependent on the levels of initial capital stock and the distribution of this between Napoleon and Boxer. However, if the economy begins with low levels of capital stock, then Napoleon will begin with an initial but temporarily low tax rate in order to provide the incentive for Boxer to create more initial capital. However, capital stock grows quickly in the model, and soon the contribution of effort in creating capital stock will be dwarfed by the ability of capital stock to re-create itself. At this point, Napoleon has very little interest in stimulati ng Boxer's effort and prefers to tax away Boxer's capital stock, up to the upper limit discussed previously.

One point should be made clear. The inverse relationship between the tax rate and Boxer's disposable income and capital stock does not imply that Napoleon is necessarily depleting Boxer's capital stock. This depends on the rate of depreciation being assumed in the model. With a high rate of depreciation, Boxer's capital stock will decrease over time, and with a low rate of depreciation, it will increase over time. The only noticeable difference is that at a higher rate of capital depreciation, Napoleon's optimal tax is lower at all stages of growth. In both situations, however, whenever the total capital stock is above some low initial level, there will be an inverse relationship between Boxer's capital stock and disposable income and the tax rate, evaluated at Napoleon's optimal predatory tax rate. A related point is that Napoleon does not particularly desire to hurt Boxer. When it is in Napoleon's self-interest to encourage Boxer's capital accumulation, he does so. When it is in his self-interest to deplet e it, he does not hesitate to deplete it. However, ceteris paribus, any increase in the tax rate must harm the total economy, even though it benefits Napoleon. This is because taxes and subsidies must go through the public sector, which is assumed to be nonproductive and a drain on resources. Napoleon, of course, finds that his personal gain is worth the even greater loss to society. If Napoleon could bribe Boxer to give him some of Boxer's wealth without going through the wasteful government bureaucracy, both Boxer and Napoleon would gain relative to the tax subsidy system. However, a system of optimal bribes is not assumed in the model.

There are other features of the model that are interesting but do not particularly address the issue at hand. For example, it can be shown that the growth rates of disposable income for Napoleon and Boxer converge even though Napoleon's level of income will always exceed Boxer's in the long run. Also, the growth rates are lower for greater degrees of centralization, a conclusion supported by others (e.g., Baumol 1986) but not necessarily an inevitable conclusion (see Ehrlich and Lui 1999). Finally, following Kuznets' analysis (1955, 1963), the Gini coefficient can be plotted as a function of income growing over time. Kuznets predicted an inverted-U shape for growth models where representing democratic free markets. In the current case, where Napoleon designs the degree of centralization to maximize his own utility subject only to the passive influence function of Boxer, a normal U-shape results.

6. Summary of Results

The purpose of this paper was to demonstrate that the Chinese experience with communism parallels the predictions outlined by George Orwell's Animal Farm. The empirical data demonstrate that members of the Communist party, analogous to Orwell's Napoleon, prospered significantly above that of the average nonmember, analogous to Orwell's Boxer. At the same time, however, China has entered the stage of growth and capital accumulation in which it is optimal for Napoleon to reduce the degree of centralization. This is easily recognized by communist leaders who see members from provinces with less centralization prospering above those with greater centralization. In addition, the prosperous communist leaders would recognize that they were personally subsidizing the fixed welfare system that is part of communism. This self-serving hypothesis offers a possible explanation on why Communist leaders are willing to move away from a centralized welfare system and toward a free market economy.

The model and simulations in the paper offer one plausible description of the empirical data. The model provides an inverse relationship between the tax rate and Boxer's disposable income and between capital stock and Napoleon's disposable income but a direct relationship between the tax rate and Napoleon's capital stock. It also predicts that Napoleon will eventually find it optimal to reduce the tax rate. In particular, one has to explain why Napoleon's disposable income decreases and his human capital stock increases with increases in the degree of centralization while Boxer's disposable income and human capital stock both decrease with increasing degrees of centralization. The prediction of this model is that this empirical result occurs as long as Napoleon's self-interest-maximizing goal is close to that of maximizing his own disposable income and that there are rigidities in subsidy system and the constant inefficiency of big government.

(*.) State University of New York at Buffalo, 244 Jacobs, SUNY/AB, Buffalo, NY 14260, USA; E-mail [e-mail].

This paper was supported by a fellowship from SUNY/Buffalo. The author acknowledges the very useful suggestions of an anonymous referee.

Received March 1998; accepted July 1999.

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                 Regression Results for Boxer and Napoleon
                                  Boxer                    Napoleon
Net tax                 [R.sup.2] = 0.4, F = 1391 [R.sup.2] = 0.154, F = 57.1
                               N = 17,569                  N = 4738
  Constant                    -480.785 [*]                -665.337 [*]
                                (7.43)                     (18.09)
  Gross income                    .2204 [*]                   .2400 [*]
                                 (.0042)                     (.0081)
  Public sector                130.32 [*]                    9.154
                               (11.0)                      (26.22)
Disposable income       [R.sup.2] = 0.17, F = 593 [R.sup.2] = 0.01, F = 6.81
                               N = 17,569                  N = 4736
  Constant                   -2315.9l3 [*]              -10666 [*]
                              (149.1)                    (2575.5)
  Sex                           71.7 [*]                  -202.6 [**]
                               (18.8)                     (129.2)
  Age                           27.23 [*]                   55.81 [*]
                                 (.64)                      (9.77)
  Private enterprise           741.69 [*]                  956.51 [*]
                               (52.96)                    (440.0)
  Job security                 -53.35                    -1408.81 [*]
                               (56.6)                     (399)
  Public sector               -173.51                     -690.2 [*]
                               (21.87) [*]                (167.7)
  Years of education           283.21                     1049.42 [*]
                               (14.9) [*]                 (398.53)
Years of education      [R.sup.2] = 0.05, F = 187 [R.sup.2] = 0.06, F = 57.1
                               N = 17,569                  N = 4738
  Constant                     (10.47) [*]                 (13.38) [*]
                                 (.07)                       (.21)
  Sex                             .63 [*]                     .482 [*]
                                 (.043)                      (.095)
  Private enterprise            -1.0 [*]                    -1.123 [*]
                                 (.13)                       (.392)
  Age                            -.033 [*]                   -.062 [*]
                                 (.0014)                     (.004)
  Per capita investment           .00234 [*]                  .00678 [*]
                                 (.0013)                     (.0024)
  Public sector                  -.788 [*]                    .439 [*]
                                 (.057)                      (.111)
(*.)Significant at the 99% level.
(**.)Significant at the 90% level.