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Incentive model designed for macro-economy management system in China.


A considerable number of developing countries simultaneously are experiencing conditions of resources shortages, low efficiency and the irreversible dimension of consumption. They have to choose between the two mechanisms of planned and market economies.

In China, the particular character of the traditional planned economy is to stress the extremely centralized leadership of the economy by the government. There the regulatory functions of the market have been abolished. Government transmits to the firms its authoritative planning targets, and determines centrally the prices of all goods. It controls all production and distribution of state-owned firms large or small. Under this economic system, the main goal of the firms is not to maximize profits, but to meet the production targets. Enterprise is not a self-propelling entity but rather a "bead of the abacus" of the government administration; it lacks a necessary sense of independence and a strong economic motivation. They have neither initiative nor authority to produce according to the needs of the market, which results unavoidably in the disconnection between the production supply and the consumer demand. Furthermore, there is also a lure for the firms to produce inefficiently, requesting more inputs than are really needed and producing less output than is actually possible, thus avoiding the production targets being raised in future periods. Likewise, the firms have little initiative to try new products or to make innovations in the production process.

To eliminate the adverse effects of over-centralized economic planning, and increase factor productivity and management efficiency of the firms, market-oriented economic reform has been carried out in China since 1978. Until now, especially after the framework of the socialist market economy was proposed in 1992 (the rigid economic system in which production targets, investment, projects and materials used to be under the direct control of the state), the operative mechanism of government control of the firms has gradually changed and direct intervention by government at various levels in the operation of firms has been reduced. As a result, product targets ordered by the government have decreased drastically (before 1979 more than 95 per cent of the country's total industrial production was turned out at the order of the state - now the figure has dropped to only 7 per cent), proportions of production materials allocated by the government and commodities purchased according to the state plan have also decreased. The state gives play to the regulatory role of the market and tries its best to use economic and legal leverages to exercise macro-control so as to balance total social supply and total social demand and to optimize the economic structure. The idea of setting up a new-style, market-oriented and highly efficient macro-economy management system (MEMS) is the key to realizing the combination of a planned and market economy. In this case, however, important and difficult problems still remain. The major one is how the government could or should regulate the activities of autonomous firms by means of the economic leverages in accordance with the role of a combination between planned and market regulation, i.e. how to set up the market-oriented, indirect, control-based MEMS such that the self-interest of firms guides their behaviour in directions consistent with the whole society's interests.

According to the socialist market economy, the incentive model of MEMS is studied based on the hierarchical decision-making system of government-market-firm. The relevant strategy is also analysed. The article is composed of two parts. The first part includes: a system analysis of the general framework of socialist market economy and the corresponding macro-management system; and incentive strategy, as an effective means in MEMS. Part two includes: by means of the hierarchical decision-making theory, and the stochastic optimization theory, two concrete static models with a perfect information structure and partial information structure respectively, where the government induces Pareto-optimality by adopting a strategy which is a function of the fiscal policy parameter; the existence of the optimum affined strategy in the above models is tested.

Socialist market economy and macro-economy management

After 15 years' practice, China has set up its economic reform target for building a socialist market economy. The target is undoubtedly the continuation and development of the past 15 years of reform which has taken a market-oriented direction, and has pushed its reform into a higher stage. To build a socialist market economy means the establishment of such an economic system in which public ownership integrates with market economy internally, and where market mechanism plays a fundamental role in the development of resources under the positive and effective macro adjustment by the state. Efficiency and equitableness are fulfilled at a high level. This system is characterized by the following:

* The property right of enterprises is clearly defined, and enterprises have autonomy in their operations, are responsible for gains and losses; competition among them is conducted on a fair basis. Various kinds of registered enterprises should have the right to possession, use and disposition of their assets.

* The market is one with sound market regulations, complete organizations and standardized behaviours. Price control of the vast majority of commodities and production factors should be lifted so as to form a mechanism in which price is determined mainly by the market; a complete commodity market system and production factor market system should be formed.

* The macro-economy is managed and adjusted indirectly mainly through the means of economic policies in an attempt to promote the general economic balance and the optimum organization of the economic structure. Economic management and adjustment institutions with reasonable structure, clear duties and high efficiency should be established in order to meet the needs of the market economy.

Two basic demands have been put forward on setting up a new macro-economy management system:

(1) Until now, China's macro-economy management system in effect is unable to adapt itself entirely to the demands for augmenting its strength in competition. Competitive mechanism is the core of market economy. The comprehensive strength of competition of China's market economy lies not only in the sum total of the strength of competition of microcosmic units (enterprises, inhabitants, the government), but more at the macroscopic administrative level. The so-called ability to meet a contingency means the ability to adapt itself to external environmental changes and to the unity of the changeability of the adjustment of its internal structure. The key to improving macro-management lies in the correct manipulation of the relations between the government, the enterprises and the inhabitants as well as the respective relations within themselves, and the co-ordination of the interests and activities of the main body of the economic interests.

(2) The macro-management required by market economy should be systematic and effective. The question of system arises when with different targets and measures the main body of regulation and control consists of many parts; the essence, however, lies in linking up the parts through mutual efforts to form a whole. It is the economic legislative system of macro-management, or system of regulation and control formed by the financial, banking and planning regulation, as well as a system of two-level regulation and control, which divides work between the central and the local governments - all of them stressing, cooperation and co-ordination. All complicated systems take shape progressively. Macro-management which has only a system and no actual effect will sabotage market economy. The effectiveness of macro-management originates from the knowledge and utilization of the law of development of market economy.

Incentive strategy

Over the past years, various schemes for macro-economy management system reform have been put forward in China. Here, we only consider the basic one under the framework of the socialist market economy-government-market-firm. In this system, the previous centralized decision-making system is replaced by a new decentralized decision-making system, in which the firm is granted discretionary power and is allowed to determine prices of its own products at a profit maximizing level. The management of the government to the enterprise is through regulation and control of the market, based on a series of policies such as investment, consumption, finance policies, and so on.

Suppose the whole market is completely divided into m (m [much greater than] 1) different production markets in light of the kind of product, and there are [n.sub.i] ([n.sub.i] [much greater than] 1) markets [ILLUSTRATION FOR FIGURE 1 OMITTED].

Let [x.sub.i], [y.sub.ij], be the government's decision variable and the firm j's (j = 1, ..., [n.sub.i]) decision variable in ith market respectively. Here, [x.sub.i] is defined as [k.sub.i0] ([k.sub.i0] [much greater than] 1) dimensions vector of policies' parameters, [y.sub.ij] is defined as a [k.sub.i] ([k.sub.i] [much greater than] 1) dimensions vector (i = 1, ..., m, j = 1, ... [n.sub.i]).

On the basis of the hierarchical decision-making theory, MEMS can generally be described with the following bi-level hierarchical optimization decision-making model.

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

and [y.sub.ij] satisfy Max [f.sub.ij]([x.sub.i], [y.sub.ij])

[Mathematical Expression Omitted] (1)

where [Mathematical Expression Omitted].

[f.sub.i0], [Mathematical Expression Omitted] are government's decision objection function (such as social welfare function) and decision space, respectively in the ith market;

[f.sub.ij], [Mathematical Expression Omitted] are firm j's decision objection function (such as profit function) and decision space, respectively, in the ith market. For

i = 1, ..., m j = 1, ..., [n.sub.i]


[Mathematical Expression Omitted]

[Z.sub.i] (i = 1, ..., m) is called the feasible solution set of the bi-level hierarchical decision model (equation (1))

Under such a decision-making system, the government is concerned with the interests of the whole society. On the other hand, however, as one relative independent economic entity, the firm has a tendency to concentrate on its own partial interests, regardless of the interests of the whole society. Thus a conflict of interests between the firm and the government is likely to occur. At this time, if the government adopted the former administrative methods to interfere with the firm's operation directly, there would be a reverse of the reform which would go against the goal of the MEMS reform controlling the firm indirectly by incentive method with the aid of economic leverages, i.e. the government should design an efficient strategy [x.sub.i] = t ([y.sub.i1], ..., [y.sub.[in.sub.i]]) in MEMS, to guide the firm to make its decision (which is most beneficial to the government and gives consideration to the firm's own interests):

[x.sub.i] = t ([y.sub.i1], ..., [y.sub.[in.sub.i]]) satisfy

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

where, ([Mathematical Expression Omitted], [Mathematical Expression Omitted], ..., [Mathematical Expression Omitted]) is the optimum solution of the government's objection model (equation (2)):

Max [f.sub.i0] ([x.sub.i], [y.sub.i1], ..., [y.sub.[in.sub.i])

s.t. ([x.sub.i], [y.sub.i1], ..., [y.sub.[in.sub.i]]) [element of] [[Omega].sub.i0].(2)

this strategy is called the incentive strategy.

For simplicity, the subsymbol "i" will be omitted, and the other definitions will be unchanged.

The model designed

Under the framework above, one concrete market is considered in our following discussion. This is characterized by the following:

* The market considered here is limited to a single product market, in which the supply is at least equal to the demand and there is neither supplement effect nor substitute effect between its product or with others.

* Firms in the market are not oligopolyistic firms. Among all firms, there is a non-co-operation Nash-equilibrium relationship.

* The government adjusts the firm's decision behaviour only by taking a series of consumer tax (subsidy) policies.

* The consumer demand function in the market is,

P = l (Q, I)

where l(.) is a continuous function

Q = [Sigma][q.sub.i]

I = [I.sub.0] + [i.sub.0]

P is market price

[q.sub.i] is output of firm i (i = 1, ..., n)

Q is total output of firm

I is real income of consumer

[I.sub.0] is normal income of consumer

[i.sub.0] is consumer's income affected by the government's taxes (subsidies).

Since [i.sub.0] can be considered as the index of the government's regulation and controlling strategy, we can rewrite the consumer demand function as follows to simplify our discussion:

P = l (Q, [i.sub.0]).

Let [Mathematical Expression Omitted]

where [Mathematical Expression Omitted] is the lowest limit of consumer taxes and

[Mathematical Expression Omitted] is the highest limit of consumer taxes.

In addition, there are two assumptions about the decision behaviours of the government and the firm, respectively:

(1) The objective of the firm is to maximize its own profits, and firm i's (i = 1, ..., n) behaviour model is

Max [f.sub.i]([i.sub.0], [q.sub.i]) = P[q.sub.i] - [h.sub.i]([q.sub.i])

[Mathematical Expression Omitted]

where [Mathematical Expression Omitted]

[Mathematical Expression Omitted]

[Mathematical Expression Omitted] is maximum output of firm i under its own current production level

[h.sub.i] ([q.sub.i]) is cost function of firm i

[f.sub.i](.) is profit function of firm i, which is strictly concave.

(2) The objective function of the government is the difference between the convex combination of all firms' profit functions and the cost of the government's policing, which is a convex function. Its behaviour model is

[Mathematical Expression Omitted]

[Mathematical Expression Omitted] (3)

where [Mathematical Expression Omitted]

[[Alpha].sub.i] [greater than or equal to] 0, [Sigma][[Alpha].sub.i] = 1

c(.) is a cost function of government.

Deterministic incentive model

According to Salman and Cruz (1981), the information structure of the firm's decision behaviour is completely available to the government, i.e. the government grasps the characters of the firm's decision-making behaviour completely, and the reaction of the firm to the control strategy of the government is deterministic, i.e. when the government adopts the strategy x = t ([y.sub.1], ..., [y.sub.n]) in management, firm i's decision must be y, where y satisfies P{[y.sub.i] [element of] [[Gamma].sub.i] [where] x = t ([y.sub.1], ..., [y.sub.n]), [y.sub.i] [element of] [[Omega].sub.i], i = 1, ..., n} [equivalent to] 1, (i = 1, ..., n). MEMS can be designed easily as the following model on the basis of model (1) and the above analysis.

In this case, an incentive model of MEMS can be designed as follows:

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

and [q.sub.i] satisfy [Mathematical Expression Omitted]

[Mathematical Expression Omitted] (4)

where [[Alpha].sub.i] [much greater than] 0, [Sigma][[Alpha].sub.i] = 1 and t([q.sub.1], ..., [q.sub.n]) is an incentive strategy which is adopted by the government.

We call this model a deterministic incentive model of MEMS (DIMEM).

Stochastic incentive model

In practice, however, the market is a complicated system where firms adjust their behaviours constantly to meet the changeable market demands. However, it is impossible for the government to grasp the firm's decision-making information completely, especially its decision-making parameters. On the other hand, the reaction of the firm to the government strategy is often uncertain. Therefore the function of DIMEM is rather limited. To counter the defects which exist in DIMEM, we will analyse the model of MEMS further.

Obviously, the reaction of the government indicates the complex characteristics of the firm's decision behaviour. In order to make MEMS more feasible and effective, the government must pay more attention to such uncertainty of the firm when it makes its own decision. To simplify, we consider firm's decision variable subject to a known probability distribution.

Suppose that all firms' decision variable outputs are stochastic variables, and the combined probability distribution function of all firms' output G(q) can be determined by means of the market investigation and statistical analysis.

In light of the stochastic optimization theory, the incentive model of MEMS with partial information structure can be set up. It has the following form:

[Mathematical Expression Omitted]

s.t. t (q) [element of] [A.sup.t]

P{t (q) [element of] [Omega] [where] q [approximately] [G.sub.q] (q)} [less than or equal to] a (5)

where q = ([q.sub.1], ..., [q.sub.n])

[i.sub.0] = t(q) is the incentive strategy adopted by the government

[Omega] = {([q.sub.1], ..., [q.sub.n]) [where] [q.sub.i] [element of][[Omega].sub.i], (i = 1, ..., n)}

[[Alpha].sub.i] [greater than or equal to] 0, [[less than or equal to] a [less than or equal to] 1, [Sigma] [[Alpha].sub.i] = 1

g(q) is the combined probability density function of the stochastic vector q

[A.sup.t] is the optimum selection set of DIMEM.

At this time, the macro-economy management problem is described on the basis of: the combined probability distribution of the firm's decision behaviour; the government's choice of a strategy to realize the maximum interests of the whole society taking account of the partial interests of the firm. Here, we call model (5) a stochastic incentive model of EM (SIMEM).

Strategy analysis

From the above discussion, we notice that it is crucial to map out a rational, effective incentive strategy in MEMS. For this reason, the relevant strategies of DIMEM and SIMEM are analysed.

There are various concrete forms of the incentive strategy [i.sub.0] = t (q); however, we only focus our attention on the affine one, i.e. t(x) = [i.sub.0] - C (x - q) (C is constant, x [element of] [R.sup.n]).

Before our discussion, we introduce one lemma.

Lemma: for the incentive problem

min [J.sub.0] (u, v)

and v satisfy min [J.sub.1] (u, v)


[J.sub.0], u, U are objective functions, decision variables, and decision space of leader respectively;

[J.sub.1], v, V are objective functions, decision variables and decision space of follower respectively.

If [J.sub.1] is strictly convex on U x V and the leader is in a position to announce and enforce an incentive strategy u = t (v), which is a Borel-measurable mapping of V into U, and set [Pi] = {(u, v) [element of] U x V [parallel] [J.sub.1] (u, v) [much less than] [J.sub.1]J ([u.sup.*], [V.sup.*])} is strictly convex, [J.sub.1] (u, v) is Frechet-differentiable with [Mathematical Expression Omitted], there exists an optimum incentive strategy for the leader, in the form

u = t(v) = [u.sup.*] - Q (v - [v.sup.*])

where Q: V [right arrow] U is the linear operator such that

[Mathematical Expression Omitted] (Zheng and Basar, 1981).

Deterministic affine incentive strategy

First, we discuss the strategy with perfect information, i.e. strategy of DIMEM.

Let [Mathematical Expression Omitted]

where [Mathematical Expression Omitted] is the optimum solution of the government's objective model (3). (If [Mathematical Expression Omitted] is not unique, we can choose any one of them; if [Mathematical Expression Omitted] does not exist, we can choose [Mathematical Expression Omitted], where [Mathematical Expression Omitted] is a strategy which is most beneficial to the government.)

[Mathematical Expression Omitted]

let [Mathematical Expression Omitted].

Since [Mathematical Expression Omitted] is strictly concave, i.e.

[Mathematical Expression Omitted]

then [Mathematical Expression Omitted].

Hence, [Beta] ([i.sub.0], q) is also strictly concave; then [Gamma] ([i.sub.0], q) = - [Beta] ([i.sub.0], q) is strictly convex.

Since [Mathematical Expression Omitted]

then [Mathematical Expression Omitted]

we deduce ([Mathematical Expression Omitted], [Mathematical Expression Omitted]), so set [Pi] is strictly convex.

On the other hand, since [f.sub.k] ([i.sub.0], [q.sub.k]) = P[q.sub.k] - [h.sub.k] ([q.sub.k]) is differentiable, (k = 1, ..., n). Obviously [Beta] ([i.sub.0], q) is differentiable. So [Gamma] ([i.sub.0], q) is also differentiable.

For [Mathematical Expression Omitted] there are two cases:

(1) [Mathematical Expression Omitted], hence [Mathematical Expression Omitted].

(2) [Mathematical Expression Omitted].

In case (1), since [Gamma] ([i.sub.0], q) is differentiable and [Mathematical Expression Omitted], so for the problem

min (-[f.sub.0] ([i.sub.0], [q.sub.i], ..., [q.sub.n])) and

[y.sub.i] satisfy

min (-[f.sub.i] ([i.sub.0], [q.sub.i])) (i = 1, ..., n),

there exists optimum affine incentive strategy in the form: [Mathematical Expression Omitted] (where W: [Omega] [right arrow] [[Omega].sub.0] is the linear operator such that [Mathematical Expression Omitted] by lemma.

In case (2), obviously, ([Mathematical Expression Omitted], [Mathematical Expression Omitted]) is the optimum solution of DIMEM, which means no incentive strategy needed in MEMS, or in other words the optimum strategy can be designed as t(q) = [i.sub.0].

Therefore, we have the following conclusion for DIMEM:

P1: for DIMEM (4), there exists optimum affine incentive strategy, in the form:

[Mathematical Expression Omitted]

where (1) [Mathematical Expression Omitted], [Mathematical Expression Omitted] is the linear operator such that [Mathematical Expression Omitted]

(2) if [Mathematical Expression Omitted], W = 0.

For P1 the optimum coefficient W in [Mathematical Expression Omitted] can be solved by a combination of models (3) and (4) (if [Mathematical Expression Omitted], W = 0), and then the corresponding optimum strategy can be further determined. We called such strategy the deterministic optimum affine incentive strategy.

Stochastic affine incentive strategy

Now we will discuss the strategy under the imperfect information structure, i.e. strategy of SIMEM.

By the above analysis and the definition of [A.sup.t], we have

[Mathematical Expression Omitted]

where W = ([W.sub.1], ..., [w.sub.n]) [element of] [R.sup.n].

Let [Mathematical Expression Omitted].

Since the linear function t(.) is a Borel function and q is a stochastic vector, then the incentive strategy [i.sub.0] = t(q) is a stochastic variable.

Let [F.sub.i0] ([i.sub.0]) is the probability distribution function of [i.sub.0]

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]. (5a)

From [Mathematical Expression Omitted] we reduce [Mathematical Expression Omitted]

Then [Mathematical Expression Omitted].

Therefore, the restrain conditions of model (5) is equal to the following form.

[Mathematical Expression Omitted].

Let [Mathematical Expression Omitted].

Hence, model (5) can be transformed into the following ordinary optimization model,

[Mathematical Expression Omitted]

[Mathematical Expression Omitted] (6)

where [K.sub.i0] ([i.sub.0], W) is determined by model (5a), furthermore, we get the following conclusion:

P2: For SIMEM (4), there exists an optimum affine strategy in SIMEM, which can be solved by the ordinary optimization model (3) and (4).

In this case, optimum coefficient W in [Mathematical Expression Omitted] can be solved by the combination of model (3) and model (6) (if [Mathematical Expression Omitted]). Then the optimum strategy can be determined further. We called such strategy the stochastic optimum stochastic affine incentive strategy which satisfy:

* deterministic optimum: [i.sub.0] = t(q) [element of] [A.sup.t];

* statistical optimum: the expectation of the government's objective is maximum;

* reliability: the probability of the strategy's efficiency is greater than a constant a (a [greater than] 0).


On the basis of incentive idea, two kinds of incentive model of macro-economy management (DMEM and SIMEM) have been set up. Not only the existence of one kind of incentive strategy is testified, but ways to implement the strategy have also been provided. All the studies are expected to be helpful to aid the mechanism of China's economic reforms.

References and further reading

Deaton, A. and Muellbauer, J. (1987), Economics and Consumer Behaviour, Cambridge University Press, MA.

Lei, M. (1992), "An analysis of macroeconomic control models", Systems Engineering, Vol. 10 No. 2, pp. 1-7.

Lei, M. (1994), "Behaviour systems analysis and the contract responsibility enterprises and incentive model design", Systems Engineering - Theory and Practice, Vol. XIV No. 6.

Lei, M., "Model designed for the State's guiding enterprises technological progress", Systems Engineering - Theory and Practice (forthcoming).

Lei, M. and Feng, S. (1992), "Analysis of incentive strategy in economy control systems", Systems Engineering - Theory and Practice, Vol. XII No. 4, pp. 8-15.

Salman, M.A. and Cruz, J.B. (1981), "An incentive model of duoplay with government ordination", Automatic, Vol. 17 No. 6, pp. 821-9.

Zheng, Y.P. and Basar, T. (1981), "Existence and derivation of optimal affine incentive schemes for Stacklbery games with partial information: a geometric approach", International Journal of Control, Vol. 35 No. 6, pp. 897-1101.
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Author:Ming, Lei
Publication:International Journal of Social Economics
Date:Oct 1, 1996
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