Output and Price Determination: A Theoretical and Empirical Study

Copyright © IFAC 12th Triennial World Congress. Sydney. Australia. 1993

OUTPUT AND PRICE DETERMINATION: A THEORETICAL AND EMPIRICAL STUDyl A. Fusarl InstituJe ofStw:iiesfor Economic Programming (ISPE). Corso Vil/oria Emanuele . 282.00186 Roma. ltaly

Abstract. This paper develops a model aimed at representing the functioning of the whole economic mechanism with a high degree of detail and avoiding some typically unrealistic assumptions of general equilibrium models. both of the Walras and Arrow-Debreu or von Neuman kind. Some econometric estimation allows a bctter understanding of the reliability and usefulness for applied analysis of the theory proposed . Key Words. Economics; economic systcms,modeling ; parameter cstimation.

1. INTRODUCTION

2. THE MODEL

This study mainly aims to show the feasibility of building a general equilibrium model based on the theory of the firm but following a scheme much more realistic and flexible than the neoclassical theory of general equilibrium. In particular, it develops an explanation of sectoral output which is not strictly based on either consumer demand or production function, together with a theory of price formation which is consistent with the notion of dynamic competition. Entrepreneurial role is at center stage in this work .

Variation of output results from entrepreneurial decision-making that , in turns, is strongly influenced by profitability. The rate of profit is crucially influenced by uncertainty and cannot be explained by a well determined theory and/or ascribed to specific factors; it is considered a mere residue of the difference between revenue and costs. Besides actual profit rate, as defined above, profit must also be defined to relate to a precise theory of entrepreneurship. This will be called desired or partial equilibrium rate of profit, towards which the actual rate of profit gravitates. The analysis of such a gravitation is the core of our explanation of sectoral output and prices.

General economics has limited itself to represent the entrepreneur in a way which eludes the substance of entrepreneurial activity, owing largely to the partial nature of the analyses of entrepreneurship. This has unfortunate implications both in theoretical and empirical fields. In particular, it precludes the formulation of an acceptable theory of economic development and undermines existing theories of prices, market process and production. The model proposed does not imply a specific theory of firm, but its structure is flexible enough to incorporate developments on this subject. It rejects the idea of static competition, in favour of dynamic competition propelled by Schumpeterian creative distruction and entrepreneurial search for profit, which is consistent with entrepreneurial function and market process.

Not unexpectadly, reality often contradicts expectations; this implies that the entrepreneur, to regulate his supply of entrepreneurship, must judge, in the light of some other relevant factors, if the profit rate2 earned is adequate. Such factors may be listed as follows: -The habitual rate of profit for the entrepreneur, that expresses his differential skills and the degree of success he can expect to achieve. -The non-pecuniary benefits attached to the entrepreneurial role. -Expectations on demand, profitability and uncertainty, that influence the rate of profit required to supply entrepreneurship. -A measure of market power related to specific legal,

11 wish to acknowledge Dr. D.Richard and Dr. C .R. Wymer for their useful comments and suggestions .

2 We may refer to any other expression of profitahility we consider relevant , e .g . profit share .

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Exogenous EP = Availability of entrepreneurial skills. T = Non-pecuniary benefits attached to the entrepreneurial role. 11" = Sectoral degree of monopoly, excluding market power due to successful innovation w Column vector of unit money wages. Nominal interest rate. National income. Y Column vector of labour coefficient. I Column vector of the capital stock. K Matrix of intermediate goods coeffiA cients, inclusive of amortization costs. = Matrix of transition of capital from the B sectors of utilization to those of origin. Differential operator. D Symbol of transposition. Symbol of diagonalization.

size and financial barriers to entry (but excluding the barriers due to differential skills, the latter being part of the habitual profit), as entrepreneurs will govern their initiative in the way required to improve the above degree of monopoly. Therefore, the sectoral (or global,in the case of only one sector) supply of entrepreneurship, derived by aggregating over agents the individual supply of entrepreneurship, can be expressed as follows: a) E' = HJu < 0; tJ1t'hr < 0 and E' is the supply of entrepreneurship to the sector. The other variables are defined below. At the sectoral level, another explanating variable of equation (a) is the availability of entrepreneurial skills (BP), which is a proxy for the habitual rate of profit that incorporates differential skills. The demand for entrepreneurial skills depends, in turn, on the level of output and uncertainty. Note that in the absence of uncertainty no entrepreneurial skills would be need and only an efficient bureaucracy would suffice; the higher the uncertainty, the greater the need for entrepreneurs to manage it. Thus,

Equation (2) gives the vector of actual sectoral profit rates as the difference between revenue and costs divided by the current value of capital employed. Note that the coefficients of production and capital (matrices A and B) vary over time, as does the number of sectors, owing to the appearence of new products. This variability is unpredictable, since it results from innovation the effects of which are by definition unexplained particularly at the maximum level of sectoral disaggregation .

b) Ed = 'It(X,u) where Ed indicates the sectoral demand for entrepreneurial skills, X the level of output and u the degree of uncertainty. E' and Ed are equal if output X is produced. Solving the equality between the equations (a) and (b) for r gives:

Equation (3) defines sectoral actual prices as a function of excess demand. A realistic and accurate explanation of actual prices would require additional equations incorporating entrepreneurs' pncmg strategies, potentially unlimited. This is outside the scope of this essay. For its part, equation (4) gives the demand for each commodity as the sum of final consumption, intermediate goods and investment.

(1)

r*

With t?f/t?BP
...

A

A

rKp "'"

= X(p-A 'p-lw)-iKp + KDp

Dp

=

Xd DX/X DK/K EP

Equation (5) expresses the process under which actual profit rate (r) gravitates toward the partial equilibrium one (r*) as output varies . In equation (1) we saw that r* is the profit requested (or desired) for producing X units of output. Therefore, if r* is equal to r, output will not change as entrepreneurs get their desired profit rate. If r is greater than r*, entrepreneurs then earn profits in excess of the desired levels. This encourages a net entry in the sector. The contrary happens if r is lower than r*. The explanation of output given by (5) takes into account in a simple way the whole set of variables influencing production decision making (costs, prices, demand, entrepreneurship and expectations, innovation, uncertainty), these variables being included in the definition of rand r*. This gives a more complete theory of sectoral and aggregate output than those based on demand, aggregate production function or actual profit. Growth follows from entrepreneurial actIvity. The production function links technology, costs and employment.

f 2(X d - X) = f3(p,Y) + AX+BDK o(r - r*) o,(r - rk*) f 4 (X)

(2) (3) (4) (5) (6) (7)

Endogenous r* = Column vector of sectoral partial equilibrium rates of profit. u Degree of uncertainty. r Column vector of actual rates of profit. p Column vector of actual sectoral prices. X Column vector of sectoral output. Column vector of the demand for each Xd commodity.

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If we define demand and supply of entrepreneurship with respect to capital employed (K) instead of output, thus substituting K to X in equations (b) and (1) above, we obtain equation (6). r k '" comes from an equation like (1) but with different parameters, mainly due to a different behavior toward uncertainty.

Equilibrium of steady-state

The second and third equations give equilibrium prices and output; 0' is a constant rate of growth. We put U,7r and T constants and (3J36=(3) so that r'" is constant (but the steady-state only requires the constancy of c, not even of r"'), then even p'" is constant if real i and ware constant. Therefore, prices appear to be irrelevant; this is due to the nonexistence in the model of scarce resources. By substituting q to OX/X and r"'+c to r, into equation (5), we obtain c=q/o linking prices to quantities.

Finally, equations (7) expresses the availability of entrepreneurial skills (EP) as a function of output, under the hypothesis that to the monotonic increase of the latter corresponds an increase in EP due to learning by doing and the entry in the sector of new entrepreneurs. The above model expresses the dynamics of disequilibrium. At the micro level, we need to substitute ri,r"'I,X1,K;, to r,r"',X,K, add X = E1x i and K = Eix i, where i indicates firm, and substitute equation (7) by a more detailed explanation of the birth of firms.

If we add in the model innovations and an expression explaining u as a function of OK, i.e. the mechanism of dynamic competition (both in the sense of Schumpeter and Kirzner) and of development given by the interaction between innovations and uncertainty (innovati ve-adapti ve entrepreneurship), a cycle of u,r"', X and OK arises. The stationary and steady-state equilibria require a constant or zero value of u and no innovations, as we said. In a dynamic economy, the gravitation toward such equilibria appears to be a mere tendency, continuously frustrated not only by fluctuations of r'" but even of r; so, in reality , the disequilibrium model from (1) to (7) works.

2.Provided that innovations are non-existent, i.e. investment is only repetitive, the equilibrium conditions for the model are: r

= r'"

X

= Xd

(3a) (Sa)

Identity (Sa) also implies the convergence of the model toward a steady-state equilibrium, if demands grow at a constant rate of growth (0'). In a steady state with constant growth, the equilibrium condition (3a) will be substituted by the following: r

=

r'"

+

c

The second and third equations give a solution of the model as a Leontief system of output and its dual solved for r=r'" or r=r"'+c. This shows that Leontiers approach (which is not subjected, in this version, to the dual stability paradox) is relevant to the equilibrium position towards which the economic system gravitates. Indeed, with reference to the dynamics of disequilibrium, it is simply a consistency tool required by national accounting.

(3b)

where c is a constant given by 0'/0. The above model outlines a theory that explains the general equilibrium between demand and supply through variations of profit rates (Kirzner's entrepreneurial alertness and dynamic competition) instead of Walras's prices "cries au hasard", and as a result of the dynamics of disequilibrium described by the system 1 to 7 (e.g., if X> Xd , it will become r < r"', therefore X will decrease according to (5) toward X=Xd , and r will rise toward r=r .... This introduces the problem of stability). By substituting identities (3a), (Sa) or (3b) into the disequilibrium model and assuming that in equilibrium investment is proportional to output (r'" = rk "'), we obtain the following equilibrium models:

The proof of stability or, more precisely, of the gravitation of r towards r'" requires an analysis of the shape of r and r'" curves, both expressed as functions of output. For space reasons, we do not discuss this aspect here. However, the proof of stability is of paramount importance, as it tells us that the dynamics of disequilibrium is attracted towards the simpler structure revealed by the stationary model. This structure facilitates the analysis of the more complex model with innovation and uncertainty expressed endogenously.

Stationary equilibrium

r'"

"" r"'Kp'" X EP

= f,(X,u,EP,T,7r) .H .." = X(p"'-A'p"'-lw)-iKp'" = f 3(p ... , Y) + AX = f4(X)

3. ECONOMETRIC ESTIMATION. We present some estimates of the core of the model, i.e. equations (5),(1),(2). The estimated equation is: 653

R2

DlogVAj=a(rj - r/) with r/,'= log-y + ,6\log(NE/eA' )-,6pr-,63(DlogNErlogV A) and rj =(VAlrWri~Pkj)/~Pkj

DlogVA2

= 0.565(r2 (2.03)

-r*~

r2* = -1.119 +0.09810g(N~/e-O·\281)-0.394Dr2(I. 79) (2.28) (2.92) (2.62) 0.148(DlogNE2-logV A2) (4.19)

For estimation, the equation of rj* has been substituted in the equation of DlogV A; , so that r/ (which is not observable) disappears. After estimation, however, rj* can be determined by solving the identity r/=rj - D10gV A;/a. Hence P/ can be found simply by substituting r/ to rj in the equation of actual profit rate: This provides the whole solution of quantities and prices. VA = Value added in real term. r* = Partial equilibrium profit rate. r = Actual profit rate. NE = New entreprises P = Prices W = Nominal wages, including salaries of management KP k = Stock of capital in nominal term = Nominal interest rate = Time trend a = Adjustment parameter expressmg the entrepreneurial alertness ,6 = Structural parameter A = Growth rate of new firms -y = Intercept D = Symbol of derivative log = Natural logarithm j refers to sectors, withj = 1 indicating manufacturing industry and j = 2 indicating commerce.

R2 = 0.85 The parameter ,6\ attached to the tension between demand and supply of entrepreneurship denotes the availability of entrepreneurial skills, then the dimension of the differentials of profit rates, while,62 and ,63 translate the state of expectations and aggressiveness. Through the above parameters and a, our equation of output gives some important information on the performance of each sector and the way to improve it by promoting the formation of entrepreneurs, as well as on the impact on economic system of fluctuations in the actual profit rate. The estimated parameters express a higher entrepreneurial alertness and availability of entrepreneurial skills in manufacturing industry than in commerce, therefore a much higher capacity of the first sector to react to shocks and economic and social changes.

4. CONCLUSION .

The term NE/e A' stands for the excess demand for entrepreneurship; more accurately, it indicates the tension between the availability of entrepreneurship an (eA1 ) and the entrepreneurship employed; increase in this tension causes an increase in the differential of the profit rates among firms, thus in the sectoral partial equilibrium profit rate (r*). Dr refers to expectations, which influence the profit rate required to stay in business, then r*. DNEIV A is aimed at capturing other influences on r* due to entrepreneurs' supply; it assumes that the ratio between the variation rate in the birth of new firms and sectoral output expresses variations in the supply of entrepreneurship.

This exposition has omitted, for space reason, some deepenings on entrepreneurship leading, among other things, to an explanation of the cycle, to which we have dedicated only a skatch. Econometric estimation shows that the model may offer some useful insight even in applied analysis. We project to extend it in the near future and to perform some simulation experiment.

5. REFERENCES Kirzner, M.1. (1973). Competition and entrepreneurship. The University of Ch:ago Press, Chicago and London. Leontief, W. (1986).lnput-output economics Oxford University Press, New York. Schumpeter. J. A. (J 961). The theory of economic development, Harvard University Press. Walras, L. (1952).Element d'economie politique, Pinchon & Durand Auzias, Paris. Wymer, R. C. Resimul manual and program for simultaneous estimation.

The continuous time estimates of the equation of DlogVAj are: DlogVA\

= 0.95

= I. 322(r\ - r\*)

(4.12) r\* = -3.392+0.077log(NI;/e-O·\381)-0 .366Dr\(3.27) (3.66) (3.42) (5.47) 0. 167(DlogNE\-logV A\) (6.34)

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