A dynamic theory of economics: What are the market forces?

Dannenberg, Alia Asha; Estola, Matti; Dannenberg, Anna Working Paper A dynamic theory of economics: What are the market forces? Economics Discussion Papers, No. 2017-110 Provided in Cooperation with: Kiel Institute for the World Economy – Leibniz Center for Research on Global Economic Challenges Suggested Citation: Dannenberg, Alia Asha; Estola, Matti; Dannenberg, Anna (2017) : A dynamic theory of economics: What are the market forces?, Economics Discussion Papers, No. 2017-110, Kiel Institute for the World Economy (IfW), Kiel This Version is available at: https://hdl.handle.net/10419/172321 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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Licensed under the Creative Commons License - Attribution 4.0 International (CC BY 4.0) Discussion Paper No. 2017-110 | December 11, 2017 | http://www.economics-ejournal.org/economics/discussionpapers/2017-110 A dynamic theory of economics: What are the market forces? Alia Asha Dannenberg, Matti Estola, and Anna Dannenberg Abstract The main weakness in the neoclassical theory of economics is its static nature. By a static model one cannot explain the observed time paths of economic quantities, like the flows of production of firms, the flows of consumption of consumers, and the prices of goods. The error in the neoclassical framework is that economic units are assumed to be in their optimum state and thus not willing to change their behaviour. Therefore, in neoclassical models a static equilibrium prevails. In this paper, the authors change this assumption so that economic units are assumed to be willing to improve their current state that may not be the optimal one. In this way, one can explain economic dynamics where every economic unit is changing its behaviour towards improving its welfare. The authors define the economic forces acting upon the production of firms, the consumption of consumers, and the prices of goods are changing in time. They show that in this dynamic system, business cycles and bankruptcies of firms emerge in a natural way like in the real world. (Published in Special Issue Agent-based modelling and complexity economics) JEL D11 D21 C63 C02 Keywords Econophysics; Newtonian economics; dynamic economics Authors Alia Asha Dannenberg, Lukema Oy, Joensuu, Finland, [email protected] Matti Estola, University of Eastern Finland Anna Dannenberg, University of Helsinki Alia Asha Dannenberg thanks the Jenny and Antti Wihuri Foundation and Emil Aaltonen Foundation for the research grants that have enabled her work Citation Alia Asha Dannenberg, Matti Estola, and Anna Dannenberg (2017). A dynamic theory of economics: What are the market forces? Economics Discussion Papers, No 2017-110, Kiel Institute for the World Economy. http://www.economicsejournal.org/economics/discussionpapers/2017-110 Economics Discussion Papers 1 Introduction The fundamental weakness in the current macroeconomic theory is the absence of a consistent micro level foundation. Here we present a new microeconomic theory where the macro state of a system is the aggregate of states of the micro units as proposed by Lux and Westerhoff (2009) in the spirit of classical analytical mechanics. Throughout our framework, we define and apply a consistent unit system for economics presented by De Jong (1967), comparable to that of physics. As e.g. Lux and Westerhoff (2009) state, the neoclassical economic theory is widely known of its inability to model the behaviour of real economic phenomena. The most fundamental shortcoming in the prevailing neo-classical framework, acknowledged e.g. by Mas-Colell et al. (1995), is that it is essentially static in nature, whereas real economic systems are dynamic. There have been attempts to dynamise the neoclassical theory for both consumers by e.g. Ramsey (1928); Cass (1965); Koopmans (1965) and for firms by Evans (1924), but these theories are, according to e.g. Estola (2013), inconsistent with the static neo-classical framework. Within the neoclassical framework, economic units are assumed to be in their optimum state, resulting in that the equations do not cover situations outside the optimum. This article introduces a dynamic theory of economics, compatible with real economic phenomena. It can be considered as a dynamic extension to the neoclassical framework, including the latter one as a special case with a static setup. Our theory is able to deal with observed dynamic economic phenomena also outside the optimum. Therefore it can be used to simulate economic systems in a realistic way, such as economic crises that the neo-classical framework is unable to forecast or handle according to Lux and Westerhoff (2009). Our theory has been tested with extensive simulations and two empirical evaluations, and it has been found consistent with real data, as shown in Estola and Dannenberg (2012); Estola (2015). 2 Firm and production In building our theory, let us begin from the basics. Let the profit Πwith unit e/time of a multi-product firm under perfect competition be Π= K ∑ k Pk˙ Qk−C(˙ Q Q Q),k=1,...,K,(1) www.economics-ejournal.org 2 Economics Discussion Papers where ˙ Qkis the flow of production of good kwith unit piecek/time,Pkthe price of product kwith unit e/piecek, and C(˙ Q Q Q)with unit e/time the costs at production flow vector ˙ Q Q Q. Now, one can solve the optimum conditions as ∂ Π ∂ ˙ Qk=Pk− ∂ C(˙ Q Q Q) ∂ ˙ Qk=0,(2) where ∂ C(˙ Q Q Q)/ ∂ ˙ Qkwith unit e/piecekdenotes marginal costs. This is the neoclassical optimum that corresponds to the “zero-force” situation in Newtonian mechanics: a body does not change its state of motion unless there is a force acting upon it. If the flows of production of a firm yield the maximum profit, the firm does not want to change them (compare with Newton’s first law). But what if Pk− ∂ C(˙ Q Q Q)/ ∂ ˙ Qk6=0? The firm is not in its optimum and, according to Fisher (1983); Varian (2006), should either increase or decrease its flow of production of good kto gain higher profit. For a profit-seeking firm, there is a ”force” driving it to adjust its flow of production. In the neoclassical theory, these economic forces have been acknowledged but never defined exactly which, according to Mirowski (1989), has led to the static framework. Theorem 1: Quantity F˙ Qk=Pk− ∂ C(˙ Q Q Q)/ ∂ ˙ Qkis the economic force acting upon the production of good kof the firm. The unit of economic force is the same as the unit of price, i.e., e/piecek. Theorem 2: F˙ Qk=m˙ Qk¨ Qk. Economic force F˙ Qkcauses either positive or negative acceleration on production. This is similar to Newton’s second law. Qkis the accumulated production of good k,¨ Qkthe acceleration of accumulated production, and m˙ Qkthe inertia of production1(it takes time to speed up or wind down production). The unit of inertia is e×time2/piece2 k. The work done by the economic force acting upon production can be calculated like the work of physical force, see Estola and Dannenberg (2016): ∆W=ZF F F˙ Q·dQ Q Q=∑ k m˙ QkZ¨ QkdQk =∑ k m˙ QkZd˙ Qk dtdQk=∑ k m˙ QkZdQk dtd˙ Qk =∑ k 1 2m˙ Qk˙ Q2 k,final −∑ k 1 2m˙ Qk˙ Q2 k,initial.(3) 1We are assuming that inertias of production and consumption are time-independent. Timedependent masses are possible, though would complicate the equations. www.economics-ejournal.org 3 Economics Discussion Papers The equation for kinetic terms suggests that kinetic energy of production exists in the production process. The unit of economic kinetic energy and work is e, see e.g., Dragulescu and Yakovenko (2000); Kusmartsev (2011). On the other hand, work ∆Wkis ∆Wk=ZQk,f Qk,i F˙ QkdQk=Ztf tiPk˙ Qk−˙ Qk ∂ C ∂ ˙ Qkdt=Ztf ti ˙ QkPk− ∂ C ∂ ˙ Qkdt,(4) where Rtf tiPk˙ Qkdtare the revenues from sales, and the term Rtf ti˙ Qk ∂ C/ ∂ ˙ Qkdtrepresents costs within the time interval ∆t=tf−tiif unit cost equals marginal cost. If Pk> ∂ C/ ∂ ˙ Qk, force F˙ Qkdoes work to change the kinetic state of production, increasing the flow of production (note that ˙ Qk≥0). If Pk< ∂ C/ ∂ ˙ Qk, production does work against the force F˙ Qk. 3 Consumer and consumption For a consumer, the corresponding theorems are the following: Theorem 3: There exists a force acting upon the consumption of a consumer of good k:F˙ Xk= ∂ H(˙ X X X)/ ∂ ˙ Xk−Pk. This is similar to Theorem 1. H(˙ X X X)with unit e/time is the willingness to pay of a consumer for the consumption flow ˙ X X X, and ∂ H(˙ X X X)/ ∂ ˙ Xkis the marginal willingness to pay that corresponds to the marginal costs of a firm, see Dannenberg and Estola (2017). The consumer surplus (measured in unit e/time, similarly to the profit of a firm) is φ =H(˙ X X X)−∑K kPk˙ Xk, and its optimum corresponds to the zero force acting upon consumption, i.e., F˙ Xk=0⇔ ∂ H(˙ X X X)/ ∂ ˙ Xk=Pk. Consumers’ marginal willingness to pay for a good can be measured, e.g., by making consumer surveys, as proposed by Cameron and James (1987). Theorem 4: The force acting upon consumption causes either positive or negative acceleration in consumption, i.e, F˙ Xk=m˙ Xk¨ Xk. This is similar to Theorem 2. The consumption of good khas kinetic energy 1 2m˙ Xk˙ X2 k. Since according to e.g., Dannenberg and Estola (2017) the theories of a firm and a consumer are symmetrical and have the same mathematical form, similar work effects for force F˙ Xkare obtained for consumer dynamics. 4 Market mechanism as a spring system Let us next consider a simple physical problem: two masses, say mXand mQ, are attached to each other with a spring with spring constant k, length Land rest length www.economics-ejournal.org 4 Economics Discussion Papers Figure 1: A simple spring system. zero. The masses have initial velocities ˙ X0and ˙ Q0towards the direction of the symmetry axis. Moreover, mXis drawn by force FXand there is dragging force −FQaffecting mQ. Figure 1 illustrates the setup. The forces are, according to Hooke’s law, mQ¨ Q=Fk−FQ(5) mX¨ X=FX−Fk(6) Fk=kL =k(X−Q).(7) Now one can calculate the time evolution of the system. As Theorems 1 and 3 state, the form of economic forces is similar to the spring force. Most notably, price Presembles the harmonic force Fkthat in economics connects production with consumption. We observe the following similarities: (i) Fk∼P. (ii) FQ∼ ∂ C/ ∂ ˙ Q, and FX∼ ∂ H/ ∂ ˙ X. Marginal costs and marginal willingness to pay are external forces. (iii) The time derivative of Eq. (7) yields the law of demand and supply ˙ P=k(˙ X−˙ Q)that relates price changes to excess demand or supply, as shown e.g. by Samuelson (1941, 1942). Forces ∂ C/ ∂ ˙ Qand ∂ H/ ∂ ˙ X depend on the corresponding velocities. (iv) Natural constraints are ˙ X≥0, ˙ Q≥0, and P≥0, because it is impossible to produce or consume negative amounts of goods or pay negative prices. Theorem 5: Price Pis a harmonic force that connects the flows of production and consumption. Recall Hooke’s law and Theorems 1 and 3. Price is an external force for individual consumers and firms, because they all participate on determining the “right” price. Theorem 6: For each action, there is equal reaction in opposite direction. The law of mutual forces of action and reaction (Newton’s third law) holds in economics as well. The sum of forces of a closed system is zero. However, most economic systems are open, as is our simulation example. The whole real global economy is naturally a closed system. www.economics-ejournal.org 5 Economics Discussion Papers 5 Simulated economic crises Now, one can construct an arbitrarily large system consisting of i=1...Ifirms, j=1...Jconsumers and k=1...Kgoods. The equations governing the dynamics are m˙ Qi,k¨ Qi,k=Pk− ∂ Ci(˙ Q Q Q) ∂ ˙ Qi,k,(8) m˙ Xj,k¨ Xj,k= ∂ Hj(˙ X X X) ∂ ˙ Xj,k−Pk,(9) k−1 Pk˙ Pk=∑ j ˙ Xj,k−∑ i ˙ Qi,k.(10) The law of demand and supply in Eq. (10) is familiar from the neo-classical theory, e.g. Samuelson (1941, 1942). Equations governing production (8) and consumption (9) do not exist in the neo-classical theory, but they are fundamental in the dynamic theory of economics, as shown by Estola and Hokkanen (2008); Estola (2017). The effects of production and consumption on prices cannot be treated separately. The neoclassical optimum is obtained by setting all masses m˙ X∨˙ Q→0 and 1/kP→0. For simulating economic crises, we use a standard cost function Ci(˙ Q Q Q) = Ai+∑k(Bi,k˙ Qi,k+Di,k˙ Q2 i,k)for firm i, where Airepresents fixed costs and Bi,k,Di,k are the constants of variable costs. Each firm produces three randomly chosen products. Moreover, we use utility function Uj=uj∑k(1−exp(−Ej,k˙ Xj,k/˙ X0 j,k)) that obeys positive and decreasing marginal utility, see e.g. Varian (2006). Our utility function has some advantages over the usual logarithmic utility functions used by e.g. Varian (2006), most notably that utility can never be infinite. Our utility-money conversion factor η j=Fj(1−exp(−GjMj/ < M>)) obeys the law of decreasing marginal utility of money presented by e.g. Bernoulli (1738); von Neumann and Morgenstern (1953). Constants Ej,k,˙ X0 j,kdescribe which goods consumer jprefers. Constants Fj,Gjdescribe whether consumer jprefers spending or saving. Mj=M0 j+ ρ jrWjis the income that consists of labour income M0 j and interest earnings or payments on wealth rWj.<M>is the average wage income of all consumers. Capital gains or losses rWjdepend on whether the net worth Wjof consumer jis positive or negative. ris the interest rate (see Dannenberg and Estola (2017) for more details; for simplicity, the same rate is assumed for interest income and costs). ρ jis a consumer specific factor that magnifies the wealth effect if ρ >1 or dilutes it if ρ <1.2 The consumer spending problem is an open optimisation problem with soft boundaries, similar to the optimisation problem of a firm as shown by 2Corresponding units of our parameters and new functions are: [uj∧Uj] = util/time;[ η j∧ Fj] =e/util;[Mj∧M0 j] =e/time;[Wj] =e;[r] = 1/time;Ej,kGjand ρ jare pure numbers. www.economics-ejournal.org 6 Economics Discussion Papers 0 1000 2000 3000 4000 5000 6000 7000 104 106 108 Time (days) Capital (b) (a) GDP 0 1000 2000 3000 4000 5000 6000 7000 0 1 2 3x 106 0 1000 2000 3000 4000 5000 6000 70000 0.02 0.04 0.06 Interest rate Figure 2: (a) GDP and central bank interest rate of the simulated economy. Lowering interest rate temporarily increases GDP. (b) Capitals of firms. If the capital of a firm decreases to zero, the firm is declared into bankruptcy. The amount of bankruptcies affects the interest rate adjusted by central bank. www.economics-ejournal.org 7 Economics Discussion Papers 0 1000 2000 3000 4000 5000 6000 7000 0 1000 2000 Production (a) 0 1000 2000 3000 4000 5000 6000 7000 0 2000 4000 6000 8000 (b) Consumption 0 1000 2000 3000 4000 5000 6000 7000 0 50 100 150 200 (c) Time (days) Price Figure 3: (a) Production, (b) consumption and (c) price of goods in the simulated economy. A business cycle of 300–500 days is clearly visible in consumption. Production and prices follow consumption, but they are slower to react to changes in the market. www.economics-ejournal.org 8