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# A dynamic extension of the classical model of production prices determination

Our research was supported by CSIC-UDELAR (project "Grupo de investigación en Dinámica Económica"; ID 881928)
• This paper generalizes the classical model of determination of production prices for two commodities by introducing a dynamics generated by the possibility that the profit rate can be computed using prices of different stages. In this theoretical framework, the prices show a codependency between the two sectors, given by the rate of profit, and inter-industry transactions. In this setup and using discrete time, the general model can be represented by a nonlinear two dimensional dynamical system of difference equations of second order. The study shows that the dynamical system admits a unique solution for any initial condition and that there is a unique nontrivial equilibrium. In addition, it can be shown that locally the dynamical system can be represented in the canonical form $x_{t+1} = f(x_{t})$ and that the stability of the equilibrium depends on the parameters of the production process. Future research includes the extension of the model to the case of several commodities and the closed solution of the model.

Mathematics Subject Classification: Primary: 91B55, 93C55.

 Citation: • • Table 1.

 $a_{11}$ $a_{12}$ $a_{21}$ $a_{22}$ $l_{1}$ $l_{2}$ Qty. of eigenvalues with modulus smaller than one $0.96$ $0.02$ $0.01$ $0.94$ $0.09$ $0,91$ zero (repulsor) $0.89$ $0.06$ $0.06$ $0.75$ $0.53$ $0.47$ one (saddle point) $0.17$ $0.23$ $0.8$ $0.17$ $0.19$ $0.81$ two (saddle point) $0.04$ $0.18$ $0.02$ $0.27$ $0.99$ $0.01$ three (saddle point) $0.69$ $0.28$ $0.14$ $0.49$ $0.29$ $0.71$ four (attractor)

Table 2.

 type of equilibriums frequency percent repulsor $18$ $0.011$ saddle point $16711$ $0.972$ attractor $29$ $0.017$
• Tables(2)

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