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In an economy producing n commodities - verifying the Leontief pricemodel assumptions with two productive factors: labour and capital -, we define a quasi-equilibrium set of prices for the period k+1 as the vectors p(k+1) such that p(k+1)=ATp(k+1)+r(k)BTp(k)+BT[p(k)-p(k+1)]+p0(k+1)a0, where p0(k) is the wage rate in period k,r(k) is the interest rate (including a risk premium supposed identical for all the sectors), A is the square matrix of technical coefficients, B the square matrix of capital coefficients and a0 the vector of labour inputs per unit of production. The main points of our study can be summarized in two questions: a) given prices p(k) and rate of interest r(k) in period k is it always possible to find a set of quasi-equilibrium prices for period k+1 when the wage rate is p0(k+1)? b) if this is not the case what sufficient conditions can be found in order to guarantee the existence of a vector of quasi-equilibrium prices in period k+1? In this paper we show that for some economies that behave according to the Leontief price model assumptions there are no Walrasian quasi-equilibrium prices and therefore no equilibrium prices. We also show that with some assumptions regarding matrices A and B it is possible to find vectors of labour costs per unit of production that make possible the existence of quasi-equilibrium prices. [ABSTRACT FROM AUTHOR]

In an economy producing n commodities - verifying the Leontief pricemodel assumptions with two productive factors: labour and capital -, we define a quasi-equilibrium set of prices for the period k+1 as the vectors p(k+1) such that $$ p(k + 1) = A^T p(k + 1) + r(k)B^T p(k) + B^T [p(k) - p(k + 1)] + p_0 (k + 1)a_0 ,$$ where p0 (k) is the wage rate in period k, r(k) is the interest rate (including a risk premium supposed identical for all the sectors), A is the square matrix of technical coefficients, B the square matrix of capital coefficients and a0 the vector of labour inputs per unit of production. The main points of our study can de summarized in two questions: a) given prices p(k) and rate of interest r(k) in period k is it always possible to find a set of quasi-equilibrium prices for period k + 1 when the wage rate is p0 (k + 1)? b) if this is not the case what sufficient conditions can be found in order to guarantee the existence of a vector of quasi-equilibrium prices in period k + 1? In this paper we show that for some economies that behave according to the Leontief price model assumptions there are no Walrasian quasi-equilibrium prices and therefore no equilibrium prices. We also show that with some assumptions regarding matrices A and B it is possible to find vectors of labour costs per unit of production that make possible the existence of quasi-equilibrium prices. [ABSTRACT FROM AUTHOR]