Nonlinear input-output balance for open economy with Hautakker-Johansen production function (Q2740083)

The author studies the input-output balance model for a multi-branch open economy with a non-negative export-import balance. The Hautakker-Johansen model is presented. Let the pure branch produce a homogeneous product, using \(n\) kinds of production factors. In the branch there are different technological processes of manufacture, each of them set by a vector \(a\in R^{n}\) norms of expenses of production factors on the output of a unit of production. The intensity of the use of technologies \(u(a)\) are bounded by capacities available in a branch. Let's designate \(\mu(\cdot)\) the measure which is called the distribution of capacity on technologies. The task of optimal distribution of the industrial resources flow \(l=(l_1,\ldots,l_{n})\) coming into the branch with purpose of branch output maximization has the form \(\int_{R^{n}_{+}}u(a)\mu(da)\to\max_{u(a)}\); \(\int_{R^{n}_{+}}au(a)\mu(da)\leq l\) \(0\leq u(a)\leq 1\). The production function \(F(l)\) is the function which defines the greatest possible output of a branch in the considered problem of optimal distribution for given \(l\). The author investigates the optimizing problem at balance restriction in the model for a multi-branch open economy.