The effect of economic policy in oligopoly. A variational inequality approach

Directional derivatives are the ideal tool to model simultaneous shifts of the instruments of economic policy. Provided the equilibrium solution of an oligolistic model are differentiable with respect to the parameter, such a problem can be easily solved considering shift in single instruments, i.e. partial derivatives, and then multiplying these derivatives by a vector rapresenting the direction of the simultaneous shifts. However even differentiability of the objective functions may not be enough to guarantee differentiability of the equilibrium. Byformulating an oligopolistic model with transportation costs by variational inequalities, we solve this problem even for non differentiable equilibrium solution.