Maths for economics - Dynamic systems

A version of the Obst macroeconomic model is given by the following pair of linear differentia! equations: Where u E % (i.e the ratio of money demand and money supply). p is the rate of inflation, q, is the S exogenous rate of growth of the real national product, 111, is the rate of monetary expansion and v is a positive constant. Given the equilibrium of the model occurs at (p, p) : (m q, 1), write out the Jacobian matrix evaluated at the equilibrium, determine the eigenvalues of the system and hence the local stability of the system. Which of the following statements is correct? (i) The first and second row vectors of the Jacobian at the steady state can be written [0 v] and [1 0] (ii) The eigenvalues of the Jacobian evaluated at the steady-state are = ix/Tw (iii) The steady-state is not stable (iv) All the above are correct (v) None of the above are correct