Discrete Optimal Control Theory In The Money Supply

In this paper, first we establish the money supply mathematical model of the na-tional monetary policy while considering the deposit derived effect. We treat the amount of rediscount, central bank lending and open market operation as different variables which is different from the formal money supply model that consider all the monetary policy tools as one variable. Secondly, using the Maximum principle and linear quadratic optimal control of discrete system we get some optimal results of the two models. Fi-nally, we obtain the stability property of the two models.