Optimal Control of Dynamic IS-LM Bussiness Cycle Model with Two Time Delay

One of the business cycle model in the dynamics economy is the IS-LM business cycle model with time delay. This model talks about stability in the micro-economic system. Meanwhile, the time delay in the IS-LM business cycle model involve a change in stability at the equilibrium point so that a bifurcation is occurs. In this study, analysis of stability and optimal control on the IS-LM business cycle model with time delay. Based on simulation with numerical computation, show that there is a change in the stability when the delay value was given exceed the critical delay value. The stability change occur when the delay value arose a pure eigen value so that there was a limit cycle that show a Hopf bifurcation. Furthermore, optimal control in the IS-LM business cycle model given when the system changes to be unstable, i.e. when the delay value passed the critical delay value. Variable control use in the interest rate function. While the objective function maximize the total money supply from the country, the optimal solution is obtained by using the Pontryagin Maximum Principle. The results of this simulations with numerical computation show that maximizing the rate of income, the rate of interest rates, and the rate of capital stock lead to the stability point at thirtieth time.