Optimal military spending, trade and stochastic economic growth

In this paper, based on dynamic programming we investigate the military spending, trade and wealth accumulation in a stochastic endogenous growth model. For the CobbDauglas utility function, explicit solutions of the optimal problem in the home country are obtained, and the optimal consumptions of domestic goods and foreign goods, the share of domestic capital stock and foreign bond holdings are derived. The comparative dynamic analysis shows that when intertemporal substitution in consumption is relative elastic, the lower the foreign military spending, the higher variance of foreign military spending and lower volatility in the return of capital or bonds will result in lower consumption ratio and higher economic growth rate.