Optimal Military Spending, Trade and Stochastic Economic Growth

Based on the procedure of dynamic programming, this paper investigates the military spending, trade and wealth accumulation in a stochastic endogenous economic growth model. For the Cobb-Dauglas utility function, explicit solutions of the optimal problem of the home country are obtained. Meanwhile, the optimal consumptions of domestic goods and foreign goods, the share of domestic capital stock and foreign bond holdings are derived explicitly. The comparative dynamic analysis shows that when intertemporal substitution in consumption is relative elastic, economic growth has a positive correlation with foreign military spending, has a negative correlation with variance of foreign military spending, and has a positive correlation with variance of capital or bonds if capital and bonds yields the same benefits. However, in the case of inelasticity, variance of foreign military spending may stimulate or weaken economic development.