How does military spending affect long-run economic growth? The standard framing is linear: more guns means less butter, military spending crowds out productive investment, growth suffers. Chakraborty (arXiv: 2603.23980) shows the relationship is non-linear in an AK endogenous growth model: moderate militarization temporarily accelerates growth, but excess military burden kills it.
The mechanism: in an AK economy, all capital is productive and output scales linearly with the capital stock. Military spending diverts capital from civilian production, which should reduce growth. But the model includes a security externality — military strength deters threats that would destroy capital. Below a threshold, increasing military spending increases the effective capital stock by reducing expected destruction. Above the threshold, the diversion exceeds the protection.
The non-linearity creates an optimal military burden that depends on the threat environment. A more threatened economy has a higher optimal military share. The paper analyzes an asymmetric conflict between an advanced economy and a sanctioned middle-income nation, showing that sanctions shift the middle-income nation's optimal point — the sanctioned economy needs more military spending per unit of deterrence because its economic base is smaller.
The through-claim: security is an investment with diminishing returns that eventually go negative. A small military budget buys large increments of protection (the first divisions deter the most likely threats). A large military budget buys marginal protection at the cost of significant productive capacity. The curve from positive to negative returns is smooth, but the location of the peak depends entirely on the threat — and nations routinely spend past it, not because they don't know the economics, but because the threat assessment is endogenous to the spending.
Chakraborty, 2603.23980. Economic theory / military economics / endogenous growth / AK model / defense spending.