Long-Run Comparative Statics

What are the long-run effects of permanent changes to the economy? We characterize long-run comparative statics for a broad class of models in terms of expenditure shares, substitution elasticities, and capital supply elasticities. Our key insight is that long-run analysis can be performed using an as-if static economy where capital is treated as an intermediate input subject to endogenous markups. These markups, which measure deviations from the Golden Rule of savings, equal the ratio of capital income to investment. This reframing yields a surprising result: long-run consumption responses follow second-best principles even in efficient economies. In particular, reallocations have first-order effects since the envelope theorem does not apply. Furthermore, sales alone do not summarize industries’ importance for long-run consumption. To show how these points matter in practice, we develop a quantitative model of the world economy to study how markups, tariffs, and productivities affect long-run consumption. The model features input-output linkages, imperfectly elastic capital supply, heterogeneous returns, and endogenous net foreign asset positions. We find large negative first-order effects of tariffs and markups, even when initial tariffs and markups are zero. We also find that the productivities of industries upstream of investment goods have substantially larger long-run consumption effects than their sales shares would suggest.