Factor substitution and economic growth in a Romer-type model with monopolistic competition

This paper studies the relationship between the elasticity of factor substitution (EOS) and steady-state values in a simplified Romer-type model with an expanding variety of products. Final goods production uses a nested CES technology, allowing substitution both among intermediate goods and between a composite intermediate good and labor. Consumption is a fixed fraction of output, and the cost of new intermediate production is constant and exogenous. The existence of an interior steady state requires an EOS between labor and the composite intermediate good above one, and an EOS among intermediates that exceeds the output–consumption ratio. Under these conditions, for a developing economy with an increasing variety of products, a higher EOS between labor and the intermediate composite good results in lower per capita output. This finding contrasts with results from infinite-horizon growth models, where a higher capital–labor EOS tends to boost per capita income (or the long-run growth rate) if baseline capital per capita is below its steady-state level. If the EOS between labor and the intermediate composite good is below unity and income per capita converges asymptotically to a constant as the number of intermediates continues to grow without bound, the usual positive relationship between the EOS and income per capita reappears.