Upscaling an Extended Heterogeneous Stefan Problem from the Pore-Scale to the Darcy Scale in Permafrost

Peszynska, Malgorzata; Vohra, Naren; Bigler, Lisa

doi:10.1137/23M1552000

Abstract How does an increase in market size, say due to globalization, affect welfare? We study this question using a model with monopolistic competition, heterogeneous markups, and fixed costs. We characterize changes in welfare and decompose changes in allocative efficiency into three different effects: (1) reallocations across firms with heterogeneous price elasticities due to intensifying competition, (2) reallocations due to the exit of marginally profitable firms, and (3) reallocations due to changes in firms’ markups. Whereas the second and third effects have ambiguous implications for welfare, the first effect, which we call the Darwinian effect, always increases welfare regardless of the shape of demand curves. We nonparametrically calibrate demand curves with data from Belgian manufacturing firms and quantify our results. We find that mild increasing returns at the microlevel can catalyze large increasing returns at the macrolevel. Between 70 and 90% of increasing returns to scale come from improvements in how a larger market allocates resources. The lion’s share of these gains are due to the Darwinian effect, which increases the aggregate markup and concentrates sales and employment in high-markup firms. This has implications for policy: an entry subsidy, which harnesses Darwinian reallocations, can improve welfare even when there is more entry than in the first best.

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