This paper estimates the global welfare cost of climate change using a Spatially Integrated Assessment Model (SIAM), accounting for climatic uncertainty by integrating over different climate scenarios. SIAMs have the ability to account for adjustment mechanisms (e.g., trade and migration) to climate change. However, most work in the literature fails to account for uncertainty around the future realizations of climate. Jensen’s inequality suggests that failing to integrate over the full distribution of future climate in a SIAM leads to a biased estimate of the welfare cost when the welfare function has curvature. We show theoretically that the curvature of welfare to climate depends on the strength of migration, the spatial correlation of climate shocks, and the curvature of the utility function. We then show that these second order effects are quantitatively important using simulations of a baseline model.

The household’s price elasticity of demand is a key input to many economic models’ construction of markups and the assessment of consumer surplus. We measure the price elasticity of demand for around 14,000 products by region-year using retail scanner data. In all, we estimate over 7.5 million demand elasticities. We find that the distribution of these elasticities is stationary over time. However, we document substantial spatial heterogeneity in consumers’ price sensitivity: consumers in the largest markets are the most price elastic. As demand elasticities are a key input into the measurement of markups, our results suggest that any conclusions that markups are rising in retail markets must be driven by assumptions on conduct.

Ideas that challenge the status quo either evaporate or dominate. The study of opinion dynamics in the socio-physics literature treats space as uniform and considers individuals in an isolated community, using ordinary differential equation (ODE) models. We extend these ODE models to include multiple communities and their interactions. These extended ODE models can be thought of as being ODEs on directed graphs. We study in detail these models to determine conditions under which there will be consensus and pluralism within the system. Most of the consensus/pluralism analysis is done for the case of one and two cities. However, we numerically show for the case of a symmetric cycle graph that an elementary bifurcation analysis provides insight into the phenomena of clustering. Moreover, for the case of a cycle graph with a hub, we discuss how having a sufficient proportion of zealots in the hub leads to the entire network sharing the opinion of the zealots. This article is part of the theme issue ‘Stability of nonlinear waves and patterns and related topics’.