Robert Shimer, University of Chicago

"The General-Equilibrium Incidence of Personalized Pricing"

Abstract:

I characterize the incidence of nonlinear personalized pricing in general equilibrium with two classes, workers and capitalists. Monopolistically competitive firms sell differentiated goods to households with heterogeneous incomes and preferences.

With a constant elasticity of substitution between goods, allocations coincide whether no firm or every firm personalizes prices, and every household is worse off when only some firms do. When each household has hyperbolic absolute risk aversion and a finite choke price for each good, the elasticity of demand aggregates exactly over preferences and incomes and each household's expected demand satisfies Marshall's second law whenever the density of log taste is log-concave.

Under these conditions, I prove that (i) under personalized pricing, the average markup a household pays for a good is increasing in the amount the household consumes of that good; (ii) every worker prefers nonlinear personalized prices to linear third-degree price discrimination, while the profit share of income is higher under linear pricing; (iii) households below a class-specific income threshold prefer nonlinear personalized prices to a uniform-price monopoly, while those above the threshold prefer uniform prices; and (iv) with elastic hours, personalizing every price is equivalent to firms charging a uniform price and the government levying a progressive income tax and subsidy, balanced by a lump-sum tax on or transfer to firms.

Contact person: John Vincent Kramer