A firm raises capital from multiple investors to fund a project. The project succeeds only if the capital raised exceeds a stochastic threshold, and the firm offers payments contingent on success. We study the firm's optimal unique-implementation scheme, namely the scheme that guarantees the firm the maximum payoff. This scheme treats investors differently based on size. We show that if the distribution of the investment threshold is log-concave, larger investors receive higher net returns than smaller investors. Moreover, higher dispersion in investor size increases the firm's payoff. Our analysis highlights strategic risk as an important potential driver of inequality.
The extent to which like-with like marry is particularly important for inequality as well as for the outcomes of children that result from the union. In this paper we discuss approaches to the measurement of changes in assortative mating. We derive two key conditions that a well-defined measure should satisfy. We argue that changes in assortativeness should be interpreted through a structural model of the marriage market; in particular, a crucial issue is how they relate to variations in the economic surplus generated by marriage. We propose a very general criterion of increase in assortativeness, and show that almost all indices used in the literature are implied by our criterion with one notable exception, that moreover violates one of our conditions. Finally, we use our approach to evaluate the evolution of assortative matching in the US over the last decades, and conclude that assortative matching has increased, particularly at the top of the education distribution.
The extent to which like-with like marry is important for inequality as well as for the outcomes of children that result from the union. In this paper we present evidence on changes in assortative mating and its implications for household inequality in the UK. Our approach contrasts with others in the literature in that it is consistent with an underlying model of the marriage market. We argue that a key advantage of this approach is that it creates a direct connection between changes in assortativeness in marriage and changes in the value of marriage for the various possible matches by education group. Our empirical results do not show a clear direction in the change in assortativeness in the UK, between the birth cohorts of 1945-54 and 1965-74. We find that changes in assortativeness pushed income inequality up slightly, but that the strong changes in education attainment across the two cohorts contributed to scale down inequality.
The U.S. economic expansion since 2009 is the longest on record since 1854, according to the National Bureau of Economic Research Business Cycle Dating Committee. This paper seeks to understand this phenomenon better by looking at the time paths of popular narratives over this interval, of stories that people have been telling that offer clues into their economic behavior. Six constellations of narratives are studied, identified by keywords “Great Depression,” “secular stagnation,” “sustainability,” “housing bubble,” “strong economy,” and “save more.”
Consider a market with identical firms offering a homogeneous good. A consumer obtains price quotes from a subset of firms and buys from the firm offering the lowest price. The “price count” is the number of firms from which the consumer obtains a quote. For any given ex ante distribution of the price count, we derive a tight upper bound (under first-order stochastic dominance) on the equilibrium distribution of sales prices. The bound holds across all models of firms’ common-prior higher-order beliefs about the price count, including the extreme cases of full information (firms know the price count) and no information (firms only know the ex ante distribution of the price count). A qualitative implication of our results is that a small ex ante probability that the price count is equal to one can lead to a large increase in the expected price. The bound also applies in a large class of models where the price count distribution is endogenously determined, including models of simultaneous and sequential consumer search.
We study the incidence and the optimal design of nonlinear income taxes in a Mirrleesian economy with a continuum of endogenous wages. We characterize analytically the incidence of any tax reform by showing that one can mathematically formalize this problem as an integral equation. For a CES production function, we show theoretically and numerically that the general equilibrium forces raise the revenue gains from increasing the progressivity of the U.S. tax schedule. This result is reinforced in the case of a Translog technology where closer skill types are stronger substitutes. We then characterize the optimum tax schedule, and derive a simple closed-form expression for the top tax rate. The U-shape of optimal marginal tax rates is more pronounced than in partial equilibrium. The joint analysis of tax incidence and optimal taxation reveals that the economic insights obtained for the optimum may be reversed when considering reforms of a suboptimal tax code.