Two rationales, often tangled together
The economic case for a minimum wage rests on two distinct ideas. The first is efficiency. In a labor market where only a handful of employers compete for workers, firms can push wages below what workers are actually worth, shrinking overall employment. A minimum wage set at the right level can counteract that, nudging firms to hire more and pay more. The second is redistribution. Even setting efficiency aside, a higher wage floor transfers income from profits to paychecks.
These two motivations tend to get blended together in policy debates. Part of what the authors set out to do is build a model that can pull them apart and assign a dollar figure to each.
Their framework features local labor markets with a finite number of firms that compete strategically for workers. Firms differ in productivity. Workers differ by education (non–high school, high school, college) and by whether they derive their income mainly from wages or from capital and business ownership. The model captures three channels through which a minimum wage could improve efficiency: a direct effect at firms that were underpaying, a spillover effect as competing firms raise their own wages in response, and a reallocation effect as workers move from less productive to more productive employers.
Testing the model against real-world evidence
Before using the model to evaluate policy, the authors checked whether it reproduces findings from recent empirical studies. They replicated results from a study of Germany’s 2015 minimum wage introduction, which documented that small, low-productivity firms shrank or exited while larger, more productive firms expanded. They also reproduced findings on how competitors responded when Amazon voluntarily raised its minimum wage to $15 in 2018, a change that lifted competitor wages by about 4.7 percent.
The model also reproduced patterns showing that minimum wage increases can have positive employment effects in concentrated labor markets and negative effects in less concentrated ones, and it matched evidence on how wage increases at the bottom of the distribution spill upward to higher earners, drawing on data from Brazil’s large minimum wage hikes.
Separating efficiency from redistribution
The key methodological move in the paper is this: the authors ask what minimum wage a government would choose if it also had access to lump-sum transfers between households to handle any redistribution goals separately. If redistribution is taken care of through the tax and transfer system, the minimum wage is left to do only what it does best on efficiency grounds.
Without that separation, the optimal minimum wage bounces around wildly depending on whose welfare the government weights most heavily. Under a utilitarian view that treats every person equally, the model picks $15.12 per hour. Weight college-educated workers more heavily and it climbs to $31.53. Use weights that reflect the current distribution of consumption in the U.S. economy and it falls to $6.97.
Once lump-sum transfers are allowed to handle redistribution, the answer tightens dramatically: the optimal minimum wage lands between $7.50 and $10 per hour, regardless of which group the government favors. And the welfare gains from this efficiency-focused minimum wage are small, equivalent to roughly a 0.1 percent increase in total factor productivity. That recovers only about 2 percent of the efficiency losses caused by employer market power in the first place.
The authors then turn the decomposition around. Under a $15 minimum wage chosen with utilitarian weights, less than 5 percent of the welfare gains come from efficiency improvements. More than 95 percent come from shifting income from business owners and high earners toward lower-wage workers.
Why efficiency gains stay small
The researchers identify three reasons why the efficiency story, though real, is limited in scale. First, the firms that stand to gain from a binding minimum wage are lower-productivity firms that were already paying fairly close to their competitive wage. The room for improvement at those firms is narrow, and a modest wage bump quickly shifts them to efficient employment levels.
Second, the marginal revenue product of labor is relatively flat in their calibration, which means once firms start rationing jobs in response to higher wages, they ration a lot, quickly.
Third, the biggest potential efficiency gains would come from squeezing the largest markdowns at the most productive firms, which have the most market power. But those large firms barely notice when their small, low-wage competitors are forced to raise pay, because those competitors hold small shares of the market. Spillovers up the wage ladder, in other words, are muted.
Robustness and regional differences
The authors stress-tested their findings. They recalibrated for Mississippi, the state with the lowest per-capita income, and found an optimal minimum wage under utilitarian weights of $14.89, essentially identical to the national figure. Mississippi has lower average wages, which pushes toward a lower optimum, but also a larger share of high-school-educated workers, who benefit most from a higher floor. The two forces roughly cancel.
Splitting the country into low-, medium-, and high-income regions produced similar results: the welfare gains from region-specific minimum wages are only marginally larger than from a single national minimum wage. Varying the Frisch elasticity of labor supply by 50 percent in either direction barely moved the answer. And when the authors fixed capital in the short run, the optimal minimum wage fell by only about a dollar.
What the results don’t say
The paper is careful about what its findings rule out and what they don’t. It doesn’t say minimum wages fail to reduce inequality. The model produces declining wage inequality and a rising labor share as the minimum wage goes up. It doesn’t say a $15 minimum wage is welfare-reducing under reasonable assumptions; under utilitarian weights, it improves welfare. The authors’ point is that commonly watched indicators like wage compression and a rising labor share can keep moving in a favorable direction even as overall welfare starts falling. Those metrics don’t reliably track welfare.
The researchers also note they don’t model several channels documented elsewhere, including pass-through of minimum wages to consumer prices and firms substituting capital for labor. Adding those would tend to weaken the redistributive effects to low-wage workers. And the authors point to complementary work by Erik Hurst and coauthors suggesting that other tools, like the Earned Income Tax Credit, can do a better job of redistribution than a minimum wage can for most non-college workers.
The authors frame their exercise as a return to the original minimum wage debate: whether a wage floor can fix the inefficiencies caused by employer market power. Their conclusion is that it can, a little, but that the scale of those efficiency gains is modest, and the bulk of what a $15 minimum wage would accomplish is redistribution, achievable in principle through other means.
