The program has paid a daily wage that was often higher than what local employers had offered. As a result, private-sector employers needed to make their jobs more attractive to retain workers.

The government’s wage served as a de facto floor on the wage others could offer for similar work. Several studies found that the program caused local wages to increase 4 percent to 5 percent when it was active. In Indian states that carried out the program most effectively, the increase in the private-sector wage was even bigger.

That higher wage applied to a vast amount of private employment, so it has added up to a lot: For each $1 the government paid out in wages, workers earned an additional 50 cents to $4.50 from higher wages in private sector jobs. The Indian government, in effect, created a matching program: For each $1 it paid out, the private sector kicked in 50 cents to $4.50 more. And this from a government program that has many deficiencies in how it is run. It suggests that even if the United States were to provide health insurance in an inefficient way, the indirect benefits to consumers could be substantial.

Shaking up the private market is especially useful if the labor market isn’t very competitive to start with. Powerful employers in such a market can get away with paying a lower wage, allowing them to earn fatter profits (although this entails a probable sacrifice in output). Adding a public option to a market like this is not a zero-sum game where higher wages just shift money from employers to workers. Instead, with better paid workers, the size of the economic pie, or “surplus,” increases.

In fact, there is evidence that India’s workfare program has increased both wages and private employment levels. This result goes against the most familiar supply-and-demand reasoning that by increasing employers’ costs, a higher wage decreases employment. That reasoning breaks down when a market isn’t competitive. Lack of competition also helps explain the related counterintuitive finding that raising the minimum wage sometimes increases employment in supposedly efficient markets like the United States.

The story plays out similarly among grocery stores in Mexico. In work with colleagues, I found that the few stores that sell beans, vegetable oil and other food staples in Mexico’s poor, remote villages often have considerable market power. We studied a program in which the Mexican government trucked boxes of staple foods into villages and delivered them to poor families.

For those families, the main benefit was the free food, but there was another boon: Local stores responded by reducing prices, and those prices dropped the most in villages with relatively few stores and little competition.