J.J. Alcantara/The Washington Post; iStock

Many readers responded to a piece we ran earlier this week on the high cost of diapers for the poor by suggesting a cheaper alternative: cloth diapers a family can buy once and then reuse.

This solution, though, has its limits for a number of reasons. Cloth diapers require a high up-front cost, which means those savings can be out of reach of cash-strapped families for the same reason that bulk purchases often are. "You do need to have several hundred dollars at once to get started, but then you are set," as one commentator dismissive of the "diaper gap" put it.

Cloth diapers, which are more time-intensive, also assume that poor parents can pay for what they can't afford with money by spending their time instead. (This is a tradeoff society often demands, for example, when the poor take long bus commutes because they can't afford cars, or sit through long ER waits when they don't have health insurance).

And many poor households simply don't have the one thing you'd need to use cloth diapers in the first place — a washing machine. To illustrate this, we pulled data from the Census Bureau's American Housing Survey. One in four households in the U.S. living on less than $40,000 a year lacks a washing machine at home. The richest families in America are about 30 percentage points more likely than the poorest to have their own washing machine:

This data covers washing machines that aren't shared with other households, so it doesn't count units in apartment buildings with communal coin-operated facilities (which, along with laundromats, can frown on washing diapers). Your chances of having a washing machine also depend on where you live. American Housing Survey data doesn't break down individual cities, so it's not possible to compare, for instance, people who live in the older housing stock of Baltimore City with households in newer homes stocked with amenities in the suburbs.

But, at the metropolitan level, there are some striking differences. This data covers all occupied housing units, not just homes among the low-income:

This is admittedly a scenario that a small share of all Americans face: whether to use cloth diapers when you're poor and don't have a washing machine. But this debate gets at the larger point that solutions we often come up with for the poor are informed by the assumptions of people with more money. And forgetting that other households may not have a washing machine is a privilege of people who can take theirs for granted.