# The Household Production Function

I was wondering whether someone can explain the household production function (HPF). Specifically, the variant presented in Patanayak et al (2005). The paper uses the HPF to determine household willingness to pay for improved water supplies. The HPF model theorizes that averting expenditures (coping costs) are lower bound to willingness to pay (WTP). However other people (e.g. Orgill-Meyer et al (2018)) talk about how including sunk costs (expensive tank assets, pumps, etc) when calculating coping can reverse this relationship causing coping costs to be upper bound to WTP. However, Patanayak et al, 2005 includes amortized sunk costs in his coping cost calculations and the HPF premise still holds.

This is confusing me a bit.

I know the question is elementary but I am really not an economist. Can someone please clarify this?

I have only read the abstracts, but the two statements aren't conflicting.

From Wikipedia, a production function gives the technological relation between quantities of physical inputs and quantities of output of goods. A household production function is a form of that idea that looks out how households combine inputs to get outputs that they consume such as water.

Under the HPF model, water is considered as an output that households consume. However, there are many ways to combine inputs to obtain water: you can use utility based water if the infrastructure for that exists or non-utility based water (involving personal tanks, pumps, etc). The assumption is that households will be willing to pay for the utility based water infrastructure at least the amount that it takes to upkeep their non-utility based water that they currently own accounting for the sunk costs of the upfront purchase of the tanks and pumps. And hence that is the "lower bound to WTP". But this assumes that the utility based water is higher quality than what households already have. As noted in the abstract of the latter paper, "[w]e attribute this departure from the traditional relationship between averting expenditures and contingent valuation to the lack of household confidence in the quality of utility-provided water." Hence, current coping costs become an upper bound to WTP. To put it differently, if households believed utility based water is exactly equivalent to what they currently have, then the WTP would be exactly equal to current coping costs.