in principle to adjust that opportunity cost to reflect differences between the amenity of work and the nonmarket activity in question to estimate the true cost of time devoted to the latter. Making this adjustment would require being able to quantify the value of enjoyment that individuals derive from different activities.
Provided that individuals are able to equalize the marginal value of time across all of the activities in which they engage, the adjusted opportunity cost measure we advocate for valuing tasks that someone else cannot be hired to perform is conceptually equivalent to the adjusted replacement cost measure that seems most appropriate for valuing time devoted to nonmarket activities satisfying Reid’s third-party criterion. To see why this is so, return to the roofing example discussed above. Let WS equal the hourly wage of a roofing specialist (replacement wage) and WOi the foregone hourly market earnings (opportunity wage) of a homeowner taking on a roofing task. The productivity-adjusted replacement cost of time the homeowner devotes to roofing would be
where, as before, bi is a parameter between zero and one that reflects the relative productivity of the homeowner as compared to the professional in the activity under consideration. The amenity-adjusted opportunity cost of time the homeowner devotes to the activity—in this case, roofing—rather than to paid employment would be
where ei represents the value of the extra enjoyment that individual i receives from spending an hour in the nonmarket activity rather than in paid employment. But for any given activity, an optimizing individual will seek to equate the value of the marginal product associated with time devoted to an activity (biWS) to the net opportunity cost of that time (WOi − ei).
This discussion implies that there are two alternative but potentially equivalent routes to arriving at a valuation for time devoted to nonmarket activity. If we know the relative efficiency of the family member, the effective wage can be calculated as the professional’s wage multiplied by that relative efficiency. We could estimate the amenity value the person attaches to the nonmarket work by subtracting the effective wage from the individual’s market value of time. Or, if we know the amenity value of the activity to the individual, we can subtract it from the family member’s market value of time to estimate the effective wage. As a byproduct, at least in the case of activities that could have been performed by a third party so that an observable wage exists for market providers, we could estimate the person’s efficiency relative to a professional in the same line of work