Marginal Rate of Substitution

The rate at which a consumer is willing to trade one good for another while keeping the same overall level of satisfaction.

Source: Varian 2014

How much of one good a person would give up to obtain one more unit of another while remaining equally satisfied overall. Geometrically it is the slope of an indifference curve at a point, and it varies along the curve because the willingness to trade depends on how much of each good is already held. Where a person has a great deal of one good and little of the other, they will surrender more of the abundant one for a unit of the scarce one. The rate is defined at a point rather than over a range, so a single figure describes the trade only in the vicinity of the levels at which it was measured.

Source: Varian 2014

Because valuing health against other goods, or one health attribute against another, is a statement about the rate at which people are prepared to trade them. Willingness to pay for a health improvement is the marginal rate of substitution between health and money. The weights obtained from a choice experiment are ratios of marginal rates of substitution between attributes. The concept therefore underlies every method that expresses one thing in terms of another. It also underlies the threshold itself, since a willingness-to-pay threshold states the rate at which a system is prepared to trade money for health at the margin of its budget.

Source: Louviere, Hensher & Swait 2000

From choices rather than from direct questioning, since people find it easier to choose between described options than to state a rate. In a choice experiment, dividing the estimated weight on one attribute by the weight on another gives the rate at which respondents traded them. Where one attribute is cost, the resulting figure is willingness to pay. The estimate describes the sample average rather than any individual, and it applies at the levels presented rather than across the whole range. Because the estimate comes from choices rather than statements, it is less exposed to the difficulty people have in naming a figure, though it remains a hypothetical trade rather than an observed one.

Source: Lancsar & Louviere 2008

That the two goods are perfect substitutes at a fixed rate, so the person is always willing to trade at the same terms regardless of how much they hold. Standard models of choice experiments assume constancy for tractability, which implies preferences are linear in each attribute. That assumption fails where a threshold exists, such as a waiting time beyond which respondents will not go at any price, and detecting such non-linearity requires the design to include enough levels. Including three or more levels of the key attributes is the practical safeguard, since two levels can only support a straight line however the underlying preferences behave.

Source: Varian 2014

It is estimated at the attribute levels the design presented, so extrapolating beyond them is unsupported. It describes an average across respondents who may differ substantially, and where preferences are heterogeneous the average may describe nobody. Rates derived from hypothetical choices exceed those observed in real transactions. And where respondents ignored an attribute entirely, the estimated rate involving it is distorted in a direction the model does not reveal. Reporting the attribute ranges alongside any estimated rate is therefore necessary, since a rate quoted without them invites application well outside the region in which it was established.

Source: Bridges et al. 2011