where zi is a vector of CSA characteristics, pi
is the price of a CSA share in terms of the
numeraire, m is a measure of income, i(pi, zi)
isaquality-adjustedpricewhere qi = i(pi, zi),
and i is an idiosyncratic unobservable. Inverting qi = i(pi, zi) provides an expression for
price as pi = πi(qi, zi), where it follows that
a marginal valuation of a characteristic, zi, is
given by the derivative of price with respect
to that characteristic as ∂pi
∂zi
=
∂πi(qi, zi)
∂zi
. This
is the increase in price that a representative consumer would be willing to pay for
an increase in characteristic zi, holding utility
constant.