The solutions to (9) and (10) yield the Marshallian demand functions
x1 = x[p,y1 + (p — p)x]
x'2 = x(p,y2).
Total demand for X is
x = αx1 +(1— α)x2.
Corresponding to (4), we have
dx1
dp
dx2
dp
x1 + x1mx = S1
pm
2
p.
(x1- χ)x1n;
(11)
Although dx2/dp < 0, dx1/dp may take either sign. Without the possibility of
resale, as discussed above, the household can only gain the implicit income when
it consumes more than its government subsidy. With resale, the type-1 household
gains an implicit income, even though it consumes less than the government sub-
sidy x. Eq. (11) shows that when the consumption x1 of DTP goods for a type-1
household is smaller than the plan-track quantity x, dx1∕dp is only negative if the
compensated demand change is numerically greater than the income effect, and
vice versa. However, when the consumption of DTP goods is greater than the
plan-track quantity for a type-1 household, dx1/dp is always negative. In Figure 4
19
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