budget constraint, which is depicted in Figure 1. In the absence of DTP the house-
hold begins with an income of one unit of Y and can trade from (0, 1) along the line
of slope -p. With DTP the household begins at the same place on the y-axis, but
can trade along the line of slope —p from x = x, i.e., up to point (X, 1 — px), which
is denoted by A in the figure. If the household purchases in this range its budget
constraint is fully represented by the intercept y = 1 and the slope —p. From x
to B(0, X + 1-p-x) on the horizontal axis, it can only purchase additional units of
X by trading along the line of slope —p. The same points could be reached if,
instead of facing DTP, it faced the price p for all units and had an endowment
of Y equal to 1 + (p — p)x, as shown by point C(0,1 + (p — p)x). Combining the
segments for x ≤ x and x > X, the entire budget constraint is represented by the
kinked thick line.
Fig 1 about here.
From (2), given that p>p), a change in the free market price p has no effect
on x if x ≤ x); but ifx > x),
dx
— = Xp + XXm.
dp
We assume throughout that Xp < 0 and Xm > 0,5 and so the sign of dX/dp is
5 A subscript is used to denote the partial derivative with respect to the variable subscripted.