2 A Representative Household Model
Consider an economy with two representative commodities, X and Y .Therep-
resentative household’s consumption of X and Y are denoted by x and y, respec-
tively. We shall assume that commodity X is subject to DTP, while commodity
Y is the numèraire (this can be viewed as leisure or as a composite commodity).
The (relative) market price of X is denoted by p, while the market price of Y
is unity. The household has an endowment of Y , which, for simplicity, we nor-
malize to unity. In the absence of DTP the household would face the standard
utility-maximization problem,
max U (x,
x,y
subject to px + y ≤ 1.
Marshallian demand can be expressed as a function of marginal unit price and
full income, m. Here, m is simply the endowment of Y , and so the Marshallian
demand function for X is x(p, 1).
With DTP, however, the household can purchase X on the ‘plan track’ up to
the quantity x at unit price p. Any quantity above x has to be purchased on the
‘market track’ (i.e., on the free market) at unit price p, where p > p. Because
we are considering a single representative household in this section, the issue of