2. The independence axiom was discarded as Edge-
worth (Mathematical Psychics, 1881) proposed to
represent total utility by a general function
U(x1,x2,..., xn). The diagram supplied by Edgeworth
for the representation of exchange under these general
conditions has become the most popular in economic
analysis. Let potatoes and eggs be measured on OX1
and OX2, respectively (Figure 2). Let C1, C2, C3,...
be John's utility isolines, a utility isoline being the loci
of all combinations of potatoes and eggs that have the
same utility. Naturally, utility increases as we move
from an isoline to a “higher” one, from C2 to C3, for
example. The alternatives open to John, whom we may
now assume to have ten bushels and be able to trade
one bushel for six eggs, are represented by the points
of the
budget line B1B2. The budget distribution that
maximizes John's total utility is the point M at which
one isoline is tangent to this budget line. Clearly, with
isolines having the shape shown in Figure 2, all other
possible distributions of John's budget lie on
lower
isolines. Therefore, John will trade four bushels of
potatoes for twenty-four eggs and retain six bushels
for his own consumption. The same solution is valid
if John has, say, six dollars and the prices are sixty cents
for one bushel and ten cents for an egg.
