Consider a two-person two-good Edgeworth box economy where u" = aYa and ub = b + Yb. The initial endowment is w = ((2, 8), (8, 2)). The price of x is denoted by p, while the price of y is normalized to 1.
this person's initial bundle.
equation for ca. Flip this equation to obtain an equation for the price consumption curve (Pcc) for person a:
B =
and C
are whole
numbers.
Step 2. The highest utility that b can achieve while keeping a on their PCC will be given by a point of tangency
slope of b's indifference curve which is -1. Find the allocation equivalent to point S in Figure 10.2: S = ((D,
E), (F, G)), where D =
, and G =
are whole numbers.
Step 3. The price of good set by person b is then
Step 4. At the allocation S calculated in Step 2, MRSa:
while MRSb = 1. Hence S is
not Pareto efficient. This establishes that when person b sets the price derived in Step 3 as a monopolist
would, the resulting allocation is not Pareto efficient.
