ECN 311: Problem Set 8
1. There are 100 units of x1and 100 units of x2. Consumers Aand Bare
each endowed with 50 units of each good. Consumer Asays, "I love x1, but I
can take or leave x2." Consumer Bsays, "I love x2, but I can take or leave x1."
(a). Draw an Edgeworth box for these traders and sketch their preferences.
(b). Identify the core of this economy.
(c). Find all Walrasian equilibria for this economy.
2. Consider a simple economy with two consumers, Aand B, a single con-
sumption good x, and two time periods. Consumption of the good in period t
is denoted xtfor t= 1;2:Intertemporal utility functions for the two consumers
are
ui(x1; x2) = ln(x1) + ln(x2),i=A; B.
Endowments are eA= (10;0) and eB= (20;5). The good is perfectly
storable, so what is not consumed in the …rst period can be saved and consumed
in the second period.
(a). Suppose the two consumers cannot trade with one another. How much
does each consume in each period? How well o¤ is each consumer?
(b). Now suppose there are competitive "spot" and "future" markets for
this good. Let p1be the (spot) price per unit in period 1, and let p2be the
(futures) price prevailing in period 1 for delivery of 1 unit of the good in period
2. What will be the equilibrium relative price, p2=p1?
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