In: Economics
Lauren’s utility function is uL(x1,x2) = min{x1, x2} and Humphrey’s utility function is uH (x1, x2) = ?(x1) + ?(x2). Their endowments are eL = (4,8) and eH = (2,0).
a) Suppose Humphrey and Lauren are to simply just consume their
given endowments. State the definition of Pareto efficiency. Is
this a Pareto efficient allocation? As part of answering this
question, can you find an alternative allocation of the goods that
Pareto dominates the allocation where Humphrey and Lauren consume
their respective endowment bundles?
b) As a function of market prices p = (p1,p2), determine Lauren’s
and Humphrey’s optimal consumption choices.
c) Determine the market equilibrium price ratio, pˆ* = p1*/p2*. What are Lauren’s and Humphrey’s equilibrium consumption bundles?