1. Consider the simple exchange economy that we talked about in class with only
ID: 1167713 • Letter: 1
Question
1. Consider the simple exchange economy that we talked about in class with only two people, Liz and Jack, and only two goods, cupcakes (our "x" good) and microwaves (our "y" good). Use the following information to answer question 1. Note that the subscripts on t and m denotes to whom the cupcakes or microwaves belong (i.e. cL is the number of cupcakes that Liz has).
MRS
cmL = 4cL/mL
MRS
cmJ = 2cJ/mJ
Total # of cupcakes = 16
Total # of microwaves = 8
a. Consider the allocation where Liz has 12 cupcakes and 4 microwaves and Jack has 4 cupcakes and 4 microwaves. Is this a Pareto efficient allocation? Why or why not?
b. What is the Pareto efficient allocation of cupcakes if Liz has only 1 microwave? Assume they consume all of the microwaves and cupcakes and justify that your answer meets the required criteria.
c. What is the MRT
cm in the allocation you found in part b?
d. What does the First Fundamental Theorem of Welfare Economics tell us will happen if we allow trade in this economy? What assumptions must be true?
Explanation / Answer
Ans)
Two people, two goods: x &y, simple exchange economy
a) Pareto efficient allocations are where the MRS for both the consumers are equal.
Thus, at the allocation where Liz has 12 cupcakes and 4 microwaves and Jack has 4 cupcakes and 4 microwaves, we have
MRSL = 4cL/mL = (4*12 / 4) =12
MRSJ = 2cJ/mJ = (2*4/4) = 2
Since MRSL MRSJ, hence the allocation is not pareto efficient.
b) mL = 1, => mJ = 7
For Pareto Efficiency, MRSL= MRSJ ,
4cL/mL = 2cJ/mJ
4cL = 2(cJ)/7
cL / cJ = 1/14
Thus, cL = 1/14*16 = 1.1428 , approx = 1
And cJ = 13/14*16 =aprrox. 15
c) MRTcm = 4 (approx) (since, MRT in production = MRS in Exchange)
d) First Fundamental Theorem of Welfare Economics states:
Suppose each consumer’s preferences are locally non-satiated. Then, any allocation ( x* ; y*) that with prices p* forms a competitive equilibrium is Pareto optimal.
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