I am studying for an exam, and this is one of the practice questions. I have the answers, but I need to understand how they got there.
Here is the question:
Anna (A) and Bill (B) have the following utility functions:
UA = (XA)0.5YA
UB = (XB)(YB)2
Where their endowments of X and Y are as follows:
XA = 16 YA = 16 XB = 4 YB = 144
A) At the endowment point, what are the marginal rates of substitutions between X and Y for Anna? For Bill?
B) If they could engage in voluntary exchange would they? If so, which goods would each offer to trade? Explain.
C) Find the competitive equilibrium price.
D) Is the allocation of resources achieved in (c) Pareto-optimal?
Answers:
A) MRSa = 5 MRSb = 18
B) Yes, Anna would trade X since she has a lower marginal value than Bill does.
C) p = 4
D) Yes this is pareto optimal, at this allocation the MRS are each equal to the relative price.
The part I'm having the most trouble with is part C. Please if you are able, can you explain your answer.
Thank you
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