Answer to Question #70485 in Microeconomics for mani

Question

Hungry Henry Hippo and Ravenous Rachel Raccoon live in different parts of the forest, but they happen to have the exact same preferences over three goods: apples, bananas, and cherries. The prices facing Henry are , 19B , pc) = (1, 1, l) , and the prices facing Rachel are (PA, , pc) = (3, l, 2) . You observe that Henry chooses consumption
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vector a,b , c- = (6, 24, 6), and you observe that Rachel chooses ê = 8. Unfortunately,
you were distracted by a lion, so you did not observe Rachel's choices or b . You also do not directly observe Henry's wealth i' or Rachel's wealth i . You do know that their preferences are locally non-satiated.
a. Find the set of values of ,b that are consistent with the weak axiom of revealed preference. Draw a graph of that set.
b. Now suppose that the lion tells you that Henry and Rachel's preferences can be represented by a Cobb-Douglas utility function u(a,b,c) = a Œ b P cY where > 0. Find ô,b). Does it lie in the set that you found in part a?