Consider the following two-person, two-good exchange economy. Amy has an endowment of

e units of good 1, and 1 e units of good 2, and utility function:

uA = ln x₁^A+ (1 a ) ln x₂^A, 0 < a < 1

Bob has an endowment of 1 unit of good 2, and utility function:

u_B = min{x₁^B, x₂^B/B}

Also, we assume B < 1 / (1-a)

(i) Assume that e = 1.

(a) Find the Marshallian demands for the two goods by Amy and Bob as functions only

of prices p1, p2 of the two goods. (5 marks)

(b) Using your answers in (a), find the Walrasian equilibrium prices. Is there a unique

Walrasian equilibrium? [Hint: take good 2 as the numeraire.] (5 marks)

(c) Using your answers in (b), find the Walrasian allocation for each of Amy and Bob.

How does this allocation depend on the preference parameters? Comment on what

you find. (5 marks)

(ii) Assume that e = 0.5.

(a) Find the Marshallian demands for the two goods by Amy and Bob as functions only

of prices p1, p2 of the two goods. (5 marks)

(b) Using your answers in (a), find the Walrasian equilibrium prices. Is there a unique

Walrasian equilibrium? [Hint: take good 2 as the numeraire.] (5 marks)

Note: in your answer to part (ii), you may use the formulae for the Marshallian demands

that you derived in part (i), with the appropriate modifications.