Alice has strictly convex and monotonic preferences over consumption bundles con

Question

Alice has strictly convex and monotonic preferences over consumption bundles con- taining goods x and y.

Where (x, y) is the consumption bundle, Alice’s preferences are as follows: (1, 4) (1, 2) (4, 1) (2, 1)

(a) (1 point) Write a utility function that can represent Alice’s preferences. (Hint: Try a Cobb-Douglas)

(b) (1 point) Write another one.

(c) (1 point) Derive Alice’s demand functions for x and y, where the budget set is m pxx + pyy.

(d) (1 point) Is good x a luxury good, a necessary good, or neither? Explain.

Explanation / Answer

Utility function of Alice is as follows:

Ua = f ( X, Y)

The Indifference curve can show Alice's preferences as follows:

Qx Qy

5 2

4 2

3 2

3 5

3 6

c) Alice utility preferences are not strictly convex, rather it forms a righ angle. Which shows X and Y are complementory goods used in a specific ratio.

d) The demand functions will be as follows:

Ua = f (X, Y)

x = (Px, Py, m) or x = m/px

similarly, y = (Px, Py,m) or y = m/Py

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