For Ali good A and good B are perfect substitutes : 1 unit of good A is a perfect substitute for
2 units of good B. Draw Ali’s indifference curve that goes through the bundle (2, 4). [2 units
of good A, 4 units of good B]
(2, 4)
Slope = −2
Good A
For Veli good A and good B are perfect complements : he always ‘pairs’ 1 unit of good A
with 2 units of good B, otherwise he cannot consume them. Draw Veli’s indifference curve
that goes through the bundle (2, 4). [2 units of good A, 4 units of good B]
(2, 4)
Good A
I like coffee but when I drink more than 2 cups, it makes my stomach a bit upset, so after 2
cups, drinking more coffee makes me worse off. The problem gets worse and worse, the more
coffee I am forced to drink (above 2 cups). I don’t have the same problem with cookies. I like
them, and could eat them all day and never get tired.
(a) Sketch my preferences for coffee and cookies by drawing two representative IC’s. Show
the direction of increasing preference.
cookies
coffee
2
UTILITY FUNCTION
Consumer X has complete, transitive, monotone, and convex preferences. Consider the
following bundles :
bundle A = (20, 10)
bundle B = (14, 20)
bundle C = (17, 15)
bundle D = (18, 16).
Note that C is a convex combination of A and B.
Consumer X says that A is at least as good as B, B is at least as good as A and he is not
indifferent between A and C.
a. What must be the preference ordering between A and C? (Since he is not indifferent, he
must have a strict preference for either A or C, but which one?)
b. Find a utility function that represents his preferences over these bundles. (you must assign
a number to each bundle to represent Consumer X’s preferences.)
By the statements of the consumer we know that A is indifferent to B. By convexity of
preferences C is strictly preferred to A and B. By monotonicity of preferences D is strictly
preferred to C. u(D) = 3, u(C) = 2, u(A) = u(B) = 1.