Shomu Banerjee
ECON 201
Drawing Indifference Curves for “Min” Utility functions
Suppose you’re given a utility function
u
(
x
1
,
x
2
) = min{
x
1
, 2
x
2
}, i.e., the minimum
of the two values
x
1
or 2
x
2
. Here is how one draws the indifference curves that
correspond to this utility function. Pick a particular utility level for which you
wish to draw the indifference curve, say, the utility level 4. Then all those (
x
1
,
x
2
)
combinations that satisfy
4 = min{
x
1
, 2
x
2
}
lie on the same indifference curve. To find these combinations, begin with a few
combinations at random. If you pick the point (1, 1), the utility level is min{1, 2} =
1—in other words, this combination only yields a utility level of 1, not 4.
1
2
3
4
5
6
7
8
1
2
3
4
5
6
7
x
1
x
2
8
(4, 4)
(4, 3)
(4, 2)
u
= 4
u
= 1
(1, 1)
Try (4, 4) instead. Then the utility level attained is
u
(4, 4) = min{4, 8} = 4, so this
combination would certainly lie on the indifference curve for utility level 4. Try
reducing the consumption of the second good: pick (4, 3). Then the utility level