Perfect complements.
The perfect complements are represented by an utility function U(x,y)=min{x,y/A}
which is equivalent to the function U(x,y)=min{Ax,y}.
1
In this case the consumer cares about one good only to the extent it can be paired to the
other good in a given proportion. Hence from U(x,y)=min{x,y/A} we gather that the
consumer values units of y only if the can be paired with units of x with a proportion of A
units of y for one unit of x.
Examples:
Left shoes=x and right shoes=y. The utility is U=min {x,y} (see power point presentation
for a graph if the indifference curves of this utility).
Say that you exactly want two tsp of sugar (S) for each cup of coffee (C). Then your
utility from C and S can be expressed by U(C,S)=min {C,S/2} or equivalently
U(C,S)=min {2C,S}.
The indifference curves are L shaped with kinks on the line 2C=S, that is C=S/2. Try to
draw the graph.
Some more remarks
Fact: to go from one kink to another you increase C and S in this proportions “sugar
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 Spring '09
 VG
 Utility, Ordinal utility, Kink, )=min{x,y/A}

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