Suppose product i (i  1, 2) costs $ci per unit. If xi(i 1, 2) units of products 1 and 2 are purchased, then a utilityxa1x1a 2 (0  a  1) is received.a If $d are available to purchase products 1 and 2, howmany of each type should be purchased? b Show that an increase in the cost of product i de-creases the number of units of product i that should be purchased.c Show that an increase in the cost of product i doesnot change the number of units of the other product thatshould be purchased.

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Suppose product i (i  1, 2) costs $ci per unit. If xi(i
1, 2) units of products 1 and 2 are purchased, then a utility
xa
1x1a 2 (0  a  1) is received.
a If $d are available to purchase products 1 and 2, how
many of each type should be purchased?
b Show that an increase in the cost of product i de-
creases the number of units of product i that should be
purchased.
c Show that an increase in the cost of product i does
not change the number of units of the other product that
should be purchased.
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