# Mary has a utility function U(x1, x2) = min (x1, 5*(x2)) Suppose Mary has an income of\$110, the price of x1 equals \$10 and the price of x2 equals \$5 (b). Calculate Mary’s optimum demand on x1 and x2; and calculate the maximized utility when Mary purchases the optimum bundle. (Hint:we cannot use the same method of CobbDouglas utility function to solve perfect complements utility function.

Mary has a utility function U(x1, x2) = min (x1, 5*(x2))

Suppose Mary has an income of\$110, the price of x1 equals \$10 and the price of x2 equals \$5

(b). Calculate Mary’s optimum demand on x1 and x2; and calculate the maximized utility when Mary purchases the optimum bundle. (Hint:we cannot use the same method of CobbDouglas utility function to solve perfect complements utility function.

$Max U(x1,x2)$

with respect to budget

P1X1+P2X2=M

10X1+5X2=110

Here, the consumption in equal quantities so

X1=X2

10X1+5X1=110

X1=X2=7.33

so the optimum bundle is (7.33,7.33)

b)

U(x1,x2)

=Min(7.33,7.33*5)

=7.33

so the utility is 7.33

Asked on February 14, 2018 in