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.

 

 

 

Answer:

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 economics.
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