. Harry Mazzola, who consumes only corn chips and french fries. His utility func

Question

. Harry Mazzola, who consumes only corn chips and french fries. His utility function is u(x1, x2) = min{x1 + 2x2, 2x1 + x2} where x1 is his consumption of corn chips and x2 is his consumption of french fries.

a) If the price of corn chips is p1 = 3, the price of french fries is p2 = 2, and income is m = 10.How many units of corn chips and how many units of french fries should he consume to maximize his utility subject to this budget?

b) What if the price of corn chips is 1, the price of french fries is 3, and Harry’s income is 6. How many units of corn chips and how many units of french fries will Harry consume?

c) At what prices will Harry consume only corn chips and no french fries? At what prices will he consume only french fries and no corn chips?

Explanation / Answer

(a) Here the goods are complement in nature such as x1* + 2x2* = 2x1* + x2*

or 2x1 - x1 = 2x2 - x2

or x1 = x2 ... eq i

and we have budget constraint as Income = x1*Px1 + x2*Px2

10 = 3x1 + 2x2

from eq 1

10 = 3x1 + 2x1

x1 = 10/5 = 2 units

and x2 = 2 units.

Hence 2 units of corn chips and 2 units of french fries should be consume to maximize his utility subject to this budget

(b) Budget function: 6 = x1 + 3x2

from eq i

6 = x1 + 3x1

x1 = 6/4 = 1.5 units and x2=1.5 units.

Hence, 1.5 units of corn chips and 1.5 units of french fries should he consume to maximize his utility subject to this budget.

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