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

Question

11. 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

Given the utility function: u(x1, x2) = min{x1 + 2x2, 2x1 + x2}

Equating x1 + 2x2 = 2x1 + x2

This gives x1 = x2

This relation will be used in the below subparts.

a)

Budget constraint: 3x1+2x2=10

Substituting x1=x2 gives the equation as:

3x1+2x1=10

5x1=10

x1=x2=5 units

b)

Budget constraint: 1x1+3x2=6

Substituting x1=x2 gives the equation as:

1x1+3x1=6

4x1=6

x1=x2=1.5 units

c)

Both goods will be consumed together in equal quantities

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