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11. Young Del Mar, who consumes only corn chips and french fries. His utility fu

ID: 1126369 • Letter: 1

Question

11. Young Del Mar, who consumes only corn chips and french fries. His utility function is u(x1, x2) = mln/x! + 2x2, 2x! +x2} where xi is his consumption of corn chips and x2 is his consumption of french fries. a) If the price of corn chips is pi 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

Budget constraint: m = p1x1 + p2x2

For a fixed-proportion utility function, utility is maximized when

x1 + 2x2 = 2x1 + x2

x1 = x2

(a) Budget line: 10 = 3x1 + 2x2

10 = 3x1 + 2x1 = 5x1

x1 = 2

x2 = x1 = 2

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

6 = x1 + 3x1 = 4x1

x1 = 1.5

x2 = 1.5

(c) Budget line: m = p1x1 + p2x2

When x2 = 0, m = p1x1

p1 = m / x1 (Price at which he consumes only corn chips)

When x1 = 0, m = p2x2

p2 = m / x2 (Price at which he consumes only french fries)