The answers on chegg are all WRONG. You are suppose to figure out which of the m

Question

The answers on chegg are all WRONG. You are suppose to figure out which of the min function is the minimum and solve it from there

11. Young Del Mar, 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) Being a minimum function, we need to find the ratio in which two goods are consumed. Here we see that x1 + 2x2 = x2 + 2x1 or x1 = x2. Hence both the goods are needed in 1:1 ratio. For given prices and income, budget is

10 = 3x1 + 2x2

10 = 3x1 + 2x1 (x1 = x2)

10 = 5x1 and so x1 = x2 = 2

At this level utility is U = min (2 + 2*2, 2*2 + 2) = 6 utils. Hence the optimum bundle is (2, 2)

b) Now the budget changes to 6 = x1 + 3x2

6 = x1 + 3x1

x1 = x2 = 1.5

Hence optimumal bundle now is (1.5, 1.5)

c) Indifference curves are L-shaped lines so no corner solution is possible. Hence there is no price at which one good is consumed and other is not because it violates the preferences of perfect complements.

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