Question

Miss Quested has the following quasi-linear utility function over bread (b) and housing (h): U(b, h) = 2b1/2 + h Assume that Miss Quested’s total income is $24, the price of bread is $1 per unit and the price of housing is $4 per unit. What is Miss Quested’s utility maximizing combination of bread and housing?

Answer 1

Answer:

For b = 16 and h = 2, Miss Quested will get the maximum utility

Explanation:

Total income = $24

Price of bread = $1 per unit

Price of housing = $4 per unit

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Constraint on Income: b + 4*h = 24

Maximizing U(b,h) = 2*(b)^(0.5) + h = 2*b^0.5 + (6 - b/4)

To calculate maximum utility, we solve for b for which

1. derivate of function = 0

2. double derivate = negative (< 0)

Step 1: Derivate = 0 => d(U)/db = 2*(1/2)*b^(-0.5) - 1/4 = 0

=> 1/b = (-1/4)^2 = 1/16

Step 2: Double Derivate < 0 => d2(U)/db^2 = (-0.5)*b^(-1.5) = Negative !