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 !
