Homework Answers
Consumption function is U (X,Z) = X0.5 + Z0.5
New Price of X (Px) = $4/unit , Price of Z (Pz) = $6/unit, Total Income (M) = $900
Budget Constraint: X.Px + Z.Pz = M
To find the demand of X and Z, first find MRS = partial derivative of U with respect to X / partial derivative of U with respect to Z = MUx/MUz
=> MRS = 0.5X-0.5/ 0.5Z-0.5 = (Z/X)0.5
Note that MRS (slope of Indifference curve) = Px/Py (slope of budget line) for optimal bundle
=> (Z/X)0.5 = 4/6 (divide by 2 throughout) = 2/3 => Z =4X/9 (after squaring both sides) ---(1)
Budget Constraint: X.Px + Z.Pz = M => 4X + 6Z = 900 --- (2)
Putting (1) in (2) we get,
4X + 6 (4X/9) = 900 => 4X + 8X/3 = 900
(multiplying throughout by 3) 12X + 8X = 2700 => 20X = 2700 => X = 2700/20 = 135
from (1), Z = 4X/9 = 4(135)/9 = 60.
Therefore, Optimal bundle is (X,Z) = (135,60)
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