Problem Set 1
Consumer Theory
Utility maximization with calculus. Use the optimality conditions below to work through each problem before selecting your answer.
Key Conditions
Tangency condition:
MUx/MUy = px/py
MUx/MUy = px/py
Budget constraint:
pxx + pyy = I
pxx + pyy = I
Cobb–Douglas U = xαy1−α:
x* = αI/px y* = (1−α)I/py
x* = αI/px y* = (1−α)I/py
Leontief U = min{ax, by}:
Optimum at kink: ax* = by*
Optimum at kink: ax* = by*
MRS definition:
MRS = −dy/dx = MUx/MUy
MRS = −dy/dx = MUx/MUy
MUx = ∂U/∂x
MUy = ∂U/∂y
MUy = ∂U/∂y