Intermediate Microeconomics - Exam 2

Cobb-Douglas Utility Function

u = x₁^ax₂^b

Cobb Douglas Optimal Bundle

x₁^* = a/(a+b) (m/p₁) , x₂^* = b/(a+b) (m/p₂)

Perfect Complements Utility Function

u = min{ax₁,x2}

Perfect Complements Optimal Bundle

x₁^* = m/(p₁+ap₂) , x₂^* = am/(p₁+ap₂)

Perfect Substitutes Utility Function

u = ax₁+x₂

Perfect Substitutes Optimal Bundle

If p₁<ap₂, then x₁^* = m/p₁, x₂^* = 0

If p₁=ap₂, then any combination within budget of the two

If p₁>ap₂, then x₁^* = 0, x₂^* = m/p₂

Quasi-Linear Utility Function 

u = ax₁²+x₂

Quasi Linear Optimal Bundle

MRS = -p₁/p₂

m = p₁x₁+p₂x₂