Microeconomics Answers

Consider the utility function u¹(x₁, x₂, x₃) = x²_1,x³₂ x₃ .

Find a monotone transformation of u¹(x₁, x₂, x₃) such that the new utility function is of the form u³(x₁, x₂, x₃) = a In x_{1 +} b In x₂ + c In x_3.

Consider the utility function u¹(x₁, x₂, x₃) = x²_1,x³₂ x₃ .

Find a monotone transformation of u¹(x₁, x₂, x₃) such that the new utility function is of the form u²(x₁, x₂, x₃) = (x₁^a, x₂^b, x₃^c)

Where a + b + c= 1. 

 Assume U(x, y) = √4 xy.

a) Derive the indirect utility function v(p, Y ).

b) Now assume a consumer is considering a gamble that has a 50% chance of returning 121% of the initial investment (a gain of 21%) and a 50% chance of returning 81% (a loss of 19%). If a consumer’s initial budget is 100, what is the expected outcome of this gamble?

c) Now using the indirect utility function from a), the gamble from b) and assuming prices are equal to 1, find an optimal allocation of consumer’s initial wealth between risky asset from gamble in b) and a risk-free asset. Assume the return on risk-free assets is 1 (no gain/loss).

Explain the IS-LM model