The Indirect Utility Function for a Consumer with a Utility

question 26

Essay

The indirect utility function for a consumer with a utility function U(x₁, x₂) is defined to be a function V(p₁, p₂, m) such that V(p₁, p₂, m) is the maximum of U(x₁, x₂) subject to the constraint that the consumer can afford (x₁, x₂) at the prices (p₁, p₂) with income m.
a. Find the indirect utility function for someone with the utility function U(x, y) = 2x + y.
b. Find the indirect utility function for someone with the utility function U(x, y) = min{ 2x, y}. Explain how you got your answers.

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Definitions:

Umbilical Cord

The cord connecting the fetus to the placenta, carrying oxygen and nutrients to the fetus and removing waste products.

Stem Cells

Cells with the unique ability to develop into different types of cells in the body and to self-renew.

Simple Squamous Epithelial

A single layer of flat cells lining surfaces involved in diffusion and filtration, such as blood vessels and air sacs of the lungs.

Basement Membrane

A thin, fibrous layer that underlies and supports the epithelial tissue.