A Consumer Has the Following Utility Function for Goods X

question 77

Essay

A consumer has the following utility function for goods X and Y:
U(X,Y)= 5XY³ + 10
The consumer faces prices of goods X and Y given by pₓ and pᵧ and has an income given by I.
a.Write out the Lagrangian expression for the consumer's utility maximization problem.
b.Write out the first order conditions necessary for maximizing utility subject to the budget constraint.
c.Show that the first order conditions imply the budget constraint and MRS condition.Provide the economic (i.e.non-mathematical)interpretation of these conditions - specifically,why are they necessary for the consumer to be at the optimal bundle?
d.Solve for the Demand Equations,X*(pₓ,pᵧ,I)and Y*(pₓ,pᵧ,I)
e.Show that the demand equations are homogeneous of degree zero.That is,show
X*(cpₓ,cpᵧ,cI)= X*(pₓ,pᵧ,I)
for any positive constant,c.

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Definitions:

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A measure of genetic similarity between individuals, often used in the context of family and ancestry.

Stepfather

A man who is married to one's mother after the divorce or separation from one's biological or legal father and may assume a role in raising the child.

EEA

Stands for the Environment of Evolutionary Adaptedness, a concept in evolutionary psychology referring to the set of environmental conditions under which human cognitive abilities are presumed to have evolved.

Trait Function

A characteristic or quality ascribed to someone, often influencing their behavior or responses.