Consider an individual with the following utility function:

Ms$.$ Jones: $U(x,y)=x+lny$

a$.$ Use the Lagrange method to find the demand functions for $x$ and $y$ for Ms$.$ Jones. You

may assume that she has income I and that the prices of $x$ and $y$ are $p_x$ and $p_y$ respectively.

b$.$ Now suppose you are told that $I=600,p_x=10$ and $p_y=20.$ Use these values to find

the utility maximizing quantities of $x$ and $y$ consumed by Ms$.$ Jones.

c$.$ Find expression for the income elasticity of demand for good $x$ for Ms Jones. Find

expression for the $($own$)$ price elasticity of demand for good y for Ms$.$ Jones.