Consider a consumer whose preferences are represented by the utility function:

U $($ x $,$ y $)=3$ xy where x and y are two goods on which the consumer spends all her income.

Let px and py denote the prices of the two goods and suppose that the consumer has income I

to spend. Assume that the consumer maximises utility.

i$)$ Derive this consumer's demand functions for goods x and y$.[25$ marks$]$

ii$)$ Using the same utility function and prices, find the compensated demand function for this

consumer. $[25$ marks$]$

iii$)$ Explain the difference between the two types of demand curves. $[15$ marks$]$

iv$)$ Suppose I$=20,$ Px$=2$ and Py$=4,$ using your results in part $($i$)$ Calculate the consumer's

demand elasticity of good y with respect to py $($indicate formulas, proceed and then insert the

values$).$ Similarly, calculate the consumer$$s demand elasticity of good x with respect to I and

the cross$-$price elasticity of x for py$.[20$ marks$]$

v$)$ Interpret your elasticity results in section $($iv$).[15$ marks$]$