$($i$)$ When the price of a product falls from $10$ to $9$ the demand increases from $20$ units to $25.$ Estimate the price elasticity of demand $($you must use the formula sheet attached to find the solution$).$

$5$ Marks

$($ii$)$ Suppose that this good $($the one referred to in a part i $),$ has a complement, and following the price fall the demand for the complement increases from $40$ to $50$ units, what is the cross price elasticity? $($you must use the formula sheet attached to find the solution$).$

$5$ Marks

$($iii$)$ If a person's income increases from $20,000$ to $25,000$ and demand for the good increases from $10$ units to $15,$ what is the income elasticity of the good? $($you must use the formula sheet attached to find the solution$).$

$5$ Marks

$($iv$)$ Using indifference $-$ preference analysis, show what would happen if your income increased and you were consuming two normal goods.

$5$ Marks

$($v$)$ Using indifference $-$ preference analysis, show what would happen if your income increased and you were consuming one normal good and one inferior good.

$5$ Marks