$1.$ Suppose that a consumer has a utility function u$($x$1$; x$2)=$ x$1+$ x$2.$ Initially the consumer faces prices $(1$; $2)$ and has income $10.$ If the prices change to $(4$; $2)$; calculate the compensating and equivalent variations. $[[$ans: Since the two goods are perfect substitutes, the consumer will initially consume the bundle $(10,0)$ and get a utility of $10.$ After the prices change, she will consume the bundle $(0,5)$ and get a utility of $5.$ After the price change she would need $$20$ to get a utility of $10$; therefore the compensating variation is $2010=10.$ Before the price change, she would need an income of $5$ to get a utility of $5.$ Therefore the equivalent variation is $105=5$: