John's quasi-linear utility function is (, ) = + ln where , are the quantities consumed per month of the only two goods he buys.

(a) Find John's demand functions for x and y.

(b) If John's income is $100 per month and px = $20 and py = $5, how much of each good would John buy per month?

(c) Find John's compensated demand function for x.

(d) Using your answers to (a) and (c), verify the elasticities form of the Slutsky equation for x.