The utility that Rachel receives by consuming food F and clothing C is given by U(F, C) = FC. Rachel's has $800 to spend on the two goods the prices of food and clothing are $1 and $1 respectively. The price of food suddenly increases to $2. a) Before the price change how many food and clothing does Rachel buy? b) How many food and clothing does she buy at the new price? c) How large would Rachel's income, m', be if after the increase in prexactly could afford her old consumption bundle? d) How many food and clothing would she buy if she was faced with pr', pe and m'? e) Draw three budget lines on a graph. One illustrating the budget line before the price decrease, one after the price decrease, and finally the budget line he would face if he had income m' and the new prices. Denote his original consumption bundle by A, the final bundle by C, and the bundle she would buy at (pr', pc, m') by B. f) How large a decrease in the total demand for x is due to the income effect? and how large a decrease in the demand for x is due to the substitution effect