4. [2010-1 Mid-term exam] Donald derives utility from only two goods, carrots () and donuts (9). His utility function is given as follows : UV = %2 Donald has an income (I) of $120 and the price of carrots () and donuts (%) are both $1. (a) What quantities of and / will maximize Donald's utility? (b) Holding Donald's income and % constant at $120 and $1, respectively, what 1s Donald's demand function for carrots? (c) Suppose that a tax of $1 per unit is levied on donuts, while the price of a carrot remains at $1. How will this alter Donald's utility maximizing market basket of goods? How much amount of tax will he have to pay for his consumption of donuts? [levy: vt. (M2 s=) Fo[E oIt ] (d) Suppose that, instead of the per unit tax in (c), a lump sum tax of the same dollar amount that Donald paid in (c) is levied on Donald. What is Donald's utility maximizing market basket? [lump sum: n. ZA|Z(E X|Z5t= =2U)]