Donald derives utility from only two goods, carrots (Qc) and donuts (Qd). His utility function is as follows:
U(Qc,Qd) = (Qc)(Qd)
The marginal utility that Donald receives from carrots (MUc) and donuts (MUd) are given as follows:
MUc = Qd MUd = Qc
Donald has an income (I) of $120 and the price of carrots (Pc) and donuts (Pd) are both $1.
a. What is Donald's budget line?
b. What is Donald's income-consumption curve?
c. What quantities of Qc and Qd will maximize Donald's utility?
d. Holding Donald's income and Pd constant at $120 and $1 respectively, what is Donald's demand curve for carrots?
e. Suppose that a tax of $1 per unit is levied on donuts. How will this alter Donald's utility maximizing market basket of goods?
f. Suppose that, instead of the per unit tax in (e), a lump sum tax of the same dollar amount is levied on Donald. What is Donald's utility maximizing market basket?
g. The taxes in (e) and (f) both collect exactly the same amount of revenue for the government, which of the two taxes would Donald prefer? Show your answer numerically and explain why Donald prefers the per unit tax over the lump sum tax, or vice versa, or why he is indifferent between the two taxes.
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