Donald Derives Utility from Only Two Goods, Carrots (Qc) and Donuts

question 65

Essay

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.

---

Definitions:

Scientific Method

A systematic process for investigating phenomena, acquiring new knowledge, or correcting and integrating previous knowledge, based on empirical or measurable evidence.

Functional Fixedness

A cognitive bias that limits a person to using an object only in the way it is traditionally used.

Representative Heuristic

A mental shortcut that involves making judgments based on how well something matches existing prototypes or stereotypes in our minds.

Heuristics

Mental shortcuts or rules of thumb that simplify decision making, often leading to a solution that is good enough rather than perfect.