# Economics 4351 assignment

**Problem 1 (15 points; 5 points per part) **Please define or explain the following terms. A complete answer will include a graph, equation, and/or example as part of each definition.

- Consumer surplus
- Giffen good
- Income elasticity of demand

**Problem 2 (10 points) **Yao’s weekly demand for basketballs is given by Q_{d }= 3 − P^{2 }where P is the price of basketballs. At the current price, Yao’s demand for basketballs is unit elastic. What is the current price of a basketball, and how many basketballs is Yao buying at this price?

**Problem 3 (20 points) **Each day Akiko, who is in third grade, eats lunch at school.

She likes only Twinkies (t) and soda (s), and these provide her with utility of

U(t,s) = t^{3 }· s − 3

Twinkies cost $0.15 each and soda costs $0.30 per cup at the school cafeteria. Akiko’s parents give her $1.20 each day for lunch.

- Find the marginal utility of Twinkies (MU
_{t}) and marginal utility of soda (MU_{s}) if Akiko buys t Twinkies and s sodas. - What
**two**equations must hold at the bundle (t,s) that maximizes Akiko’s utility? Solve for her optimal combination of Twinkies and sodas. - The school is considering several possible policies to curb Twinkie consumption. Among the policies being considered are (1) limiting students to one Twinkie per day; and (2) raising the price of Twinkies to $45 each. The PTA (Parent-Teacher Association) has hired you to guide its decision. Discuss the expected effects of these two policies, using graphs and/or equations, as appropriate. (You may assume that all students have preferences identical to Akiko’s.) Which policy will you recommend?

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**Problem 4 (20 points) **Jacques gets utility from atoms and molecules. Last week, Jacques had a weekly income of $150, and the price of atoms was $12. Jacques consumed seven atoms and eleven molecules. This week, the price of a molecule is $10; Jacques’s income and the price of atoms are unchanged. Suppose Jacques consumes six molecules this week.

- Indicate both budget constraints and both bundles on a well-labeled graph, with atomson the x-axis.
- Is Jacques better off or worse off this week relative to last week? Explain.
- Are atoms and molecules complements or substitutes for Jacques? Explain.
- Next week, prices are expected to be the same as this week, but Jacques’s incomeis expected to increase to $ Add this future budget constraint to your graph. Relative to last week, will Jacques be better off next week, worse off, or can’t you tell? Explain.

**Problem 5 (10 points) **After observing Olga’s consumption choices for two days in a row, Pavel, an economics student, tells here: “You must not be rational. Yesterday, when bananas were on sale for $1 and peaches were $5, you bought five bananas and one peach. Today, bananas are back to $2 and peaches are still $5, and you’re still buying five bananas!”

- Show graphically Olga’s budget constraint and chosen bundle from yesterday.
- Are there any explanations other than irrationality that are consistent with Olga’sbehavior? Use words, diagrams, and equations in your answer.

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