# Microeconomics Problem Set

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I need the questions in file to be solved with answers and solutions.

Try to give short, but precise answers, and always justify your solutions.

In any case, you are asked to identify all your collaborators on the front page of your solution. If you obtain a solution through research (e.g., on Internet), you must acknowledge your source (on page 2 of this PDF) and write up the solution in your own words. If you have solved the problem set without consulting any sources, write “none”.

1. According to my *Kindle*, Cunningham’s novel “The hours” typically takes 3 hours and 39 minutes to read. Daldry’s movie, based on the book, runs for 1 hour and 54 minutes. Assume that these numbers are representative for reading novels and watching movies in general.

(a) Considering the time spent, what is the price of reading a novel in terms of watching a movie? 1 point

2. Your grandma buys you a hideous-looking sweater for ¥8000 and gives it to you. In her opinion it was worth even more than ¥8000. You value it at only ¥500 and can sell it on *Mercari *for ¥2000.

(a) Would you rather have had the ¥8000 in cash? 1 point

(b) How much richer does the gift make you? 1 point

3. When in Spain, Mario spends a monthly income of €100 in the following way:

· Bread

– Price of bread: €2 / kilogram

– How much bread Mario buys: 20 kilograms

– Therefore, how much he spends on bread: €40

· Wine

– Price of wine: €5 / bottle

– How much Mario buys: 12 bottles – How much he spends on wine: €60

Now he moves to France, where he spends €110 on bread and wine. But he spends it this way:

· Bread

– Price of bread: €3 / kilogram

– How much bread Mario buys: 22 kilograms

– Therefore, how much he spends on bread: €66

· Wine

– Price of wine: €4 / bottle

– How much Mario buys: 11 bottles – How much he spends on wine: €44

(a) When in Spain, earning €100 and facing the Spanish prices, could he have bought the French bundle (that is, 22 kilograms of bread and 11 bottles of wine)? 1 point

(b) Apparently, then, which bundle does he prefer? 1 point

(c) When in France, could he have bought the Spanish bundle? 1 point

(d) According to the evidence of part (c), which bundle does he prefer? 1 point

(e) Is Mario consistent between Spain and France? 1 point

4. Zsuzsanna is a consumer of housing and food with a *Cobb-Douglas *utility function, that is, U(H,F) = HαFβ, where α and β are positive constants.

(a) Will Zsuzsanna increase her consumption amounts of housing and food in proportion to increases in her income (prices held constant)? Justify your answer mathematically. 1 point

(b) Will Zsuzsanna spend the same shares of her income on housing and food regardless of their prices or her income? Justify your answer mathematically. 1 point

5. For the sake of this exercise, let’s accept interpersonal comparisons of utility based on identical curves of the marginal utility of income. Let’s also assume that the sum of utility lost due to income taxation is to be as small as possible.

Now consider Mrs. Rich and Mrs. Poor, with income levels that are in line with surnames.

(a) Under the assumptions detailed above, is it true (or false) that only Rich should be taxed (unless the government wants so much tax revenue that Rich’s income is driven down to Poor’s)? 1 point

(b) What if the government wants so much tax revenue that Rich’s income is driven down to Poor’s? 1 point

6. George values only food until he has consumed 10 units of it; beyond this point he values only shelter.

(a) Sketch George’s indifference curves between food and shelter. 1 point

7. No story. Just the mathematical model of consumer choice.

Consider a consumer whose preferences are represented by the following utility function

(defined over bundles of *exes *and *whys*): u(x, y) = 2√x + y.

(a) Are the consumer’s preferences convex? 1 point

(b) Find the consumer’s marginal rate of substitution, and show that its absolute value decreases as the consumption of *exes *increases. 1 point

(c) Find the consumer’s demand function of *exes*. In other words, find her optimal consumption level of *exes *when the unit prices of *exes *and *whys *are px and py, respectively, and her income is m. 1 point

(d) Find the mathematical expression that describes the consumer’s Engel curve for *exes*, and represent it graphically. 1 point

(e) Find the mathematical expression that describes the consumer’s income-offer curve, and represent it graphically. 1 point

(f) Find the mathematical expression that describes the consumer’s demand curve for *exes*, and represent it graphically. 1 point

(g) Suppose that the government levies a per-unit tax (t) on *exes*, so that their new unit price is p′x = px + t. Show that the change in the consumer’s demand for *exes *is entirely due to the substitution effect. You are allowed to ignore corner solutions in this part of the exercise. 1 point

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