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Microeconomics Exercises

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Submitted By telmabatista
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Microeconomics

Topics covered I. Optimal choice II. Comparative statistics

1. You receive from your parents 180 € per month to cover living expenses. You spend the entire amount on pizzas P and phone calls C . Your utility function is represented by the following expression: U P; C

3P 2 C 100 , where P is the number of pizzas

consumed, and C is the number of hours of phone calls. Each pizza costs 8€, whereas the price of one hour of phone calls is 2€. a) How many pizzas and hours of phone calls will you consume?

Now your parents no longer send you the 180€ per month. Instead, they send you 20 coupons that you can trade for one pizza each, plus a 20€ check per month. You cannot use the coupons to pay your phone bill. b) Has your optimal bundle changed? Justify without doing any additional calculations. If so, what is your new optimal bundle? c) Are you better off or worse off than before? Justify you answer by intuition and calculations. d) Redo part b) if what your parents send you is 5 coupons plus a 140-€ check per month. e) Go back to your initial situation (your parents were giving you 180 € cash) and suppose that they decided to increase your allowance to 200 €. How would this affect your demand for pizzas? And your optimal choice?

2. Madalena considers peach juice and orange juice to be perfect substitutes. She spends
5€ a month on these two goods. Initially, the price of peach juice is 1€/L and the price of orange juice is 1.25€/L. Then, the price of peach juice increases to 1.5€/L. The income that Madalena allocates to juice does not change, however. a) How does Madalena’s consumption change when the price of peach juice changes? b) Show the effect of the price change on the utility level attained by Madalena. Represent it graphically. c) How much must her income increase in order to allow her to reach the original utility level? d) Derive and graph the demand curve for orange juice, both for the case when the price of peach juice is 1€ and for the case when the price of peach juice is 1.5€. e) Derive and graph the Engel curve for orange juice (under the assumption that the price of peach juice is 1.5€ /L).

3. In her economics course, Ana takes two examinations. Her overall grade for the course will be the maximum of her scores on the two examinations. Ana decides to spend a total of 400 minutes studying for these two examinations. If she spends m1 minutes studying for the first examination, her score on this exam will be x1

m1 . If she 5

spends m2 minutes studying for the second examination, her score on this exam will be

x2

m2 10
a) Obtain the expression for the time constraint that represents the various combinations of scores on the two exams that she can achieve with a total of 400 minutes of studying. Represent it graphically. On the same graph, draw the indifference map for Ana. On your graph, find the point on Ana´s constraint that gives her the best overall score in the course. b) Given that she spends a total of 400 minutes studying, which values for x1 and

x 2 Ana is going to choose?
c) Suppose now that new rules for defining the final grade are introduced. The final grade is now calculated by Grade and x 2 is Ana going to choose now?

3Min x1 , x2 . Which values for x1

4. Inhabitants of a certain town consume two goods, theatre tickets (good X) and other goods (good Y). The preferences of a representative consumer are given by U(x,y)=y+20 x0,5. The income of this consumer is M=500 and the price of good y is p y =1. There is only one Theatre in town and its prices are set by the Mayor. 1. Are these preferences well-behaved? Justify. 2. Sketch the indifference map of this individual. What is the distinctive graphical characteristic of these indifference curves? Under what conditions are these indifference curves an adequate description of the individual’s preferences? 3. Determine the individual demand functions. Assuming the Mayor fixes the Theatre price at px=2, what is the consumer’s optimal choice?

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