Reference no: EM133195720

Assignment:

Question 1. Jen likes only chocolate and economics textbooks. Her demand functions for chocolate and textbooks are given by

Q_c = I/ p_c + p_t

Q_t = I/ p_c + p_t

where I denotes her income and p_c and p_t the price of chocolate and textbooks respectively.

a. Are chocolate and textbooks complements or substitutes for Jen?

b. Is chocolate a normal good?

c. Assume we observe the following: Q_t = 5, p_c = 2, p_t = 2.

If the price of textbooks doubles, by how much does the income have to increase to keep the textbook consumption constant? What happens to chocolate consumption? Explain.

Question 2. Remember Alexander, the frequent traveller who likes economics textbooks? He has an income of $750 to spend on air travel and economics textbooks. Currently, air travel costs $100 and economics textbooks $50. Due to increased environmental regulation, the price of airfare increases to $150.

a. Assume Alexander has smooth and convex indifference curves. Depict his initial and new consumption decisions. Put air travel on the x-axis.

b. Decompose the change in air travel consumption into a substitution and an income effect, assuming both goods are normal goods.

c. In a new diagram, decompose the change in air travel consumption into a substitution and an income effect, assuming that textbooks are inferior goods.

d. Redo (a) and (b), putting air travel on the y-axis.

Question 3. Max is on a trip to Italy where he cannot find any chicken wings - but instead he discovered his love for tiramisu (which he still likes to consume with beer).

His preferences over beer and tiramisu are given by min {2b; 5t} ;

where b denotes the liters of beer and t the servings of tiramisu consumed by Max. Max's parents gave him an allowance to spend on the trip of I = 100, the price of beer is pb = 10 and the price of tiramisu is pt = 5.

a. Analytically derive Max's optimal consumption point.

Depict Max's budget line and optimal consumption point in a well-labelled diagram (beer is the x-axis good).

His Eurotrip also brings him to Germany where beer is much cheaper: pb˜ = 5.

b. Derive analytically and show in the same diagram Max's new optimal consumption point.

c. Decompose the change in beer consumption into a substitution and an income effect.

d. By how much could his parents reduce his allowance without making him worse off, compared to his time in Italy?

Question 4. The Consumer Price Index (CPI) tracks the average cost of a fixed bundle of goods over time; the resulting inflation rate is regularly used to compute cost-of-living adjustments (e.g. for pensions).

Explain in words and using an appropriate diagram why a cost-of-living adjustment based on CPI makes recipients better off if the prices of the goods in the CPI change at different rates (e.g. the price of shoes increase by 10% but the price of pants remains constant).

Question 5. Florian works as a waiter in a restaurant. He earns $10 per hour and he is free to work as many hours as he likes. Florian has no other source of income.

a. Derive Florian's budget line representing the trade-off between leisure and consumption, and draw it in a well-labelled diagram. (Take the time period to be one week, 168 hours.)

Florian decides to work 30 hours/week. However, because it's a busy week, the owner offers him an extra $5 for every additional hour he stays at work.

b. Derive the new budget line. Is Florian going to work more hours now? Assume now that the owner makes him work at least 30 hours every week.

c. In this case, is it possible that Florian would choose not to work more hours when offered the $5 bonus?