Zeynep is at the supermarket buying her bi-weekly groceries. As she arrived at the store right before closing, not much is left on the shelves; so her purchases are limited to beef, B, and an assortment of organic vegetables, V. Beef costs £50/kg and vegetables Ł10/kg. Her utility function is expressed as U(B,V) = B0.6v°.3. She has £150 to spend. Please answer the following questions using this information: %3D A) Given the vegetables cost less than beef, explain why Zeynep would not only buy vegetables. B) Write Zeynep's constrained maximization problem (objective function subject to her budget constraint). C) Using the Lagrangian technique, find how much beef and vegetables would Zeynep buy?

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Zeynep is at the supermarket buying her bi-weekly groceries. As she arrived at the store right
before closing, not much is left on the shelves; so her purchases are limited to beef, B, and an
assortment of organic vegetables, V. Beef costs £50/kg and vegetables Ł10/kg. Her utility function
is expressed as U(B,V) = B0-6v0.3. She has ±150 to spend. Please answer the following questions
using this information:
A) Given the vegetables cost less than beef, explain why Zeynep would not only buy
vegetables.
B) Write Zeynep's constrained maximization problem (objective function subject to
her budget constraint).
C) Using the Lagrangian technique, find how much beef and vegetables would
Zeynep buy?
D) Show that for the preferences represented as above, demand for beef is a function
of only its own price, pg, and income, m, but not the price of vegetables, py. Note: Rather
than using the given prices and income, use PB, Py and m. Find and comment on the
comparative statics, i.e., how do changes in income and prices affect the demand for beef?
E) What is the degree of homogeneity of the beef demand function you found in part
(d)?
F) Suppose there is a promotion for beef and the price falls to Ł40/kg. Calculate the
compensated income, m°, for Zeynep to consume the same amount of beef and vegetables
under the new prices. Under the promotional price, how much beef does Zeynep buy?
Decompose the change in her demand for beef into substitution and income effects using
Slutsky decomposition. Comment on signs of these effects, i.e., is beef a normal or an inferior
good for Zeynep?
Transcribed Image Text:Zeynep is at the supermarket buying her bi-weekly groceries. As she arrived at the store right before closing, not much is left on the shelves; so her purchases are limited to beef, B, and an assortment of organic vegetables, V. Beef costs £50/kg and vegetables Ł10/kg. Her utility function is expressed as U(B,V) = B0-6v0.3. She has ±150 to spend. Please answer the following questions using this information: A) Given the vegetables cost less than beef, explain why Zeynep would not only buy vegetables. B) Write Zeynep's constrained maximization problem (objective function subject to her budget constraint). C) Using the Lagrangian technique, find how much beef and vegetables would Zeynep buy? D) Show that for the preferences represented as above, demand for beef is a function of only its own price, pg, and income, m, but not the price of vegetables, py. Note: Rather than using the given prices and income, use PB, Py and m. Find and comment on the comparative statics, i.e., how do changes in income and prices affect the demand for beef? E) What is the degree of homogeneity of the beef demand function you found in part (d)? F) Suppose there is a promotion for beef and the price falls to Ł40/kg. Calculate the compensated income, m°, for Zeynep to consume the same amount of beef and vegetables under the new prices. Under the promotional price, how much beef does Zeynep buy? Decompose the change in her demand for beef into substitution and income effects using Slutsky decomposition. Comment on signs of these effects, i.e., is beef a normal or an inferior good for Zeynep?
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