Ms Smith likes to drink wine; in particular, a french bordeaux (ƒ) at $40 per bottle and a California varietal wine (c) priced at $8. She allocates $600 to these two each month; and her utility is: U(ƒ, c) = ƒ²/³c¹/³ (a) Write out her (constrained) utility maximization problem. Solve for the optimal consumption of wine f and c. (b) Suppose the price of f falls to $20, but c continues to be priced at $8. How much
Ms Smith likes to drink wine; in particular, a french bordeaux (ƒ) at $40 per bottle and a California varietal wine (c) priced at $8. She allocates $600 to these two each month; and her utility is: U(ƒ, c) = ƒ²/³c¹/³ (a) Write out her (constrained) utility maximization problem. Solve for the optimal consumption of wine f and c. (b) Suppose the price of f falls to $20, but c continues to be priced at $8. How much
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Only part C. Thank you!
![**Exercise 3***
Ms. Smith enjoys drinking wine, specifically a French Bordeaux \((f)\) priced at $40 per bottle and a California varietal wine \((c)\) priced at $8 each. She dedicates $600 to these two types of wine every month. Her utility function is given by:
\[ U(f, c) = f^{2/3}c^{1/3} \]
**Tasks:**
(a) Formulate her (constrained) utility maximization problem. Solve for the optimal consumption of wines \( f \) and \( c \).
(b) Assume the price of \( f \) decreases to $20, while \( c \) remains priced at $8. Determine the quantities of each wine she will purchase under these new conditions.
(c) Calculate the monetary value associated with the increased utility derived in part (b).
*[Hint: You can determine either the Equivalent Variation (the additional income an individual is willing to receive instead of the price reduction) or the Compensating Variation (the amount of money an individual is willing to give to remain as well off as before the price reduction)]*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc3585354-64d7-4f4a-b055-4a9b75b3799d%2F87d1f75a-c0c9-478a-a6a5-98adfd2c0670%2F7ntb6x7_processed.png&w=3840&q=75)
Transcribed Image Text:**Exercise 3***
Ms. Smith enjoys drinking wine, specifically a French Bordeaux \((f)\) priced at $40 per bottle and a California varietal wine \((c)\) priced at $8 each. She dedicates $600 to these two types of wine every month. Her utility function is given by:
\[ U(f, c) = f^{2/3}c^{1/3} \]
**Tasks:**
(a) Formulate her (constrained) utility maximization problem. Solve for the optimal consumption of wines \( f \) and \( c \).
(b) Assume the price of \( f \) decreases to $20, while \( c \) remains priced at $8. Determine the quantities of each wine she will purchase under these new conditions.
(c) Calculate the monetary value associated with the increased utility derived in part (b).
*[Hint: You can determine either the Equivalent Variation (the additional income an individual is willing to receive instead of the price reduction) or the Compensating Variation (the amount of money an individual is willing to give to remain as well off as before the price reduction)]*
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