Suppose that an individual gains utility from Consumption today (c) and Consumption tomorrow (C). There are...
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Suppose that an individual gains utility from Consumption today (c₁) and Consumption tomorrow (C₂). There are only two periods - today and tomorrow. The individual gains utility from consumption in each of these periods according to their utility function: U(C₁, C₂) = C₁ ¹/2c₂¹/2 Assume also that this individual has income in both periods. an income today (m₁) = $100 and an income tomorrow (m₂) = $200. An individual can always borrow $1 today, at the cost of $1(1+r) tomorrow, or can always save $1 today and receive $1(1+r) tomorrow. The interest rate (r) is equal to 20%. 15. Write down this individual's budget constraint. [1 point] 16. What is this individual's current utility-maximizing choice of c; and c₂? Show your work. [2 points] Suppose now that the interest rate increases to 40%. 17. What is this individual's new utility-maximizing choice of c, and c₂? How much of this change in c₁ and c₂ can be attributed to the substitution effect and how much to the income effect? Use the Hicksian Decomposition for these calculations. Show your work. [3 points] Suppose that an individual gains utility from Consumption today (c₁) and Consumption tomorrow (C₂). There are only two periods - today and tomorrow. The individual gains utility from consumption in each of these periods according to their utility function: U(C₁, C₂) = C₁ ¹/2c₂¹/2 Assume also that this individual has income in both periods. an income today (m₁) = $100 and an income tomorrow (m₂) = $200. An individual can always borrow $1 today, at the cost of $1(1+r) tomorrow, or can always save $1 today and receive $1(1+r) tomorrow. The interest rate (r) is equal to 20%. 15. Write down this individual's budget constraint. [1 point] 16. What is this individual's current utility-maximizing choice of c; and c₂? Show your work. [2 points] Suppose now that the interest rate increases to 40%. 17. What is this individual's new utility-maximizing choice of c, and c₂? How much of this change in c₁ and c₂ can be attributed to the substitution effect and how much to the income effect? Use the Hicksian Decomposition for these calculations. Show your work. [3 points]
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Financial Management Principles and Applications
ISBN: 978-0134417219
13th edition
Authors: Sheridan Titman, Arthur J. Keown, John H. Martin
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