2018SpringUN3213Lecture8ConsumptionSaving (1).pdf

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Intermediate Macroeconomics Economics UN3213 Professor: Jón Steinsson Lecture 9 1
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Announcements Readings: Today: Jones ch 16 (ch 15 in 2 nd edition) Next week: Jones ch 3, Levitt-Dubner, Mankiw, Thompson, Dell’Antonia, Hodgekiss. 2
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The Consumption-Savings Model Suppose Robinson Crusoe lives for two periods Let’s simplify by ignoring both production and labor-leisure decision Instead: Robinson Crusoe gets a set endowment of coconuts in each of the two periods Denote them as 𝑌𝑌 1 and 𝑌𝑌 2 Robinson Crusoe knows values of both 𝑌𝑌 1 and 𝑌𝑌 2 in period 1 3
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A Storage Technology In addition, Robinson Crusoe has access to a “savings technology” (safe investment opportunity) He can choose to save some of 𝑌𝑌 1 If he saves 𝐵𝐵 coconuts at time 1, the savings technology yields 1 + 𝑅𝑅 𝐵𝐵 coconuts at time 2 We say that the savings technology has a gross return of 1 + 𝑅𝑅 and a net return of 𝑅𝑅 𝑅𝑅 is the “interest rate” in the economy 4
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Saving and Borrowing Suppose that the “savings technology” is such that Robinson Crusoe can either “save” coconuts or “borrow” coconuts We can think of the savings technology as borrowing and lending with a neighboring islander (i.e., Friday) If Robinson Crusoe borrows, 𝐵𝐵 < 0 In both cases, the return is 𝑅𝑅 (for simplicity) 5
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The Consumption-Savings Model Robinson Crusoe’s resource constraints (budget constraints) are then: In period 1? In period 2? 6 𝐶𝐶 1 + 𝐵𝐵 = 𝑌𝑌 1 𝐶𝐶 2 = 𝑌𝑌 2 + 1 + 𝑅𝑅 𝐵𝐵
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Limits on Saving and Borrowing What are reasonable limits of saving and borrowing? What is the most Robinson Crusoe can save? 𝐵𝐵 < 𝑌𝑌 1 What is the most Robinson Crusoe can borrow? As much as he can pay off in period 2: 1 + 𝑅𝑅 𝐵𝐵 > 𝑌𝑌 2 which implies 𝐵𝐵 > 𝑌𝑌 2 1+𝑅𝑅 7
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Utility Function In general, Robinson Crusoe’s utility function can be written 𝑈𝑈 𝐶𝐶 1 , 𝐶𝐶 2 We will, however, specialize and consider the utility function 𝑈𝑈 𝐶𝐶 1 + 𝛽𝛽𝑈𝑈 𝐶𝐶 2 Here, 𝛽𝛽 is called Robinson Crusoe’s subjective discount factor 8
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Interpretation of 𝛽𝛽 Robinson Crusoe’s utility function: 𝑈𝑈 𝐶𝐶 1 + 𝛽𝛽𝑈𝑈 𝐶𝐶 2 𝛽𝛽 is the weight Robinson puts on future consumption relative to current consumption If 𝛽𝛽 < 1 , Robinson Crusoe down-weights (discounts) future consumption 𝛽𝛽 governs Robinson Crusoe’s degree of patience If period length is one year, a typical value used is something like 𝛽𝛽 = 0.98 9
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Consumption-Savings Model Robinson Crusoe maximizes 𝑈𝑈
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