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Consider the two-period model we studied in class. There are N consumers in rent and future periods. A consumer has preferences given by u(c, c) = ln(c) + 3c, c> 0 is current-period consumption, c'> 0 is future-period consumption, 3 € (0,1) count factor. Each consumer decides c and c' through savings s. She receives income pays off lump-sum taxes t in the current period. In the future period, she receives ay and pays off lump-sum taxes at, where a > 0 is constant. The market real trate is r₁ > 0. The government finances its expenditure G in the current period by ng lumpsum taxes from consumers and by issuing one-period government bonds B to

Consider the two-period model we studied in class. There are N consumers in rent and future periods. A consumer has preferences given by u(c, c) = ln(c) + 3c, c> 0 is current-period consumption, c'> 0 is future-period consumption, 3 € (0,1) count factor. Each consumer decides c and c' through savings s. She receives income pays off lump-sum taxes t in the current period. In the future period, she receives ay and pays off lump-sum taxes at, where a > 0 is constant. The market real trate is r₁ > 0. The government finances its expenditure G in the current period by ng lumpsum taxes from consumers and by issuing one-period government bonds B to

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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II. Consider the two-period model we studied in class. There are N consumers in the current and future periods. A consumer has preferences given by u(c, c') = ln(c) + 3c, where c> 0 is current-period consumption, c'> 0 is future-period consumption, 3 € (0,1) is a discount factor. Each consumer decides c and c' through savings s. She receives income y and pays off lump-sum taxes t in the current period. In the future period, she receives income ay and pays off lump-sum taxes at, where a > 0 is constant. The market real interest rate is r₁ > 0. The government finances its expenditure G in the current period by collecting lumpsum taxes from consumers and by issuing one-period government bonds B to consumers. In the future period, it finances its expenditure aG, and interest-bearing bond payments from collecting lumpsum taxes. Assume that y-t > 1/3(1+r) and a € (0, 1+1/r) for any r. Show your work on each question and explain your results. Define a competitive equilibrium as precisely as possible. CAREFULLY depict (c*,c*, s*) on a diagram and find the equilibrium condition. Is the consumer a lender or a borrower? 1. 2. 3. Suppose that the interest rate r decreases from r₁ to 7₂. Then, carefully determine the effects on (c*,c*, s*) on a diagram. Explain your results in terms of the income and intertemporal substitution effect.
Transcribed Image Text:II. Consider the two-period model we studied in class. There are N consumers in the current and future periods. A consumer has preferences given by u(c, c') = ln(c) + 3c, where c> 0 is current-period consumption, c'> 0 is future-period consumption, 3 € (0,1) is a discount factor. Each consumer decides c and c' through savings s. She receives income y and pays off lump-sum taxes t in the current period. In the future period, she receives income ay and pays off lump-sum taxes at, where a > 0 is constant. The market real interest rate is r₁ > 0. The government finances its expenditure G in the current period by collecting lumpsum taxes from consumers and by issuing one-period government bonds B to consumers. In the future period, it finances its expenditure aG, and interest-bearing bond payments from collecting lumpsum taxes. Assume that y-t > 1/3(1+r) and a € (0, 1+1/r) for any r. Show your work on each question and explain your results. Define a competitive equilibrium as precisely as possible. CAREFULLY depict (c*,c*, s*) on a diagram and find the equilibrium condition. Is the consumer a lender or a borrower? 1. 2. 3. Suppose that the interest rate r decreases from r₁ to 7₂. Then, carefully determine the effects on (c*,c*, s*) on a diagram. Explain your results in terms of the income and intertemporal substitution effect.
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