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(a) Construct and explain the lifetime budget constraint of a house- hold.

(a) Construct and explain the lifetime budget constraint of a house- hold.

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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(a) Construct and explain the lifetime budget constraint of a house- hold. (b) Derive and interpret the household's optimality conditions with respect to consumption and leisure in the two periods. (c) Derive the optimality conditions of the firm with respect to the labour input in the two periods. (d) Provide a definition of competitive equilibrium for this economy. (e) Imagine there is a positive temporary shock to the price of en- ergy. How can this shock be interpreted in the context of the model above? Use the solution to the model to analyse the equilibrium effects of this shock on the real interest rate, con- sumption, leisure, hours worked, profits and the real wage in both periods. Explain your answer intuitively. (f) Use a graphical analysis to separate income and substitution ef- fects. Which of these two effects prevails in equilibrium? Discuss whether the dynamics implied by shocks to the price of energy match the stylized facts of the business cycle.
Transcribed Image Text:(a) Construct and explain the lifetime budget constraint of a house- hold. (b) Derive and interpret the household's optimality conditions with respect to consumption and leisure in the two periods. (c) Derive the optimality conditions of the firm with respect to the labour input in the two periods. (d) Provide a definition of competitive equilibrium for this economy. (e) Imagine there is a positive temporary shock to the price of en- ergy. How can this shock be interpreted in the context of the model above? Use the solution to the model to analyse the equilibrium effects of this shock on the real interest rate, con- sumption, leisure, hours worked, profits and the real wage in both periods. Explain your answer intuitively. (f) Use a graphical analysis to separate income and substitution ef- fects. Which of these two effects prevails in equilibrium? Discuss whether the dynamics implied by shocks to the price of energy match the stylized facts of the business cycle.
2. Consider an economy that lasts for two periods, populated by firms and households. Markets are competitive. There is no government. Households' utility function is well-behaved and defined as U(C, 1) = u(C, 1) + Bu(C", l') where 0 < 3 < 1 is the preference discount factor, C and 1 is consumption and leisure in the first period, while C' and l' are consumption and leisure in the second period. h, the number of hours available to households, is normalised to 1. The per-period utility function is given by: u(C, 1) = Cl-n 1-n — v(1 - 1) where n > 0 and > 0. Firms produce output hiring labour from households. The first period production function is defined as Y = zNd where Y is output, Nd is the demand for labour and z is the to- tal factor productivity in the first period. Second period output is produced using the same technology as in the first period. Page 3 of 4 Copyright 2022 v01 Ⓒ University of Southampton ECON2004 W1 (a) Construct and explain the lifetime budget constraint of a house- hold. (b) Derive and interpret the household's optimality conditions with respect to consumption and leisure in the two periods.
Transcribed Image Text:2. Consider an economy that lasts for two periods, populated by firms and households. Markets are competitive. There is no government. Households' utility function is well-behaved and defined as U(C, 1) = u(C, 1) + Bu(C", l') where 0 < 3 < 1 is the preference discount factor, C and 1 is consumption and leisure in the first period, while C' and l' are consumption and leisure in the second period. h, the number of hours available to households, is normalised to 1. The per-period utility function is given by: u(C, 1) = Cl-n 1-n — v(1 - 1) where n > 0 and > 0. Firms produce output hiring labour from households. The first period production function is defined as Y = zNd where Y is output, Nd is the demand for labour and z is the to- tal factor productivity in the first period. Second period output is produced using the same technology as in the first period. Page 3 of 4 Copyright 2022 v01 Ⓒ University of Southampton ECON2004 W1 (a) Construct and explain the lifetime budget constraint of a house- hold. (b) Derive and interpret the household's optimality conditions with respect to consumption and leisure in the two periods.
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