Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Question
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.
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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