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ECON 352D1 Lecture Notes - Lecture 4: Macroeconomic Model, Risk Aversion, Profit MaximizationExam

Course Code
ECON 352D1
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Econ 352 2018
4. A One-Period Model of the Macroeconomy: The
Work-Leisure Decision and Profit Maximization (Ch. 4
and part of Ch. 5)
As you will see most of the analysis in this and the next two chapters has a strong
microeconomic flavor. This approach has become the dominant paradigm, at least, since
the 1980s. Before that, macroeconomics was mostly empirical. Macroeconomists
postulated some ad-hoc relationships among variables (for instance, private consumption
depends on the level of government expenditure), estimate these relationships (regress
changes in consumption on current changes in government expenditure and its lags), and
then use these estimates for policy purposes (i.e. provide some projections for the
stimulus effects on consumption, or overall demand, of a given public infrastructure
Ad hoc decision rules based on preferences and technology
Decision rules + Policy
This approach somehow presumes that the past is very informative about the future
and, intuitively, one would expect this to be the case in relatively stable environments.
Since the 1980s macroeconomists have followed a slightly different approach.
As before, the primitives of the analysis are preferences and technology. But, although
these primitives are still invariant to policy, the decision rules derived from preferences
and technology are not invariant to policy. This implies that the decision rules derived
under a certain policy environment (the past) are not very informative if we are interested
in the effects of a new and different policy (the future). In this view, the effects of public
expenditure should depend on whether this expenditure complements or substitutes
private consumption, whether the expenditure does affect the productive capacity of
firms, whether it is financed through taxes or borrowing, whether the change in
expenditure is permanent or only temporary, what does the public expect about the future
economic conditions, what are their attitudes towards risk and uncertainty…1 As a result
modern macroeconomics has become more theoretical and models are used as
laboratories where the effects of alternative policies are assessed.
1 This would require estimate individual responses under the proposed policy package or alternatively to
estimate deep (structural or relatively invariant) preference and technological parameters such as the
elasticity of substitution between private and public consumption, the output elasticity of public
expenditure, the elasticity of substitution between private and public capital, measures of individual risk
aversion, expectations about income and demand prospects, measures of the willingness to sacrifice current
for future rewards,… Using these estimates, together with a model of optimal choice, the optimal responses
of individual and firms, the decision rules, will be derived under the proposed policy environment,
assuming agents will respond optimally, on their best-perceived interest, to the policy in question.

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Econ 352 2018
Preferences + Technology + Policy
Decision rules
Specifically, in this first chapter we will look at a static model of consumption
and leisure. In the following chapter we will present a two-period model of consumption
and saving. Finally, in the last chapter we will combine the insights of the previous two
models into a complete two-period model with consumption, leisure, and investment. The
second term of the course will explore variations of this complete model.
4.1 A one-period model of consumption and leisure.
Our goal is to build a macroeconomic model from a description of consumers’
and firms’ choices. Consumer choices result from consumers’ objectives, preferences
and the constraints they face, while firm choices are the result of firms’ objectives and
the technology they have access to. In our basic model consumers will sell labor and
buy consumption goods and firms will produce goods using labor as an input.
Although the framework and analysis will resemble that used in
microeconomics, eventually we will determine prices as an endogenous object, such
that the decisions of market participants, households and firms, are consistent with one
another. Nonetheless we will begin by characterizing the behavior of households and
firms under the (most likely true) assumption that they take prices as given, since no
individual household or firm have enough market power to affect prices. The result will
be a set contingent rules that summarize the behavior of households and firms (how
much to work at different wages, how much to consume at different prices, and the like).
However, at the end of the day, these prices will be determined by the aggregate
behavior of all the firms and households in the economy.
We will begin with a one-period model, which by definition is static (as opposed
to dynamic). Many principles that we will learn in this simple, although unrealistic,
environment will extend to dynamic models.

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Econ 352 2018
4.1 The consumer problem
Consumer’s preferences are defined over two goods: consumption,
, and
, i.e. time spent not working in the market. Notice that the second is not a
physical good although it will be treated as such.
The utility function, equation (1), summarizes the tastes of consumers. This equation is
also known as the happiness, preference or felicity function.
( ) ( )
11 2 2
,,UCl UC l>
the consumer prefers bundle 1 to bundle 2 or he is better
off consuming bundle 1 than consuming bundle 2, or if he could afford both he would
choose 1.
We assume away any heterogeneity in tastes assuming all consumers are
identical (this seems a sensible assumption at the aggregate level, since individual
differences will tend to cancel out), this allows to use a representative agent, i.e. a
fictional agent that aggregates the individual choices of all of those identical consumers.
Let’s begin with some desirable features of preferences (axioms or self-evident
propositions) and let’s use these features to place restrictions on the (mathematical) shape
of (1).
1. More is always preferred to less
2. The consumer likes diversity (to some degree)
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