Matthias Doepke - Marcroeconomics - Chapter 3 ppsx
Matthias Doepke - Marcroeconomics - Chapter 3 ppsx
... )=
1
[
2
+
1
(1 + )]
(1 + )(1 + )
so we set the left-hand side to zero and solve for :
1
=
[
2
+
1
(1 + )]
(1 + )(1 + )
(3. 11)
3. 2 A Two-Period Model
23
3.2 A Two-Period Model
We begin this section with ... consumptions
.
Exercises
Exercise 3. 1 (Hard)
Consider the two-period model from Section 3. 2, and suppose the period utility is:
( )=
1
2
3. 3 An Infinite-Period Model
29
Simple m...
Matthias Doepke - Marcroeconomics - Chapter 1 docx
... we get:
$ 135
=( )($ 130 )(1) + $ 130 so:
= $ 135 $ 130 1 1 038 46154 1 =38 46154%
As another example, to calculate the annual rate of growth of GDP, compounded annually,
between 1991 and 19 93, we use ... is two years.
$ 135
=
2
($100 ) so:
= [ln($ 135 ) ln($100 )](0 5) 0 15005 230 = 15 15005 230 %
Economists generally prefer to use continuous compounding, for two reasons. First, un-
der c...
Matthias Doepke - Marcroeconomics - Chapter 2 docx
... problems of constrain-
ed maximization when it is either difficult or impossible to solve the constraints for indi-
vidual variables. At first we treat the method as a cook-book recipe. After we ... substituting the second constraint
into the first.
2 .3 Crusoe’s Choices
13
There are two principal ways to solve such a problem. The first is to substitute any con-
straints into the objective. T...
Matthias Doepke - Marcroeconomics - Chapter 5 pptx
... results in this chapter rest
solely on the general structure of the market-clearing model. We are now ready to define
an equilibrium for this economy along the lines developed in Chapter 3.
An allocation ... case, the budget constraint would be interpreted
as a present-value budget constraint, as introduced in Chapter 3. We can also incorpo-
rate uncertainty, in which case different g...
Matthias Doepke - Marcroeconomics - Chapter 6,7 doc
... endowment
in the model from Chapter 3.
The household’s maximization problem is:
max
1
2
1
2
1
(
1 1
)+ (
2 2
) subject to:
(
1
)=
1
+
1
and:
(
2
)+
1
(1 + )=
2
Refer to Chapter 3 for a discussion of: ... formula for into equation (6 .3) gives us:
=
1
1
=
1+
1
1
1
=
1+
Chapter 6
The Labor Market
This chapter works out the details of two separate models. Section 6.1 contains a one-...
Matthias Doepke - Marcroeconomics - Chapter 8 pdf
... inflation that we
will pick up later in this book. Chapter 18 is concerned with the coordination of monetary
8 .3 A Cash-in-Advance Economy
61
8 .3 A Cash-in-Advance Economy
In this section we derive the ... monetary pol-
icy. While the prime emphasis of the cash-in-advance model is the inefficiency of holding
cash instead of interest-bearing assets, Chapter 19 turns to the issue of expec...
Matthias Doepke - Marcroeconomics - Chapter 9 doc
... single shock has long-run effects, and investment goes through a full cycle in
response to this shock.
Response to a Single Shock
-0 .01
-0 .005
0
0.005
0.01
0.015
0.02
0.025
1 234 5678
Periods
Deviation ... entire post-war history of the United States and the Western European
countries there is not a single depression that caused an output loss similar to the one suf-
fered between 192...
Matthias Doepke - Marcroeconomics - Chapter 11 pot
... production function equa-
tion (11.1) exhibits constant returns to scale, which means that if we double both inputs,
output also doubles. Our choice of a constant-returns-to-scale production function ... with
1
See Chapter 1 for a discussion of growth rates and how to compute them.
Chapter 11
Economic Growth
This chapter examines the determinants of economic growth. A startling fact abo...
Matthias Doepke - Marcroeconomics - Chapter 12 pdf
... economies is 0
34 36 and 0 30 33, respectively.
What happens if we endow the representative consumer with an initial capital stock
0
=
0
03, which is far below the eventual steady-state level? We ... and the dotted line as-
suming they affect output as in equa-
tion (BC1).
0 5 10 15 20 25 30 35 40
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Interest rate
time t
r(t)
Figure 12 .3: Time path of inter...
Matthias Doepke - Marcroeconomics - Chapter 13 docx
... change in government
revenue, or:
( 13. 3)
(
[
max
(
0
)
]
[
max
(
0
)
0
]
)
(
[
max
(
1
)
]
[
max
(
1
)
1
]
)
(
1
) (
0
)
Recall that ( )=
[
max
( );
]
. Equation ( 13. 3) is true only if:
[
max
(
0
)] ... Labor
139
0 0.1 0.2 0 .3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.05
0.1
0.15
0.2
0.25
Tax revenue when γ=0.5
τ
T(τ)
Figure 13. 1: A government revenue func-
tion that exhibits a Laffer curve.
A...
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