Expert answer:Growth Formulas and Relation to Welfare

Solved by verified expert:Exercise 1
In macroeconomics there are two questions that serve as foundation to any subsequent analysis: 1) how
to measure (real) output growth? and 2) how is growth connected to wellbeing?
As for the first question, there are three ways that can be done, starting with the basic definition of
percentage difference between two numbers, say x1 compared to x0 when there is only one good (e.g.
apples). For the economy as a whole, the focus is on real GDP growth, which holds prices constant on a
given year (base year) then apply them before, during, and after that year in order to calculate the total
dollar value of all goods and services produced (i.e. we need prices to add up real quantities in dollar
terms).
In this exercise you will work out the connection between the three ways to measure GDP growth: 1. As a
percentage change holding prices constant. 2. Expressing growth in terms of a common item (converting
everything into a particular good (e.g. apples). And 3. as the weighted average of the growth in each of
the goods weighted by their expenditure shares.
The second question in macroeconomics refers to a mapping from goods and services to subjective well‐
being. Yes, there is a way.
Work out the algebraic steps to:
(1) go from the first to the second equation in slide 14;
(2) from that same top equation in slide 14 to the one in slide 15; and
(3) show the relationship in slide 16.
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Exercise 1
In macroeconomics there are two questions that serve as foundation to any subsequent analysis: 1) how
to measure (real) output growth? and 2) how is growth connected to wellbeing?
As for the first question, there are three ways that can be done, starting with the basic definition of
percentage difference between two numbers, say x1 compared to x0 when there is only one good (e.g.
apples). For the economy as a whole, the focus is on real GDP growth, which holds prices constant on a
given year (base year) then apply them before, during, and after that year in order to calculate the total
dollar value of all goods and services produced (i.e. we need prices to add up real quantities in dollar
terms).
In this exercise you will work out the connection between the three ways to measure GDP growth: 1. As a
percentage change holding prices constant. 2. Expressing growth in terms of a common item (converting
everything into a particular good (e.g. apples). And 3. as the weighted average of the growth in each of
the goods weighted by their expenditure shares.
The second question in macroeconomics refers to a mapping from goods and services to subjective well‐
being. Yes, there is a way.
Work out the algebraic steps to:
(1) go from the first to the second equation in slide 14;
(2) from that same top equation in slide 14 to the one in slide 15; and
(3) show the relationship in slide 16.
ECON 562
Macroeconomic Analysis & Public Policy
Module 1: Introduction
Copyright 2017 Montclair State University
What is Macroeconomics?
a. Definition of ‘The Economy’
b. Real vs. Nominal GDP
c. Real GDP Growth
d. Measurement of GDP (Expenditure and Income)
ECON 562
Macroeconomic Analysis & Public Policy
Module 1a: Definition of ‘The Economy’
Definition of “The Economy”
Source: Economy (c)Nick Youngson, CC BY-SA 3.0
ECON 562
Macroeconomic Analysis & Public Policy
Module 1b: Real vs. Nominal GDP
Macroeconomics
GDP stands for “Gross
Domestic Product.”
• Nominal GDP is the dollar value of all
goods and services that are produced in
the United States.
• Real GDP is a measure of the quantity
of all goods and services that are
produced.
Real vs. Nominal GDP
• Suppose everyone picks apples from trees.
• Price of an apple in year t is , .
• The number of apples picked in year t is .
• Nominal GDP in year t is , ∗ .
• Real GDP in year t is .
Real vs. Nominal GDP
Growth in nominal GDP from year t to year t+1 is
, + ∗ +
, ∗
and growth in real GDP from year t to year t+1 is
+

Real GDP increases when apples are more plentiful.
Nominal GDP increases by more than real GDP when the price of apples increases.
ECON 562
Macroeconomic Analysis & Public Policy
Module 1c: Real GDP Growth
Real GDP Growth
Then, when real GDP increases, utility has
increased.
Utility
GDP
Suppose households get utility from apples.
So in this simple example, growth in real GDP is informative
about growth in living standards (utility).
Real GDP Growth
Suppose now that households get utility from both apples and bananas.
The price of bananas in the year t is , and the number of bananas
picked is .
Nominal GDP in t is , ∗ + , ∗ .
Real GDP Growth
How do we define real GDP? And will it be informative about living
standards?
Suppose production of apples increases but production of bananas
decreases?
On net, is this bad or good?
Real GDP Growth
There are three ways to calculate real GDP growth:
Pick any arbitrary year t whose prices will be
used before, during and after, to avoid price
changes only account for quantity changes.
Express everything in terms of
one good, say, apples
(divide numerator and denominator by)
An equivalent representation.
Real GDP Growth
1. Fix a base year price,
+
, ∗ + + , ∗ +
− =
−

, ∗ + , ∗
2. Or in terms of one good, say, apples (divide numerator and denominator by , )
,
+ +
∗ +
+
,
− =
−

+ , ∗
,
In the first, real GDP is in constant year t dollars, in the second, real GDP is measured in
units of apples.
Real GDP Growth
An equivalent representation is a weighted average of the
growth in each of the goods based on their expenditure
shares.
+
+
෢
෢
− =
+ −

+
−

෢ is the fraction of nominal GDP accounted for by
where
෢ the share accounted for by
purchases of apples, and −
purchases of bananas.
Real GDP Growth
Why does real GDP growth matter? Well, suppose that households get utility from apples
and bananas every period t:
= + −
+ = + + − +
Then,
+
+ − =
+ −

+
−

෡ = , then utility increases whenever real GDP growth is positive.
So, if
ECON 562
Macroeconomic Analysis & Public Policy
Module 1d: Measurement of GDP
Measurement of GDP
C
I
G
(XM)
GDP
Measurement of GDP
C
I
G
(XM)
GDP
C = private consumption
I = private investment
G = government purchases
X = exports, M = imports, and X-M = net-exports
This is the “expenditure” approach to measuring GDP, since subdivides output into categories based on who buys the
economy’s production.
Measurement of GDP
The expenditure approach to GDP
sheds light on two often misunderstood
issues about the economy.
Trade Balance
Government Spending
Measurement of GDP
The trade balance is measured by next exports, the
difference between exports and imports: − .
And National Saving , is given by the difference
between a country’s production and what is
consumed by its households and government –not what is put away for future consumption, investment

= − − .
Measurement of GDP
This means that:
= + + + ( − ) which leads to − − = + ( − ).
Hence, = + ( − ), or − = − .
A country that runs a trade surplus (deficit) is because it saves more
(less) than what it invests; it is no related to tariffs or trade policies!
Measurement of GDP
Now the government.
For a household, its budget constraint is represented by its
disposable income, that is income net of taxes − and how
is that allocated between consumption and saving .
The portfolio choice of households can be aggregated into
(government) bonds or economy-wide (private)
investment .
Measurement of GDP
Adding up across all households, it must be the case that: +
+ = − , or + + + = .
But it is also the case that = + + , hence = + .
That is, government spending is financed by taxes and debt, and
since government debt is eventually paid back by taxes, for a
household what matters is not the timing of taxes, but the level of
government spending.
Measurement of GDP
Every time a dollar is spent a dollar is earned.
• We could have sub-divided GDP using the
“income side.”
• In practice, the difference between the expenditure
approach and the income approach is called the
“statistical discrepancy.”
Measurement of GDP
In the National Income and Product
Accounts (NIPA) income categories are
not as clean cut as the expenditure
ones.
In some entries income is clearly
associated to labor (e.g. wages and
salaries), to capital (e.g. dividends), and
some are a mix (e.g. proprietor’s
income).
Plus, there are adjustments for
depreciation and indirect taxes (to
match spending to income, for
instance).
Measurement of GDP
To sort these categories we will align to our models where capital
income and labor income are clearly distinct given that output is
produced using capital, labor, and technology.
Capital Income
Labor Income
Hence, since every dollar we spend is somebody’s income, in our
income-accounting, it will be useful to see how much output
(income) accrues to capital and how much accrues to labor.
Measurement of GDP
Let’s assume that the fraction of ambiguous income α that should be attributed to capital is
the same as the economy-wide capital share.
∗ = + ∗
This implies

=
−
The procedure produces a stable estimate for α of 0.32.
…
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