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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. For the economy, the focus is on real GDP growth, which holds prices constant on a given year (base year) the 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 quantities in dollar terms).

The second question 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 8;

(2) from that same top equation in slide 8 to the one in slide 9; and (3) show the relationship in slide 10.

3/16/2017
What is macroeconomics?
• Definition of ‘the economy’
ECON 562
Macroeconomic Analysis & Public Policy
Module 1: Introduction
• Real vs. nominal GDP
• Real GDP growth
• Measurement of GDP (expenditure and income)
• Inflation
Macroeconomics
Real vs. nominal GDP
• GDP stands for "Gross Domestic Product."
Suppose everyone picks apples from trees.
Price of an apple in year t is
• 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.
,
.
The number of apples picked in year t is
Nominal GDP in year t is
Real GDP in year t is
,
∗
.
.
.
1
3/16/2017
Real vs. nominal GDP
Real GDP growth
Growth in nominal GDP from year t to year t+1 is
Suppose households get utility from apples. Then, when real GDP increases, utility has
increased.
,
,
∗
∗
So in this simple example, growth in real GDP is informative about growth in living
standards (utility).
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.
Real GDP growth
Real GDP growth
Suppose now that households get utility from both apples and bananas.
There are three ways to calculate real GDP growth:
1. First, pick any arbitrary year t whose prices will be used before, during and after, to avoid price changes only account for quantity changes.
The price of bananas in the year t is
Nominal GDP in t is
,
∗
,
∗
,
and the number of bananas picked is
.
.
,
1
∗
,
,
∗
,
Suppose production of apples increases but production of bananas decreases? On net, is
this bad or good?
1
2. Or you can express everything in terms of one good, say, apples (divide numerator and denominator by
,
How do we define real GDP? And will it be informative about living standards?
∗
∗
1
,
,
,
,
)
∗
∗
1
In the first, real GDP is in constant year t dollars, in the second, real GDP is measured in units of apples.
2
3/16/2017
Real GDP growth
Real GDP growth
3. An equivalent representation is a weighted average of the growth in each of the goods based on their
expenditure shares.
Why does real GDP growth matter? Well, suppose that households get utility from apples and bananas
every period t:
1
1
1
1
1
where is the fraction of nominal GDP accounted for by purchases of apples, and 1
accounted for by purchases of bananas.
the share
Then,
1
So, if
1
= , then utility increases whenever real GDP growth is positive.
Measurement of GDP
Measurement of GDP
Ok, but how does it look?
Economists find it useful to disaggregate GDP (total production) into a few key components.
GDP ≡ C + I + G + (X-M)
· 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.
3
3/16/2017
Measurement of GDP
Measurement of GDP
How do these components stack up?
Going deeper.
The expenditure approach to GDP sheds light on two often misunderstood issues about the
economy.
· trade balance
· government spending
Measurement of GDP
Measurement of GDP
The trade balance is measured by next exports, the difference between exports and
imports:
.
This means that:
, is given by the difference between country’s production
and
And National Saving
and government
---not what is put away for
what is consumed by its households
future consumption, investment
.
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!
4
3/16/2017
Measurement of GDP
Measurement of GDP
Now the government.
Adding up across all households, it must be the case that:
.
For a household, its budget constraint is represented by its disposable income, that is
and saving
income net of taxes
and how is that allocated between consumption
.
The portfolio choice of households can be aggregated into (government) bonds
.
economy-wide (private) investment
or
But it is also the case that
, hence
, or
.
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
Measurement of GDP
Now, think of this, every time a dollar is spent a dollar is earned. So we could have subdivided GDP using the "income side."
In the National Income and Product Accounts (NIPA) income categories are not as clean cut
as the expenditure ones.
In practice, the difference between the expenditure approach and the income approach is
called the "statistical discrepancy."
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).
5
3/16/2017
Measurement of GDP
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.
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.
∗
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.
∗
This implies
The procedure produces a stable estimate for α of 0.32.
6
...

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Attached.

1

Assignment: Macroeconomics

Institution Affiliation

Date

2

How to Measure Real Output Growth in an Economy

Economy growth is the increase in market value for goods and services produced by a given

economy or country in given period of time usually one year. It’s measured by percentage

increase of gross domestic product (GDP). GDP shows how the country is developing.

GDP= consumption + investment + government spending + exports – imports

While factoring inflation, Real GDP=GDP/ (1+ inflation of base year)

The importance of using real GDP is that it provides actual country’s economy because it factors

in inflation rate. It usually shows the economy progress and country’s change in purchasing

power. There are three approaches used to measure the GDP

•

Income approach which calculates the sum of all the producers’ incomes

•

Expenditure approach is concerned in calculating the value of the total product which

must equal to citizens total expenditure

GDP=C + I + G + (X-M)

•

Output approach which adds together the outputs of every class of enterprise to provide

the totals.

How Is Growth Connected to Wellbeing

GDP is the measure of development in any given economy. Through a successful public

opinion policy it enhances the outside world to make decision on whether to lend a specific

country or not. A measure of per capita GDP indicates how well the society is growing. It

usually shows how a particular country growth was due to certain economic activities.

3

When you receive donation of funds due to good GDP, the common citizen benefits because

it will be used to build infrastructures and build social amenities for the public o use. It

benefits the wellbeing in other hospital sectors and also in schools for the public to use.

The government also knows how to distribute economic resources in the country for

development purposes.

Part Two

Working out The Algebraic and Differentiations

𝑟𝑒𝑎𝑙 𝐺𝐷𝑃 t+1

𝑟𝑒𝑎𝑙 𝐺𝐷𝑃𝑡

–1=

𝑝𝑎,𝑡 ∗ 𝑎𝑡+1 + 𝑝𝑏,𝑡 ∗ 𝑏𝑡+1

Pa,t∗𝑎𝑡+𝑝𝑏,𝑡∗𝑏𝑡

-1

First Order Condition (F.O.C) w.r.t to p

Take the like terms in one side and solve as follows,

=

𝑝𝑎,𝑎𝑡+1+𝑝𝑎,𝑡∗𝑎𝑡 𝑎𝑡

𝑝𝑏,𝑡∗𝑏𝑡+1+𝑝𝑏,𝑡∗𝑏𝑡

-1

Substitute the value of p while you differentiate

𝑎,𝑡+𝑏,𝑡+1∗𝑡+1

= 𝑝𝑏,𝑡∗𝑏𝑡+1+𝑝𝑏,𝑡∗𝑏𝑡

-1 turns zero because It’s not subjected to price or p

𝑎,𝑡+𝑏,𝑡+2

=𝑝𝑏,𝑡∗𝑏𝑡+ 1+𝑝𝑏,𝑡∗𝑏𝑡

4

Second order differential equation (S.O.C)

𝑟𝑒𝑎𝑙 𝐺𝐷𝑃+1

𝑟𝑒𝑎𝑙 ...

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