The second question in macroeconomics refers to a mapping from goods and services to subjective well-being. That is, why do we care about economic growth, after all?In macroeconomics there are two key questions: first, how to measure (real) output growth? and second, how is growth connected to wellbeing?

As for the first question, there are three ways to measure real GDP growth. It starts with the definition of a percentage difference between two numbers, say x1 compared to x0. When there is only one good (e.g. apples) there are no prices to worry about for the calculation. But for the economy as a whole, we need prices to be able to add up quantities (of apples, bananas, and everything else) in dollar terms. So for real GDP growth, which holds prices constant on a given base year to control for inflation, then the trick is to apply those prices before, during, and after that base year in order to calculate the total dollar value of all goods and services produced and track growth that is not affected by inflation.you will work out the connection between the three ways to measure GDP growth: A) As a percentage change holding prices constant. B) Expressing growth in terms of a common item (converting everything into a particular good (e.g. apples). And C) as the weighted average of the growth in each of the goods weighted by their corresponding expenditure shares.

The second question in macroeconomics refers to a mapping from goods and services to subjective well-being. That is, why do we care about economic growth, after all?

Instructions

Work out the algebraic steps that:

1. take you from the first to the second equation below
2. take you from that same top equation below; and
3. . Fix a base year price
4. ????????+???????????=??,????+?+??,????+???,????+??,???????real GDP?_(t+1)/?real GDP?_t -1=(p_(a,t)?a_(t+1)+p_(b,t)?b_(t+1))/(p_(a,t)?a_t+p_(b,t)?b_t )-1
5. 2. Or in terms of one good, say, apples (divide numerator and denominator by??,?p_(a,t))
6. ????????+???????????=??+?+??,???,????+???+??,???,???????real GDP?_(t+1)/?real GDP?_t -1=(a_(t+1)+(p_(b,t)/p_(a,t) )?b_(t+1))/(a_t+(p_(b,t)/p_(a,t) )?b_t )-1
7. In the first, real GDP is in constant year t dollars, in the second, real GDP is measured in units of apples.
8. An equivalent representation is a weighted average of the growth in each of the goods based on their expenditure shares.
9. ????????+???????????=????+???+??????+??????real GDP?_(t+1)/?real GDP?_t -1=(?_t ) ?(a_(t+1)/a_t )+(1-(?_t ) ? )(b_(t+1)/b_t )-1
10. where??(?_t) ?is the fraction of nominal GDP accounted for by purchases of apples, and????(1-(?_t ) ? )the share accounted for by purchases of bananas
11. prove the relationship Why does real GDP growth matter? Well, suppose that households get utility from apples and bananas every periodt:
12. ??=?????+???????u_t=?ln(a_t )+(1-?)ln(b_t )
13. ??+?=?????+?+???????+?u_(t+1)=?ln(a_(t+1) )+(1-?)ln(b_(t+1) )
14. Then,
15. ??+????=???+???+?????+?????u_(t+1)-u_t=?(a_(t+1)/a_t )+(1-?)(b_(t+1)/b_t )-1
16. So, if???=??, then utility increases whenever real GDP growth is positive.

You will find all the algebraic steps within the body of Chapter 1. Your task is to write up a two page 'study guide' that compiles the derivations of points (1)-(3) above. Given that the answers are in the book, this exercise will be graded as either submitted (100) or not (zero).

ECON 562 Macroeconomic Analysis & Public Policy Module 1: Introduction 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 GDP 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). Utlity Real GDP Growth 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. where is the fraction of nominal GDP accounted for by purchases of apples, and the share accounted for by 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, So, if = , then utility increases whenever real GDP growth is positive. ECON 562 Macroeconomic Analysis & Public Policy Module 1d: Measurement of GDP Measurement of GDP C I G (X-M) GDP Measurement of GDP C I G (X-M) 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 that should be attributed to capital is the same as the economy-wide capital share. This implies The procedure produces a stable estimate for of 0.32