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Macroeconomic Indicators

While microeconomics focuses on individual agents and markets, macroeconomics examines the economy as a whole. Key macroeconomic indicators provide insights into the overall health and performance of an economy.

Economic Activity: GDP

Gross Domestic Product (GDP)

GDP measures the total market value of all final goods and services produced within a country over a specific period (usually a year).

The output/income/expenditure (all the same value) of an economy is denoted as $Y$. It can be calculated using three approaches:

Output Approach:
Sum of value added at each production stage. The production function relates inputs $L$ (labor) and $K$ (capital) to output:
$Y=F(L,K)$

Income Approach:
Sum of all incomes earned (wages, rents, interest, profits). Income can be expressed using $L$, $K$, and their respective prices $w$ (wage rate) and $r$ (rental rate of capital):
$Y=wL+rK$

Expenditure Approach:
Sum of consumption, investment, government spending, and net exports (exports minus imports). The expenditure identity is based on consumption $C$, investment $I$, government spending $G$, exports $EX$, and imports $IM$:

Y &= C + I + G + (EX - IM) \\\\ NC &= EX - IM \end{aligned}

Net Exports $NC$ are exports less imports.

One of the shortcomings of GDP is that it does not account for non-market transactions (e.g., household labor, volunteer work) and may not accurately reflect well-being or environmental sustainability. However, rental income, for example, is counted, in the output approach as work done by the capital asset.

Compared to GDP, there are:

• Net Domestic Product (NDP): GDP minus depreciation of capital.
• Gross National Income (GNI): GDP plus net income from abroad claimed by residents, minus income earned by foreigners within the country.

Nominal vs. Real GDP

When analyzing GDP over time, it’s important to distinguish between nominal and real GDP:

• Nominal GDP: The market value at current prices. Changes in nominal GDP reflect changes in both output and prices. This is used for current economic assessments.
• Real GDP: The market value adjusted for inflation, using constant prices from a base year. Real GDP reflects changes in output only. This allows for more accurate comparisons of economic performance over time.

Dividing nominal GDP by real GDP gives the GDP deflator, a measure of the overall price level in the economy.

Cost of Living: Price Level

Price Index

A price index measures the average level of prices for a set of goods and services over time, normalized to a base period.

• Paasche Index: Price index using weights (product quantities) of the current period.
  $P_t^P=\frac{{\sum }_{i=1}^n\left(p_{i,t}\cdot Q_{i,t}\right)}{{\sum }_{i=1}^n\left(p_{i,0}\cdot Q_{i,t}\right)}$
• Laspeyres Index: Price index using weights of the base period.
  $P_t^L=\frac{{\sum }_{i=1}^n\left(p_{i,t}\cdot Q_{i,0}\right)}{{\sum }_{i=1}^n\left(p_{i,0}\cdot Q_{i,0}\right)}$

Inflation Rate

The relative change in the price level over time, typically measured as the percentage change in a price index from one period to the next:
$\text{Inflation Rate}=\frac{P_t-P_{t-1}}{P_{t-1}}$
Where $P_t$ is the price index at time $t$ and $P_{t-1}$ is the price index at time $t-1$.

GDP Deflator

The GDP Deflator is a Paasche index (based on current period) that measures price changes of domestic input.

$$\text{GDP Deflator}=\frac{\text{Nominal GDP}}{\text{Real GDP}}$$

GDP Deflator of 1.1 means a 10% increase in the overall price level since the base year.

Consumer Price Index (CPI)

The CPI is a Laspeyres index (based on base period) that measures the average change in prices paid by consumers for a fixed basket of goods and services.

$$\text{CPI}=\frac{\text{cost of basket at current prices}}{\text{cost of basket at base-period prices}}$$

The CPI is used to determine the inflation rate in Germany.

The GDP and CPI differ in their weights: While the GDP deflator uses current period quantities (Paasche), the CPI uses base period quantities (Laspeyres). Thus, the GDP deflator reflects price changes of all domestically produced goods, while the CPI reflects price changes of a fixed basket of consumer goods.

Employment: Labor Force

Labor Force $L$ is the number of people who are able and willing to supply labor. It is a subset of the working-age population $N$ and includes both employed $E$ and involuntarily unemployed $U$ individuals. There are two key metrics:

Labor Force Participation Rate

The ratio of the labor force to the working-age population:
$e=\frac{L}{N}=\frac{E+U}{N}$
Indicates the proportion of people actively engaged in the labor market.

Unemployment Rate

The ratio of unemployed individuals to the labor force:
$u=\frac{U}{L}=\frac{U}{E+U}1-u=\frac{E}{L}$
Indicates the proportion of the labor force that is unemployed and actively seeking work.

Example Problem

These are the market macroeconomic indicators problem from exercise 6 with some questions from exercise exam 2.

Economic Activity

There are 3 actors.

• Farmer: imports seeds €100k; sells grain to miller €300k
• Miller: buys grain €300k; sells flour to baker €300k, to domestic consumers €200k; exports €100k
• Baker: imports ingredients €100k; buys flour €300k; sells bread to domestic consumers €500k; exports €300k

Questions

What are the nominal GDP and Net Export?
Nominal GDP: Sum up either finished products or incomes per step. Here using the incomes approach:

$$Y=(300k-100k)+(600k-300k-100k)+(800k-300k)=900k$$

The net export is the sum of exports minus imports:

$$NC=(100k+300k)-(100k+100k)=200k$$

Cost of Living

Given these outputs and prices, with base year 2023:

Year	Fish Output (kg)	Fish Price (per kg)	Potatoes Output (kg)	Potatoes Price (per kg)	Tea Output (kg)	Tea Price (per kg)
2023	15,000	16	80,000	2.0	5,000	30
2024	15,000	17.5	80,000	2.5	5,000	45
2025	20,000	20	83,000	2.5	300	120

Questions

What are the nominal and real GDP in 2025?
Nominal GDP in 2025 is calculated using current prices:

$${\text{Nominal GDP}}_{2025}=(20,000\times 20)+(83,000\times 2.5)+(300\times 120)=400,000+207,500+36,000=643,500$$

Real GDP in 2025 uses base year prices (2023):

$${\text{Real GDP}}_{2025}=(20,000\times 16)+(83,000\times 2.0)+(300\times 30)=320,000+166,000+9,000=495,000$$

What are the GDP Deflator and CPI in 2025?
GDP Deflator in 2025:

$${\text{GDP Deflator}}_{2025}=\frac{{\text{Nominal GDP}}_{2025}}{{\text{Real GDP}}_{2025}}=\frac{643,500}{495,000}\approx 1.3$$

CPI in 2025:
Cost of basket in 2023: $(15,000\times 16)+(80,000\times 2.0)+(5,000\times 30)=240,000+160,000+150,000=550,000$
Cost of basket in 2025: $(20,000\times 20)+(83,000\times 2.5)+(300\times 120)=400,000+207,500+36,000=643,500$

$${\text{CPI}}_{2025}=\frac{\text{Cost of basket in 2025}}{\text{Cost of basket in 2023}}=\frac{643,500}{550,000}\approx 1.17$$

What is the inflation rate from 2024 to 2025 using GDP?
First also calculate the GDP Deflator for 2024:

$$\begin{array}{rl}{\text{Nominal GDP}}_{2024}& =(15,000\times 17.5)+(80,000\times 2.5)+(5,000\times 45)=262,500+200,000+225,000=687,500\\ & \\ {\text{Real GDP}}_{2024}& =(15,000\times 16)+(80,000\times 2.0)+(5,000\times 30)=240,000+160,000+150,000=550,000\\ & \\ {\text{GDP Deflator}}_{2024}& =\frac{687,500}{550,000}\approx 1.25\\ & \end{array}$$

Inflation Rate from 2024 to 2025:

$$\text{Inflation Rate}=\frac{{\text{GDP Deflator}}_{2025}-{\text{GDP Deflator}}_{2024}}{{\text{GDP Deflator}}_{2024}}=\frac{1.3-1.25}{1.25}=0.04=4\%$$

Employment

The working population is $N=100million$ people.

Questions

If labor force participation rate $e=0.6$ and there are $U=6million$ unemployed, what is the unemployment rate?
Labor force $L$ is calculated as:

$$L=e\cdot N=0.6\cdot 100\text{ million}=60\text{ million}$$

Unemployment rate $u$ is:

$$u=\frac{U}{L}=\frac{6\text{ million}}{60\text{ million}}=0.1=10\%$$

If unemployment rate $u=0.05$ and $E=76million$ are employed, what is the labor force participation rate?
Labor force $L$ is calculated as:

$$1-u=\frac{E}{L}\Rightarrow L=\frac{E}{1-u}=\frac{76\text{ million}}{1-0.05}=\frac{76\text{ million}}{0.95}\approx 80\text{ million}$$

Labor force participation rate $e$ is:

$$e=\frac{L}{N}=\frac{80\text{ million}}{100\text{ million}}=0.8=80\%$$