Gross Domestic Product

GDP can be calculated by the following three methods:

GDP §

Defined equivalently in 3 ways:

$$\begin{array}{rl}\text{GDP}=Y& =f(l,k)\\ & =I_l+I_k+\pi +\text{tax}\\ & =C+I+G_{\text{deficit}}+NE\end{array}$$

• (1) uses the production function $f(l,k)$ against the whole economy
• (2) uses the Income method
• (3) uses the Output method. Generally, $C>G>I>NE$.
  • Consumption is stable in recessions because you need to eat; Investment suffers
  • Government spending composes around $1/3$ in US, $1/2$ is EU
  • Note that $NE-\text{Export}-\text{Imports}$ and thus Net Exports can be negative.

📎 Observee (2) and (3) are same because the macroeconomic circular flow is a closed loop.

• Historically, the LR trend of GDP has been growing exponentially since the industrial revolution…
  • …GDP per capita [←a better measure of well-being] is growing too…
  • …Consumption per capita [←an even better measure of well-being] is growing too!
  • This growth seems to be coming from growth in labor income, while capital income is stagnant.
• Short-run fluctuations in GDP are due to the business cycle.
• Some economic activity is not in GDP:
  • Informal market (big in some countries; e.g. 1/3 in Brazil)
  • Home production; i.e. homemaking

Calculation Methods §

1. Output [= production] method $\begin{array}{rl}Y& ={\text{VA}}_1+{\text{VA}}_2+\cdots \\ & =(P_1)+(P_2-P1)+\cdots \end{array}$

2. Expenditure method: $Y=C+I+G+NX$ → $C$ is only for final sales, not for intermediate goods. Final sales are always to the household.

3. Income method $Y=I_K+I_N+\pi +t$ → Note that firms pass on their taxes to the consumer (HH), or corporate taxes are paid by entrepreneurs who are at the end of the day HHs.

GNI [= GNP] §

• GNI method $Y^D=I_K^D+I_N^D+\pi +t$ …$t$ if both incomes are pre-tax incomes
• GNP method $Y^D=C+I+G+NX+NI$ …where $NI$ is the net domestic income (inflow - outflow)

Deflator & CPI §

1. Deflator is the reduction of nominal GDP in years after the base year due to inflation.

$$\text{Deflator}=\frac{Y^{\text{Nominal}}}{Y^{\text{Real}}}\cdot 100$$

…thus the real gdp for year $i$ is calculated $Y_i^R=\frac{Y_i^N}{{\text{Deflator}}_i}\cdot 100$

• Deflator is 100 in the base year
• Deflator $\propto$ inflation rate

2. CPI is another index to reduce the nominal GDP. Assume the current year is $i$, base year $b$

$$\begin{array}{rl}{\text{CPI}}^{\text{current}}& =\frac{\sum p^{\text{current}}{q}^{\text{base}}}{\sum p^{\text{base}}{q}^{\text{base}}}\cdot 100\\ & =\frac{Y_{\text{of base}}^{\text{in current dollars}}}{Y_{\text{of base}}^{\text{in current dollars}}}\cdot 100\end{array}$$

…thus the real gdp for year $i$ is calculated $Y_i^{\text{Real}}=\frac{Y_i^{\text{Nominal}}}{{\text{CPI}}_i}\cdot 100$