Training Economics Macroeconomics — GDP, Inflation & Unemployment
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Macroeconomics — GDP, Inflation & Unemployment

25 min Economics

Macroeconomics examines the economy as a whole — measuring total output, the price level, and employment. GDP (Gross Domestic Product) is the market value of all final goods and services produced in a country during a period. It can be measured three equivalent ways: the expenditure approach ($C+I+G+NX$), the income approach (wages + profits + rents), and the production approach (value added at each stage). The GDP deflator and Consumer Price Index (CPI) track inflation; Okun's Law links unemployment deviations from the natural rate to output gaps. Understanding these aggregates is essential for evaluating fiscal and monetary policy.

GDP, Inflation & Unemployment

Expenditure Approach to GDP

$$GDP = C + I + G + NX$$

$C$ = private consumption, $I$ = gross investment, $G$ = government spending, $NX = X - M$ = net exports. Add only final goods to avoid double-counting.

Real vs. Nominal GDP

Nominal GDP uses current prices; Real GDP uses base-year prices to remove inflation:

$$\text{Real GDP}_t = \frac{\text{Nominal GDP}_t}{\text{GDP Deflator}_t}\times 100$$

GDP growth rate: $g = \frac{\text{Real GDP}_t - \text{Real GDP}_{t-1}}{\text{Real GDP}_{t-1}} \times 100\%$

Inflation Rate

Using CPI (Consumer Price Index):

$$\pi_t = \frac{CPI_t - CPI_{t-1}}{CPI_{t-1}} \times 100\%$$

Real interest rate (Fisher equation): $r \approx i - \pi$ where $i$ is the nominal rate.

Unemployment Rate

$$u = \frac{U}{U + E} \times 100\%$$

$U$ = unemployed (looking for work), $E$ = employed. The labor force $= U + E$. Types: frictional (search), structural (skill mismatch), cyclical (recession-driven). Natural rate $u^* = $ frictional $+$ structural.

Okun's Law

A 1 percentage-point rise in unemployment above the natural rate is associated with approximately a 2\% loss of real output:

$$\frac{Y - Y^*}{Y^*} \approx -2(u - u^*)$$

Rule of 70

If real GDP grows at $g\%$ per year, it doubles in approximately $70/g$ years.

Example 1 — Nominal to Real

Nominal GDP $= \$22\text{T}$, GDP Deflator $= 110$. Find Real GDP.

  1. Real GDP $= (22/110) \times 100 = \$20\text{T}$.
Example 2 — Okun's Law

$u^* = 4\%$, $u = 7\%$, potential GDP $= \$10\text{T}$. Estimate actual GDP.

  1. Output gap $= -2(7-4)\% = -6\%$.
  2. Actual GDP $\approx 10 \times 0.94 = \$9.4\text{T}$.
Example 3 — Real Interest Rate

Nominal rate $i = 6\%$, inflation $\pi = 2.5\%$. Find real rate.

  1. $r \approx 6 - 2.5 = 3.5\%$.
  2. Exact: $r = (1.06/1.025)-1 \approx 3.41\%$.

Practice Problems

1. $C=\$14\text{T}$, $I=\$3\text{T}$, $G=\$4\text{T}$, $X=\$2.5\text{T}$, $M=\$3\text{T}$. Compute GDP.
2. Nominal GDP $=\$25\text{T}$, deflator $= 125$. Find real GDP.
3. $CPI_{2023}=280$, $CPI_{2024}=291$. Compute inflation.
4. Real GDP growth $= 3.5\%$. When does GDP double?
5. Labor force $= 160\text{M}$, employed $= 152\text{M}$. Find unemployment rate.
6. $u^* = 5\%$, $u = 9\%$, potential GDP $=\$18\text{T}$. Estimate actual GDP via Okun's Law.
7. Nominal rate $= 8\%$, inflation $= 3\%$. Find real rate (exact and approximate).
8. If real GDP was $\$16\text{T}$ last year and $\$16.8\text{T}$ this year, what is the growth rate?
9. Distinguish frictional, structural, and cyclical unemployment with one example each.
10. GDP rises from $\$20\text{T}$ to $\$21\text{T}$ and the deflator rises from 100 to 105. Did real GDP grow?
11. If $\pi = 0$ (deflation of $-2\%$) and $i = 1\%$, find the real rate.
12. Why is government transfer spending (e.g., Social Security) excluded from GDP?
Show Answer Key

1. GDP $= 14+3+4+(2.5-3) = \$20.5\text{T}$.

2. Real GDP $= (25/125)\times 100 = \$20\text{T}$.

3. $\pi = (291-280)/280 \approx 3.93\%$.

4. $70/3.5 = 20$ years.

5. $u = 8/160 = 5\%$.

6. Output gap $= -2(4)\% = -8\%$. Actual $\approx 18 \times 0.92 = \$16.56\text{T}$.

7. Approx: $8-3=5\%$. Exact: $1.08/1.03 - 1 \approx 4.85\%$.

8. $(16.8-16)/16 = 5\%$.

9. Frictional: recent grad searching for first job. Structural: coal miner whose skills aren't needed in a tech economy. Cyclical: factory worker laid off in recession.

10. Real GDP $= 21/1.05 = \$20\text{T}$ — unchanged. All growth was inflation.

11. $r \approx 1-(-2)=3\%$.

12. Transfers are income redistribution, not payment for new production — including them would double-count GDP.

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