Purchasing Power Parity (PPP)

• Need to convert currencies when comparing GDPs across countries. Can compute exchange rates by comparing the relative prices of similar goods e.g. what is the cost of a Big Mac in London vs New York. PPP exchange rate for this good would be: $$1.00 = £ \frac{\text{Price of burger in London}}{\text{Price of burger in NY}}$$
• PPP is the rate a currency from one country would be to be converted to buy the same market basket of goods in services in another country
• Difference between PPP value and the actual exchange reveals how currencies are under or over valued relative to each other $$\frac{\text{Actual rate} - \text{PPP rate}}{\text{PPP rate}}$$

Simple Interest

Simple interest is interest accumulated only on the principle at each accumulation period:

• $100 with simple interest rate of 4%
• Year 1: $100 + 4% of $100 = $100 + $4 = $104
• Year 2: $104 + 4% of $100 = $104 + $4 = $108

Simple rate, amount accumulated after $t$ years (or accumulation periods): $N = P(1+\gamma t)$. In other words, the amount accumulated is over $t$ years is $\gamma t$% of your principle.

Compound Interest

Compound interest is simple interest but at each accumulation period interest is computed with the previously accumulated amount (i.e. earning interest on earned interest)

• $100 with simple interest rate of 4%
• Year 1: $100 + 4% of $100 = $100 + $4 = $104
• Year 2: $104 + 4% of $104 = $104(1+0.04) = $108.16

Compound rate: $N = P(1+\gamma)^t$

Rule of 70

How long does it take for the per capita real GDP to double? Can use the rule of 70 (or 72 because it has more commonly used factors): $$\begin{aligned} & 2P = P(1+r)^t \\ \implies & 2 = (1+r)^t \\ \implies & t = \frac{\log(2)}{\log(1+r)} \approx \frac{0.693}{r} \\ \end{aligned}$$

Average Labor Productivity

Economic growth rates measured by annual percentage change in per capita real GDP: $$\text{Per capita real GDP} = \frac{Y}{P} = \frac{Y}{N} \times \frac{N}{P}$$ where $Y$ is real GDP, $N$ is the number of people employed, $P$ is the total population. This expansion shows that the product of average labor productivity $Y/N$ and fraction of population that’s employed $N/POP$ is the per capita real GDP, or average economic output for all people in the population. Can also just look at this as a weighted sum, where the term is the weighted part of those contributing to GDP, and the weight for the remainder of the population is zero, as they contribute nothing due to unemployment.