Equations and Calculations in Economics (HSC SSCE Economics): Revision Notes

Equations and Calculations in Economics

Mathematical skills form an important component of HSC Economics, though the calculations required are relatively straightforward compared to natural sciences. While economics is primarily a humanities subject, it does require competence with quantitative information to understand how economies function. This note covers the essential equations and calculations you need to master.

The role of mathematics in economics

Economics requires fewer complex calculations than science subjects, but more numerical analysis than purely essay-based subjects like History or English. The mathematical component involves understanding how to use quantitative data to analyse economic performance and relationships. These calculations allow you to examine both the economy as a whole (through macroeconomic equations) and specific economic outcomes (such as unemployment levels or trade balances).

You will encounter two types of mathematical tools:

• Equations that show relationships between economic variables
• Calculations that quantify specific economic indicators

Balance of payments calculations

Understanding the balance of payments structure

The balance of payments records all financial transactions between Australia and the rest of the world. It consists of two main accounts that, under a floating exchange rate system, must sum to zero. This means if one account is in deficit, the other must be in surplus by an equal amount.

The current account

The current account measures flows of goods, services, income, and transfers. It is calculated by adding together four components.

The formula shows that: $\text{Current Account} = \text{Net goods} + \text{Net services} + \text{Net primary income} + \text{Net secondary income}$

The first two components (net goods and net services) together form the balance on goods and services, which is often the largest component of the current account.

The capital and financial account

The capital and financial account records investment flows and capital transfers. It includes: $\text{Capital and Financial Account} = \text{Capital account} + \text{Direct investment} + \text{Portfolio investment} + \text{Other investment} + \text{Reserve assets} + \text{Financial derivatives}$

The balance of payments equation

The complete balance of payments equation is: $\text{Current Account} + \text{Capital and Financial Account} + \text{Net errors and omissions} = 0$

This equation always holds true. The numerical value of the current account deficit equals the capital and financial account surplus (or vice versa). For example, if Australia's current account deficit increases by $10 billion, the capital and financial account surplus must also increase by $10 billion.

Using the formulas

You can use these formulas to calculate unknown components when given partial information. For instance, if you know the capital and financial account surplus, the net primary income deficit, and the net secondary income deficit, you can work backwards to find the balance on goods and services.

Equilibrium calculations using leakages and injections

The equilibrium condition

An economy reaches equilibrium when the total value of leakages from the circular flow of income equals the total value of injections into it. This is known as the equilibrium condition.

$S + T + M = I + G + X$ $\text{Leakages} = \text{Injections}$

Where:

• $S$ = savings by households
• $T$ = taxation by the government
• $M$ = spending on imports
• $I$ = investment spending by businesses
• $G$ = government spending
• $X$ = export revenue

Using the leakages-injections equation

This equation is useful for several types of questions:

1. Testing equilibrium: Given all six values, check if they sum equally on both sides
2. Finding missing values: If you know the economy is in equilibrium and have five values, calculate the sixth
3. Finding imbalances: Given three values plus one of the imbalances (trade deficit, budget deficit, or savings-investment gap), calculate remaining components

Aggregate demand and aggregate supply equations

Sometimes you need to calculate consumption ($C$), aggregate demand ($AD$), or national income ($Y$). The leakages-injections equation cannot help here because these variables are not part of it. Instead, you need the aggregate demand and aggregate supply equations.

Aggregate demand equation: $AD = C + I + G + (X - M)$

Where:

• $AD$ = aggregate demand
• $C$ = consumer spending by households
• $I$ = investment spending by businesses
• $G$ = government spending
• $X$ = export revenue
• $M$ = spending on imports

Aggregate supply (income) equation: $Y = C + S + T$

Where:

• $Y$ = aggregate supply or national income
• $C$ = consumer spending by households
• $S$ = savings by households
• $T$ = taxation by the government

Deriving the equilibrium condition

At equilibrium, aggregate supply equals aggregate demand: $Y = AD$

Substituting the equations: $C + S + T = C + I + G + (X - M)$

Consumption ($C$) appears on both sides, so it cancels out. Rearranging gives: $S + T + M = I + G + X$

This confirms that equilibrium occurs when leakages equal injections.

The multiplier effect

What is the multiplier?

The multiplier demonstrates that a change in injections or leakages has a magnified impact on national income. When an injection (such as increased export revenue) enters the circular flow, it initially raises business income by that amount. However, the effect does not stop there.

Businesses pay this income to workers, who then spend it on consumption, which becomes revenue for other businesses, and so on. This creates a ripple effect that multiplies the initial injection.

However, not all income is spent. Some leaks out through savings, taxation, and imports. These leakages slow down the multiplier process. The larger the leakages, the smaller the multiplier effect.

The simple multiplier formula

For HSC Economics, you only need to consider the simple multiplier, which accounts for the savings leakage only. The multiplier ($k$) is calculated as:

$k = \frac{1}{MPS}$

where $MPS$ is the marginal propensity to save.

Alternatively, since $MPC + MPS = 1$: $k = \frac{1}{1 - MPC}$

where $MPC$ is the marginal propensity to consume.

The marginal propensity to save is the proportion of additional income that households save rather than spend. A lower $MPS$ means people save less and spend more, leading to a larger multiplier.

Calculating the impact on national income

To find the total change in national income resulting from a change in aggregate demand: $\Delta Y = k \times \Delta AD$

Where:

• $\Delta Y$ = change in national income
• $k$ = the multiplier
• $\Delta AD$ = initial change in aggregate demand (injection or leakage)

Implications for economic fluctuations

The size of the multiplier indicates how volatile the economy will be in response to economic shocks:

Lower savings rate → Higher multiplier → Greater economic fluctuations

$\frac{1}{MPS} \uparrow \text{ when } MPS \downarrow$

When the marginal propensity to save is low, the multiplier is high. This means the economy experiences larger swings in response to changes in injections or leakages. Economic booms are stronger, but recessions are also deeper.

Conversely, a higher marginal propensity to save reduces the multiplier, making the economy more stable but less responsive to changes.

Policy implications

A higher multiplier creates challenges for government policy makers:

When the multiplier is lower, both fiscal policy (government spending and taxation) and monetary policy (interest rates affecting investment and consumption) have smaller impacts and are less frequently required.

Labour market calculations

Two key labour market indicators require calculations: the labour force participation rate and the unemployment rate. Understanding these formulas is essential for analysing Australia's labour market performance.

Labour force participation rate

The labour force participation rate measures the proportion of the working-age population that is economically active (either employed or actively seeking work). It is calculated as:

$\text{Labour force participation rate (\%)} = \frac{\text{Labour force}}{\text{Working-age population (15+)}} \times 100$

The labour force includes all people who are either employed or unemployed (actively seeking work). The working-age population includes everyone aged 15 and over.

A higher participation rate indicates that a larger share of the population is engaged in the labour market. This can change due to demographic factors, social trends, or economic conditions.

Unemployment rate

The unemployment rate measures the proportion of the labour force that is without work but actively seeking employment. It is calculated as:

$\text{Unemployment rate (\%)} = \frac{\text{Number of persons unemployed}}{\text{Total labour force}} \times 100$

The unemployment rate rises during recessions when businesses lay off workers, and falls during expansions when businesses hire more workers.

Key distinction

It is important to understand that these two rates measure different things:

Remember!