e UK from abroad (an injection). When we import a smartphone, money flows *out* of the UK to foreign manufacturers (a withdrawal). Think of the circular flow of income as water in a bathtub: - The **water level** represents national income ($Y$). - The **tap running** represents injections ($J$) adding water to the tub. - The **plug hole** represents withdrawals ($W$) draining water out of the tub. If the tap is running faster than the water can drain ($J > W$), the water level rises (national income increases). If the drain is wider and water leaves faster than it enters ($J < W$), the water level falls (national income decreases). --- ## 3. The Impact of Injections and Withdrawals on National Income The relationship between total injections and total withdrawals determines the direction of change in real GDP and national income ($Y$). The economy is in macroeconomic equilibrium when total planned injections equal total planned withdrawals: $$J = W$$ Or, expanded: $$I + G + X = S + T + M$$ If this condition is met, national income ($Y$) remains stable. ### When Injections Exceed Withdrawals ($J > W$) - **The Process:** There is a net injection of demand into the economy. Firms experience falling inventories (stocks) and respond by increasing production. To do this, they hire more factors of production, paying out more wages and profits to households. - **The Outcome:** National income, output, and employment rise. This leads to **economic growth**. ### When Withdrawals Exceed Injections ($J < W$) - **The Process:** Money is leaking out of the system faster than it is being replaced. Consumer demand falls, leading to rising unsold stock for firms. Firms cut back production and lay off workers. - **The Outcome:** National income, output, and employment fall. The economy experiences a **contraction** or recession. --- ## 4. Worked Example: Analyzing Changes in National Income When the government or private sector changes its spending, we can calculate the net direct effect on the circular flow. Furthermore, we can use the **Marginal Propensity to Withdraw ($MPW$)** to estimate the ultimate change in national income after the multiplier process. An economy is initially in equilibrium. The government decides to boost national infrastructure by investing £12 billion into national rail networks. At the same time, due to changes in welfare policy, national savings rise by £4 billion. Assume the economy's Marginal Propensity to Withdraw ($MPW$) is 0.4. Calculate the net injection into the circular flow and the resulting overall change in national income. **Step 1: Identify the direct changes to injections and withdrawals.** - The infrastructure spending is government spending, which is an injection ($\Delta G = +12$ billion). - The increase in savings is a withdrawal ($\Delta S = +4$ billion). **Step 2: Calculate the net injection ($\text{Net } J$).** Using the net change formula: $$\text{Net } J = \Delta J - \Delta W$$ $$\text{Net } J = 12\text{ billion} - 4\text{ billion} = 8\text{ billion}$$ Because the result is positive, this represents a net injection of £8 billion. **Step 3: Calculate the size of the multiplier ($k$).** The multiplier formula using the marginal propensity to withdraw is: $$k = \frac{1}{MPW}$$ Substitute the given value ($MPW = 0.4$): $$k = \frac{1}{0.4} = 2.5$$ **Step 4: Calculate the final change in national income ($\Delta Y$).** Now, multiply the net injection by the multiplier: $$\Delta Y = k \times \text{Net } J$$ $$\Delta Y = 2.5 \times 8\text{ billion} = 20\text{ billion}$$ **Conclusion:** The net direct injection of £8 billion leads to a total increase in national income of £20 billion. Note that this calculation assumes the $MPW$ remains constant at 0.4 throughout the process. In reality, as national income rises, the propo