Question

By how much must investment rise to bring about a \(\$ 300 \mathrm{M}\) change in income if \(\mathrm{MPC}=0.75\).

Short answer

The investment needs to rise by \(75 \mathrm{M}\) to bring about a \(300 \mathrm{M}\) change in income with a marginal propensity to consume of 0.75.

Step-by-step solution

Calculate the multiplier effect

First, we need to calculate the multiplier effect using the given value of MPC: Multiplier = \( \frac{1}{1 - \mathrm{MPC}} \) Multiplier = \( \frac{1}{1 - 0.75} \) Multiplier = \( \frac{1}{0.25} \) Multiplier = 4

Rearrange the formula to solve for the change in investment (ΔI)

Now, we need to rearrange the change in income formula to solve for the change in investment (ΔI): ΔY = Multiplier × ΔI Divide both sides of the equation by the multiplier value: ΔI = \( \frac{\Delta Y}{\text{Multiplier}} \)

Calculate the change in investment (ΔI) required

Lastly, input the given values for the change in income (ΔY) and the calculated multiplier to compute the change in investment (ΔI): ΔI = \( \frac{\$300 \mathrm{M}}{4} \) ΔI = \( \$75 \mathrm{M} \) The investment needs to rise by \(75 \mathrm{M}\) to bring about a \(300 \mathrm{M}\) change in income with a marginal propensity to consume of 0.75.

Key concepts

Marginal Propensity to Consume (MPC)

The Marginal Propensity to Consume (MPC) is a key concept in understanding economic behavior and the multiplier effect. MPC measures the portion of additional income that households use for consumption rather than saving. For instance, if a household receives an extra dollar and spends 75 cents of it, the MPC would be 0.75. This means:

• If household income increases, a large part of it (75% in this case) goes towards buying goods and services.
• The higher the MPC, the more significant the economic impact of changes in income on consumption levels.

In economies with a high MPC, changes in income can lead to considerable shifts in consumer spending. This is why MPC plays a crucial role in predicting how much economic activity can stem from new income, like an investment increase.

Change in Income

Understanding the change in income involves knowing how initial economic actions, like investment, ripple through the economy. When firms or governments make an investment, it creates jobs and incomes. With an MPC of 0.75, for each dollar earned, 75 cents is spent. This spending then becomes someone else’s income, continuing the cycle.

• This circulation of income helps expand the economic output beyond the initial investment.
• The multiplier effect here helps to explain why the change in income is often substantially larger than the initial investment itself.

If a country aims for a certain change in national income, understanding MPC and its impacts on spending behaviours can be crucial for planning effective economic policies.

Investment Increase

An increase in investment can have a profound effect on the economy, thanks to the multiplier effect. In the given exercise, the goal was to achieve a \(300 million change in income. Using the formula:\[ \Delta Y = \text{Multiplier} \times \Delta I \]Where \( \Delta Y \) is the change in income and \( \Delta I \) is the change in investment, we first calculate the multiplier:\[ \text{Multiplier} = \frac{1}{1 - \text{MPC}} = \frac{1}{0.25} = 4 \]Therefore, the required change in investment to achieve the desired change in income is:\[ \Delta I = \frac{300 \text{M}}{4} = 75 \text{M} \]What this calculation shows is that a relatively smaller increase in investment, precisely \)75M, can generate a much larger total economic impact, or $300M in income. This is significant for policy-makers and businesses because it highlights how targeted investments can efficiently stimulate economic growth.