Question

Assume that an economy is in equilibrium. Planned investment is \(£ 100\). The \(M P C\) is \(0.6\). Suppose investment rises by \(£ 30\). (a) What happens to the equilibrium output? Now suppose people decide to save a higher proportion of their income: the consumption function changes from \(C=0.8 \mathrm{Y}\) to \(C=0.5 \mathrm{Y}\). (b) What happens to equilibrium income (planned investment being \(£ 100\) )? (c) What happens to the equilibrium proportion of income saved? Explain.

Short answer

(a) Output rises to £325; (b) income falls to £200; (c) savings proportion rises to 50%.

Step-by-step solution

Calculate Initial Equilibrium Output

In equilibrium, total output (Y) equals total spending. If planned investment (I) is £100 and consumption is governed by consumption function C, where the MPC = 0.6, then the initial equilibrium output (Y) satisfies the equation:\[ Y = C + I \]Substituting the consumption function \( C = MPC \times Y = 0.6Y \) and \( I = £100 \), we get:\[ Y = 0.6Y + 100 \]Solving for \( Y \):\[ 0.4Y = 100 \quad \Rightarrow \quad Y = \frac{100}{0.4} = 250 \]

Determine Impact of Investment Increase on Output

When investment rises by £30, the new investment becomes \( I = 100 + 30 = 130 \). To find the new equilibrium output, use:\[ Y = 0.6Y + 130 \]Solving for \( Y \):\[ 0.4Y = 130 \quad \Rightarrow \quad Y = \frac{130}{0.4} = 325 \]The equilibrium output increases to 325.

Calculate New Equilibrium With Higher Savings

Given the new consumption function \( C = 0.5Y \) and \( I = 100 \), equilibrium is:\[ Y = 0.5Y + 100 \]Solving for \( Y \):\[ 0.5Y = 100 \quad \Rightarrow \quad Y = \frac{100}{0.5} = 200 \]

Determine New Equilibrium Savings

From the new equilibrium output \( Y = 200 \) and the consumption function \( C = 0.5Y \), consumption is \( C = 0.5 \times 200 = 100 \). Hence, savings \( S \) is:\[ S = Y - C = 200 - 100 = 100 \]The proportion of income saved is \( \frac{S}{Y} = \frac{100}{200} = 0.5 \).

Compare Savings Proportions

Initially (Step 1), with \( MPC = 0.6 \), the propensity to save (1 - MPC) was 0.4, meaning 40% of income was saved. Under the new scenario, 50% of income is saved, indicating an increase in the savings ratio.

Key concepts

MPC (Marginal Propensity to Consume)

The Marginal Propensity to Consume, or MPC, is a fundamental concept in equilibrium economics that describes how an individual's consumption changes in response to an increase in income. It represents the portion of additional income that a household will likely spend on consumption rather than save. For instance, if the MPC is 0.6, it implies that for every additional £1 received, 60p will be spent on consumption.

Understanding MPC helps economists predict changes in aggregate demand when there is a shift in income levels. When the MPC is higher, a larger fraction of income is used for consumption, stimulating economic activity. Conversely, a lower MPC implies more income is saved, potentially slowing down consumption-led economic growth.

In equilibrium analysis, the MPC directly influences the slope of the consumption function, which plays a crucial role in determining equilibrium output. An increase in planned investments can enhance equilibrium output, especially when MPC is high because consumption amplifies the effects of investment in national income.

Equilibrium Output

Equilibrium output occurs when total production in an economy is equal to total spendings, such that production matches the demand for goods and services. Mathematically, this is expressed as:

• Output (Y) = Consumption (C) + Investment (I)

In such a setting, there are no incentives for firms to change their production levels.

Using the exercise example, initially, the equilibrium output was determined under the assumption that planned investments were £100 and the MPC was 0.6, leading to the calculation:

• Using the equation: \[ Y = 0.6Y + 100 \]leads to: \[ Y = 250 \]

When an investment increase of £30 occurred, the additional spending trickled through the economy due to consumer spending, resulting in a new equilibrium of:

• \[ Y = 325 \]

This adjustment highlights how changes in investment levels can influence overall economic activity, driving changes in total equilibrium output.

Investment and Savings

Investments and savings are two sides of the same economic coin, each playing a crucial role in determining an economy's equilibrium. Investment refers to expenditures made to generate future income, such as business capital spending. Savings arise from the portion of income not spent by households, providing the funds for investments.

In equilibrium economics, when planned investments rise, it can catalyze greater income and output, as observed in earlier examples. However, increasing savings can alter this balance by hindering consumption, reducing current economic activity.

For instance, initially, when the MPC was 0.6, savings were 40% of income, ensuring a portion for future investments. Following a shift in behavior where people saved more (new MPC of 0.5), total savings increased to 50% of income. This reduction in consumption and higher saving propensity illustrates a higher equilibrium savings ratio and highlights the trade-off between present consumption and future economic growth driven by investment.
Thus, a higher savings ratio implies a future potential for more investment, although it comes at the cost of current consumption.