Question

Equilibrium output in a closed economy is \(£ 1000\), consumption is \(£ 800\) and investment is \(£ 80\). (a) Deduce \(G\). (b) Investment rises by \(£ 50\). The marginal propensity to consume out of national income is \(0.8\). What are the new equilibrium levels of \(Y, C, I\) and \(G\) ? (c) Suppose instead that \(G\) had risen by \(£ 50\). What would be the new equilibrium levels of \(Y, C, I\) and \(G ?\) (d) If potential output is \(£ 1200\), to what must \(G\) rise to make output equal potential output?

Short answer

(a) G = £120. (b) Y=£1250, C=£1000, I=£130, G=£120. (c) Y=£1250, C=£1000, I=£80, G=£170. (d) G must rise to £160.

Step-by-step solution

Deduce Government Spending (G) at Initial Equilibrium

In a closed economy, the equilibrium output (Y) is equal to the sum of consumption (C), investment (I), and government spending (G). Thus, we have the equation: \[ Y = C + I + G \]. Given: \( Y = £1000 \),\( C = £800 \),\( I = £80 \).Substitute these values into the equation:\[ £1000 = £800 + £80 + G \].Solving for G:\[ G = £1000 - £880 = £120 \].Therefore, initially, \( G = £120 \).

Calculate New Equilibrium after Investment Rises

When investment rises by £50, the new investment is \( I = £80 + £50 = £130 \).The change in equilibrium output (\( \Delta Y \)) is determined by the multiplier effect with the given marginal propensity to consume (MPC) of 0.8. The formula for the multiplier \( k \) is:\[ k = \frac{1}{1 - MPC} = \frac{1}{1 - 0.8} = 5 \].Therefore, the change in equilibrium output is:\[ \Delta Y = k \Delta I = 5 \times £50 = £250 \].Thus, the new equilibrium output is:\[ Y_{new} = Y + \Delta Y = £1000 + £250 = £1250 \].Consumption at the new equilibrium is:\[ C_{new} = 0.8 \times Y_{new} = 0.8 \times £1250 = £1000 \].The investment is \( I_{new} = £130 \), and government spending remains \( G = £120 \).

Calculate New Equilibrium after Government Spending Rises

Suppose government spending rises by \( £50 \), making \( G = £120 + £50 = £170 \).Again, calculating the change in output using the multiplier, we have:\[ \Delta Y = k \Delta G = 5 \times £50 = £250 \].So, the new equilibrium output is:\[ Y_{new}= £1000 + £250 = £1250 \].The new consumption level is:\[ C_{new} = 0.8 \times £1250 = £1000 \].The investment remains \( I = £80 \), and the new government spending \( G = £170 \).

Determine G to Reach Potential Output

The potential output is given as \( Y_{potential} = £1200 \).To find the necessary increase in government spending to reach this potential output, we note the required change in output is:\[ \Delta Y = Y_{potential} - Y = £1200 - £1000 = £200 \].Given the multiplier \( k = 5 \), the change in government spending needed is:\[ \Delta G = \frac{\Delta Y}{k} = \frac{£200}{5} = £40 \].Thus, the new government spending should be:\[ G_{new} = £120 + £40 = £160 \].

Key concepts

Closed Economy

A closed economy is one in which there is no economic interaction with the outside world. This means that all the goods and services consumed within the economy are produced domestically. In other words, there are no imports or exports.
In such economies, the total output or GDP is determined by three main components:

• Consumption (C): This is the total amount of goods and services consumed by households within the economy.
• Investment (I): This includes the total spending on goods that will be used for future production, such as capital equipment and infrastructure.
• Government Spending (G): This refers to the total expenditure by the government on goods and services, such as education, health, and defense.

In this exercise, the equilibrium in a closed economy is given by the equation: \( Y = C + I + G \), where \( Y \) is the total output or GDP. Understanding this equation is crucial as it forms the basis for determining the equilibrium output levels under different economic scenarios.

Marginal Propensity to Consume

The marginal propensity to consume (MPC) is a measure that depicts how much consumption changes when income changes. In simple terms, it tells us how much more people will spend out of every extra pound they earn.
For instance, if the MPC is 0.8, this indicates that for every additional £1 of income, households would spend 80p and save the remaining 20p. This concept is significant since it affects how changes in income can influence overall consumption in the economy.
When calculating economic changes, such as the impact of increased investment or government spending, the MPC plays a vital role in determining the extent of these effects. This is because the MPC is used in the multiplier effect formula, which quantifies the overall increase in economic output from these stimulative actions.

Multiplier Effect

The multiplier effect describes how an initial change in spending (such as investment or government spending) leads to a larger overall change in the economy's output. The size of this effect depends on the marginal propensity to consume (MPC).
The formula for the multiplier \( k \) is: \[k = \frac{1}{1 - \text{MPC}} \]
In our scenario, the MPC is 0.8, leading to a multiplier of 5. This indicates any initial increase in spending will lead to a total increase five times as large in the overall economic output \( Y \).
Here's how it works:

• An increase in investment or government spending increases aggregate demand.
• As demand rises, businesses increase production, leading to higher incomes for workers and suppliers.
• The increased incomes lead to more consumption, further boosting demand.

This chain reaction continues, multiplying the impact of the initial spending, which explains why even small changes can have notable effects on the overall economy. Understanding the multiplier effect helps in assessing strategies for stimulating economic growth.