Question

Planned investment is 100 . Initially, the consumption function is \(C=100+0.8 \mathrm{Y}\). There are three ways in which greater pessimism about the future might affect behaviour: (a) planned investment falls from 100 to 50, (b) autonomous consumption falls from 100 to 50 , (c) the marginal propensity to consume falls from \(0.8\) to \(0.7\) as people save more of each unit of additional income. Draw a graph of each change and its effect on short-run equilibrium output.

Short answer

Equilibrium outputs are 750 for scenarios (a) and (b), and approximately 667 for (c).

Step-by-step solution

Define the Economic Model

The macroeconomic model to be used in this exercise is the Keynesian aggregate expenditure model. The equilibrium is achieved where aggregate expenditure equals national income: \[ Y = C + I \] Given: \( C = 100 + 0.8Y \) and \( I = 100 \)

Analyze Scenario (a)

Scenario (a) involves a decrease in planned investment from 100 to 50. Substitute the new investment value into the equilibrium equation:\[ Y = (100 + 0.8Y) + 50 \] Solving for \( Y \):\[ Y = 150 + 0.8Y \] \[ 0.2Y = 150 \] \[ Y = \frac{150}{0.2} \] \[ Y = 750 \] This shows the new equilibrium output after the decrease in investment.

Analyze Scenario (b)

Scenario (b) involves a reduction in autonomous consumption from 100 to 50. Adjust the consumption function: \( C = 50 + 0.8Y \). Substitute this into the equilibrium equation with original investment:\[ Y = (50 + 0.8Y) + 100 \] Solving for \( Y \):\[ Y = 150 + 0.8Y \] \[ 0.2Y = 150 \] \[ Y = \frac{150}{0.2} \] \[ Y = 750 \] This shows the new equilibrium output as affected by the reduction in autonomous consumption.

Analyze Scenario (c)

Scenario (c) considers a reduction in the marginal propensity to consume from 0.8 to 0.7, keeping autonomous consumption and planned investment the same:\( C = 100 + 0.7Y \). Substitute this function back into the equilibrium equation:\[ Y = (100 + 0.7Y) + 100 \] Solving for \( Y \):\[ Y = 200 + 0.7Y \] \[ 0.3Y = 200 \] \[ Y = \frac{200}{0.3} \] \[ Y \approx 667 \] This calculation shows the new equilibrium output reflecting the lower propensity to consume.

Graph the Scenarios

To visualize, plot each consumption function (\( C_1 = 100 + 0.8Y \), \( C_2 = 50 + 0.8Y \), \( C_3 = 100 + 0.7Y \))and the corresponding investment functions on a graph, along with their equilibrium outputs (\( Y_0 = 1000 \), \( Y_1 = 750 \), \( Y_2 = 750 \), \( Y_3 \approx 667 \)). Label these changes clearly to demonstrate the impact of pessimism on equilibrium output.

Key concepts

Aggregate Expenditure Model

The Aggregate Expenditure Model is a foundational concept in Keynesian Economics that determines equilibrium levels of output in an economy. It emphasizes how total spending—comprising consumption (C) and investment (I)—influences aggregate demand and national income. The model is expressed as:
\[ Y = C + I \]where \( Y \) is the national income or output, \( C \) is consumption, and \( I \) is investment. In this exercise, we consider changes in factors causing shifts in equilibrium output, illustrating how output varies based on changes in planned investment, autonomous consumption, and the marginal propensity to consume.

The equilibrium is achieved when aggregate expenditure equals national income. When planned investment falls, for instance, total expenditure decreases without a change in income, shifting the entire expenditure line downward, resulting in a lower equilibrium output.

Marginal Propensity to Consume

The Marginal Propensity to Consume (MPC) is a critical element in understanding consumption behavior within the Keynesian framework. It measures the proportion of any additional income that is spent on consumption rather than saved.

MPC is typically represented by a value between 0 and 1, which in this exercise changes from 0.8 to 0.7. This represents a decrease in how much people consume out of their additional income, indicating they are saving more. The new consumption function, therefore, is given by:
\[ C = 100 + 0.7Y \]
This alteration leads to a less steep consumption line on a graph. A lower MPC results in decreased consumer spending, reducing aggregate demand and consequently lowering equilibrium output. Therefore, a decrease in MPC leads to reduced equilibrium income (\( Y \)), as shown by the calculated output of approximately 667 in the exercise.

Equilibrium Output

Equilibrium Output is where the total quantity of goods produced (aggregate supply) meets the total quantity demanded (aggregate expenditure) in the economy. This is the point at which the economy is stable, and there is neither an incentive for producers to increase output, nor a surplus urging them to cut back.

To determine the equilibrium output, we utilize the equation:\[ Y = C + I \]where equilibrium is achieved at points where planned total spending equals total production.

Different scenarios from the exercise illustrate how equilibrium output shifts with changes in various economic factors:

• When planned investment drops, equilibrium output decreases, as less investment implies lower production.
• A decline in autonomous consumption reduces the initial level of consumption, lowering the equilibrium output.
• Lastly, a reduced marginal propensity to consume (from 0.8 to 0.7) further contracts aggregate demand, leading to a lower equilibrium output.

Understanding these dynamics shows how sensitive the economy is to changes in spending behavior, investments, and consumptive habits.