Deriving the Autonomous Expenditure Multiplier

The autonomous expenditure multiplier measures the impact of changes in autonomous expenditure on the overall level of output in an economy. It is derived by considering the relationship between changes in autonomous expenditure, changes in aggregate demand, and changes in output. To derive the autonomous expenditure multiplier, we need to consider the impact of changes in the price of final goods and the rate of interest on autonomous expenditure.

Step 1: Understanding Autonomous Expenditure

Autonomous expenditure represents the spending that is independent of the level of output in an economy. It includes government spending, investment, and exports. Autonomous expenditure is not affected by changes in the price of final goods or the rate of interest.

Step 2: Understanding Aggregate Demand

Aggregate demand is the total spending on goods and services in an economy at a given price level. It consists of autonomous expenditure and induced expenditure. Induced expenditure depends on the level of output and is influenced by changes in the price of final goods and the rate of interest.

Step 3: Understanding the Impact of Changes in Autonomous Expenditure

When there is a change in autonomous expenditure, it directly affects aggregate demand. An increase in autonomous expenditure leads to an increase in aggregate demand, which results in an increase in output. Conversely, a decrease in autonomous expenditure leads to a decrease in aggregate demand and a decrease in output.

Step 4: Deriving the Multiplier

To derive the autonomous expenditure multiplier, we compare the initial change in autonomous expenditure to the resulting change in output. The multiplier represents the ratio of the change in output to the initial change in autonomous expenditure.

The formula for the autonomous expenditure multiplier is:

Multiplier = 1 / (1 - Marginal Propensity to Consume)

The Marginal Propensity to Consume (MPC) represents the proportion of additional income that is spent on consumption. It is influenced by changes in the price of final goods and the rate of interest.

Step 5: Applying the Price of Final Goods and Rate of Interest

To consider the impact of changes in the price of final goods and the rate of interest, we need to determine their influence on the MPC. Changes in the price of final goods and the rate of interest can affect consumer spending patterns and the willingness to spend.

The specific impact of changes in the price of final goods and the rate of interest on the MPC can vary depending on the specific economic conditions and factors influencing consumer behavior. Therefore, it is important to analyze the current economic situation and consider relevant data and research to determine the influence of these variables on the MPC.

Step 6: Calculating the Autonomous Expenditure Multiplier

Once we have determined the MPC taking into account the price of final goods and the rate of interest, we can calculate the autonomous expenditure multiplier using the formula mentioned earlier.

By plugging in the value of the MPC into the formula, we can calculate the multiplier, which will indicate the impact of changes in autonomous expenditure on output.

Conclusion

In conclusion, the autonomous expenditure multiplier is derived by considering the relationship between changes in autonomous expenditure, changes in aggregate demand, and changes in output. The multiplier represents the ratio of the change in output to the initial change in autonomous expenditure. To consider the impact of changes in the price of final goods and the rate of interest, we need to determine