Let's say I am given a table of information for the values of the real GDP, consumption, investment, exports, and imports. There was an equilibrium GDP where the real GDP = Aggregate Expenditure = C + I + X - IM. If the value of investments changed (went from 100 to 160), I had to calculate the new equilibrium GDP. But I did so by trial and error and was wondering if there was an easier/quicker way to do it. I have the multiplier values for consumption and imports.
To calculate the new equilibrium GDP after a change in investment, you can use the concept of the multiplier. The multiplier represents the relationship between the change in total spending and the resulting impact on GDP.
The multiplier in this case can be calculated using the formula: multiplier = 1 / (1 - marginal propensity to consume)
To use the multiplier approach, you need to know the values of the marginal propensity to consume (MPC) and the marginal propensity to import (MPM). The MPC represents the portion of additional income that individuals spend, while the MPM represents the portion of additional income that is used to purchase imports.
Once you have the MPC and MPM values, you can calculate the multiplier. Let's say the MPC is 0.8 and MPM is 0.1. Then the multiplier will be:
multiplier = 1 / (1 - 0.8*(1 - 0.1))
multiplier = 1 / (1 - 0.8*0.9)
multiplier = 1 / 0.28
multiplier ≈ 3.57
With the multiplier value determined, you can use it to calculate the change in equilibrium GDP due to the change in investment. In this case, the investment increased from 100 to 160, which is a change of +60. Multiply this change in investment by the multiplier value:
change in GDP = change in investment * multiplier
change in GDP = 60 * 3.57
change in GDP ≈ 214.2
To find the new equilibrium GDP, add the change in GDP to the initial equilibrium GDP:
new equilibrium GDP = initial equilibrium GDP + change in GDP
new equilibrium GDP = initial equilibrium GDP + 214.2
This approach eliminates the need for trial and error to find the new equilibrium GDP. Instead, you can use the multiplier concept to determine the impact of changes in expenditures on GDP.