Given the increase in government expenditures and the marginal propensity to consume, how would you find the change in equilibrium GDP?

I did the expenditures X the marginal propensity but this is wrong.

To find the change in equilibrium GDP, you need to consider the multiplier effect of government expenditures. The multiplier effect reflects how changes in autonomous spending, such as government expenditures, can generate a magnified impact on the overall economy.

Here's how you can calculate the change in equilibrium GDP:

Step 1: Determine the initial change in government expenditures (ΔG). This is the difference between the new government expenditure level and the old government expenditure level.

Step 2: Calculate the multiplier (k) using the formula: k = 1 / (1 - marginal propensity to consume)

Step 3: Multiply the initial change in government expenditures (ΔG) by the multiplier (k) to find the change in equilibrium GDP (ΔY). The formula is: ΔY = ΔG * k.

Let's say the initial government expenditure increases by $100 and the marginal propensity to consume is 0.8:

Step 1: ΔG = $100

Step 2: k = 1 / (1 - 0.8) = 1 / 0.2 = 5

Step 3: ΔY = $100 * 5 = $500

Therefore, the change in equilibrium GDP resulting from the increase in government expenditures would be $500.

It's important to note that this calculation assumes a simplified Keynesian model with only government expenditures as the autonomous spending component. In practice, other factors such as taxes, net exports, and investment may also influence equilibrium GDP.