What is the equilibrium level of income, given C = 100 + 0.75Y and I = ?

Steps to Solve

1. Set up the equilibrium condition
   The equilibrium level of income occurs when aggregate demand (AD) equals aggregate supply (Y). In this case, aggregate demand is the sum of consumption (C) and investment (I). We can express this as:
   $$ AD = C + I $$
   Thus, we have:
   $$ Y = C + I $$

2. Substitute the consumption function and investment
   The consumption function is given as ( C = 100 + 0.75Y ). We'll substitute this into the equilibrium equation along with the investment ( I ). Let's assume ( I = 500 ):
   $$ Y = (100 + 0.75Y) + 500 $$

3. Combine terms and solve for Y
   To isolate Y, we rearrange the equation:
   $$ Y = 600 + 0.75Y $$
   Subtract ( 0.75Y ) from both sides:
   $$ Y - 0.75Y = 600 $$ $$ 0.25Y = 600 $$

4. Calculate Y
   Now, we solve for Y by dividing both sides by 0.25:
   $$ Y = \frac{600}{0.25} $$
   Calculating this gives:
   $$ Y = 2400 $$

5. Check the investment options
   Since the investment level was assumed as ( I = 500 ), let's confirm if this is appropriate or if we should check the other investment options listed: 750, 150, and 250. We can repeat the process for each option if required.