To find the equilibrium level of income in a two-sector model, we need to use the equilibrium condition where aggregate demand $(AD)$ equals aggregate supply $(AS)$ or total output $(Y)$. In this simple model, aggregate demand $AD$ is the sum of consumption $(C)$ and investment $(I)$.

Given:

1. Consumption function: $C = 250 + 0.80Y$
2. Planned Investment (I): 150

Step-by-Step Solution:

The equilibrium condition is: $Y = C + I$

Substituting the values for $C$ and $I$: $Y = (250 + 0.80Y) + 150$

Simplifying this equation: $Y = 400 + 0.80Y$

Next, isolate $Y$ by moving the $0.80Y$ term to the left side: $Y - 0.80Y = 400$ $0.20Y = 400$

Now, solve for $Y$ by dividing both sides by 0.20: $Y = \frac{400}{0.20}$ $Y = 2000$

Answer:

The equilibrium level of income is 2000.

Would you like more details on how equilibrium in a two-sector economy is calculated or any other related concepts?

Related Questions:

1. How does a change in the consumption function affect the equilibrium income?
2. What happens to the equilibrium income if planned investment increases?
3. Why is the marginal propensity to consume (MPC) important in determining equilibrium income?
4. How would government spending affect equilibrium income in a three-sector model?
5. What is the effect of a change in the marginal propensity to save on equilibrium income?

Tip:

Remember that in simple two-sector models, equilibrium income depends heavily on the marginal propensity to consume (MPC) and planned investment levels.