Question

Given the consumption function \(C = 200 + 0.8Y\), \(I = 300\), find the equilibrium income.

Hint:

To find equilibrium income, set total income equal to the sum of consumption and investment, and solve for \(Y\).

Answer 1

Step 1: Define the equilibrium condition.
At equilibrium, total output (income) \(Y\) equals total expenditure, which is the sum of consumption \(C\) and investment \(I\). Therefore, the equilibrium condition is: \[ Y = C + I \]
Step 2: Substitute the given values.
We are given the consumption function \(C = 200 + 0.8Y\) and investment \(I = 300\). Substituting these into the equilibrium condition: \[ Y = (200 + 0.8Y) + 300 \]
Step 3: Solve for \(Y\).
Simplifying the equation: \[ Y = 500 + 0.8Y \] \[ Y - 0.8Y = 500 \] \[ 0.2Y = 500 \] \[ Y = \frac{500}{0.2} = 2500 \]