Question

For a closed economy with no government expenditure and taxes, the aggregate consumption function (\(C\)) is given by: \[ C = 100 + 0.75 \, Y_d \] where \( Y_d \) is the disposable income. If the total investment is 80, the equilibrium output is ____________ (in integer).

Hint:

In a closed economy with no government, equilibrium is found using \( Y = C + I \). Always express consumption in terms of income and solve algebraically.

Answer 1

Step 1: Define equilibrium condition in a closed economy.
In a closed economy with no government, the equilibrium condition is: \[ Y = C + I \] where:
\( Y \) is total output (income),
\( C \) is consumption,
\( I \) is investment.
Step 2: Use the given consumption function.
Since there are no taxes, disposable income \( Y_d = Y \). So: \[ C = 100 + 0.75Y \] Step 3: Substitute values into equilibrium condition. \[ Y = (100 + 0.75Y) + 80 \] \[ Y = 180 + 0.75Y \] Step 4: Solve for \( Y \). \[ 0.25Y = 180 \quad \Rightarrow \quad Y = \frac{180}{0.25} = 700 \] Therefore, the equilibrium output is \( \boxed{700} \).