To find the equilibrium expenditure in a two-sector economy, we need to set total output (Y) equal to total expenditure (E), which comprises consumption (C) and planned investment (I). The formula for total expenditure is:
\[ E = C + I \]
Given:
- Consumption function: \( C = 10 + 0.8Y \)
- Planned investment: \( I = R15 \)
At equilibrium, \( E = Y \), so we can set up the equation:
\[ Y = C + I \]
Substituting the consumption function into the equation:
\[ Y = (10 + 0.8Y) + 15 \]
Now, simplify this:
\[ Y = 10 + 0.8Y + 15 \] \[ Y = 25 + 0.8Y \]
Next, we want to isolate \( Y \):
Subtract \( 0.8Y \) from both sides:
\[ Y - 0.8Y = 25 \] \[ 0.2Y = 25 \]
Now, divide both sides by 0.2:
\[ Y = \frac{25}{0.2} \] \[ Y = 125 \]
Therefore, the equilibrium expenditure is R125.
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