In a two-sector economy, the equilibrium expenditure occurs when total output (Y) equals total planned expenditure (E), which is the sum of consumption (C) and planned investment (I).
The consumption function provided is: \[ C = 10 + 0.8Y \]
Planned investment (I) is given as R15.
The total planned expenditure (E) can be expressed as: \[ E = C + I \] \[ E = (10 + 0.8Y) + 15 \] \[ E = 25 + 0.8Y \]
At equilibrium, we have: \[ Y = E \] \[ Y = 25 + 0.8Y \]
Now, we can solve for Y:
- Rearrange the equation: \[ Y - 0.8Y = 25 \] \[ 0.2Y = 25 \]
- Divide both sides by 0.2: \[ Y = \frac{25}{0.2} \] \[ Y = 125 \]
Therefore, the equilibrium expenditure (Y) in this economy is R125.
Thus, the correct answer is R125.
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