To find the equilibrium GDP (Y) in the private open economy, we need to use the equation for aggregate demand (AD), which consists of consumption (C), investment (I), and net exports (NX = X - M).
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Calculate C (Consumption): \[ C = 40 + 0.8Y \]
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Investment (I): \[ I = 40 \]
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Net Exports (NX): \[ NX = X - M = 20 - 30 = -10 \]
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Aggregate Demand (AD): \[ AD = C + I + NX \] \[ AD = (40 + 0.8Y) + 40 - 10 \] \[ AD = 70 + 0.8Y \]
In equilibrium, aggregate demand equals GDP (Y): \[ Y = AD \]
So we set the equation as follows: \[ Y = 70 + 0.8Y \]
- Rearranging the equation: \[ Y - 0.8Y = 70 \] \[ 0.2Y = 70 \] \[ Y = \frac{70}{0.2} \] \[ Y = 350 \]
Thus, the equilibrium GDP in the above economy is R350.
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