To find the equilibrium level of GDP in the above economy, we can use the aggregate demand (AD) function, which is derived from the consumption (C), investment (I), and government spending (G) provided.
The aggregate demand formula can be written as:
\[ AD = C + I + G \]
Given:
- Consumption (C) function: \( C = 1000 + 0.75Y \)
- Investment (I): \( 850 \)
- Government Spending (G): \( 2500 \)
At equilibrium, aggregate demand equals GDP (Y):
\[ Y = C + I + G \]
Substituting the consumption function into the equation, we have:
\[ Y = (1000 + 0.75Y) + 850 + 2500 \]
Now, simplifying:
\[ Y = 1000 + 0.75Y + 850 + 2500 \] \[ Y = 4350 + 0.75Y \]
Next, we'll isolate Y. First, we can subtract \( 0.75Y \) from both sides:
\[ Y - 0.75Y = 4350 \] \[ 0.25Y = 4350 \]
Now, divide both sides by 0.25:
\[ Y = \frac{4350}{0.25} = 17400 \]
So, the equilibrium level of GDP for the above economy is R17400.
Answer:
R17400