To find the equilibrium level of GDP, we can use the following formula for the equilibrium condition in an economy:
\[ Y = C + I + G \]
Where:
- \( Y \) is the GDP,
- \( C \) is consumption,
- \( I \) is investment,
- \( G \) is government spending.
We are given:
- Consumption function: \( C = 1000 + 0.75Y \)
- Investment: \( I = 850 \)
- Government spending: \( G = 2500 \)
Plugging in the consumption function into the equilibrium condition:
\[ Y = (1000 + 0.75Y) + 850 + 2500 \]
Now, simplifying the equation:
\[ Y = 1000 + 0.75Y + 850 + 2500 \]
Combining the constant terms:
\[ Y = 4350 + 0.75Y \]
Next, we want to isolate \( Y \). Subtract \( 0.75Y \) from both sides:
\[ Y - 0.75Y = 4350 \]
This simplifies to:
\[ 0.25Y = 4350 \]
Now, divide both sides by \( 0.25 \):
\[ Y = \frac{4350}{0.25} = 17400 \]
Therefore, the equilibrium level of GDP for the above economy is:
R17400
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