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Answer :
The equilibrium output (Y) is 2300.
To determine the equilibrium output (Y), we need to equate aggregate demand (AD) with aggregate supply (AS). In this case, aggregate demand (AD) is represented by consumption (C) plus government spending (G), while aggregate supply (AS) is represented by output (Y).
AD = C + G
AS = Y
Given the behavioral equation for consumption (C) as C = 170 + 0.9YD, we need to determine disposable income (YD) to calculate aggregate demand (AD).
Disposable income (YD) is calculated by subtracting taxes (T) from output (Y), which in this case is YD = Y - T.
Substituting this into the equation for consumption, we get:
C = 170 + 0.9(Y - T)
C = 170 + 0.9(Y - 100)
C = 170 + 0.9Y - 90
Now, we can express aggregate demand (AD) as:
AD = C + G
AD = 170 + 0.9Y - 90 + 150
AD = 230 + 0.9Y
To find the equilibrium output (Y), we set AD equal to AS:
AD = AS
230 + 0.9Y = Y
Simplifying the equation:
0.9Y - Y = -230
-0.1Y = -230
Y = -230 / -0.1
Y = 2300
Therefore, the equilibrium output (Y) is 2300.
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Rewritten by : Barada
The equilibrium output is 1400.
To find the equilibrium output in the given economy, we need to solve for Y where aggregate demand equals aggregate output. The behavioral equations provided are:
- C = 170 + 0.7YDI
- I = 170
- G = 150
- T = 100
We first calculate disposable income (YDI):
- YDI = Y - T
Then substitute YDI into the consumption function:
- C = 170 + 0.7(Y - 100)
Aggregate demand (AD) is the sum of Consumption (C), Investment (I), and Government spending (G):
- AD = C + I + G
Substituting the values we get:
- AD = (170 + 0.7(Y - 100)) + 170 + 150
Simplifying the equation:
- AD = 170 + 0.7Y - 70 + 170 + 150
- AD = 420 + 0.7Y
At equilibrium, aggregate demand equals aggregate output:
- Y = AD
- Y = 420 + 0.7Y
Solving for Y:
- Y - 0.7Y = 420
- 0.3Y = 420
- Y = 1400
Therefore, the equilibrium output equals 1400.
Complete Question:
Suppose that the economy is characterized by the following behavioral equations:
C = 170 + 0.7YDI
I = 170
G = 150
T = 100
What does equilibrium output equal?
