Assume the economy is closed and there is no government. The aggregate demand components are described below:C = 100 + 0.6Y (1)I = 200 (2)Now there is a boost in investment, and total investment is now 300. What is the consumption of equilibrium?
Question
Assume the economy is closed and there is no government. The aggregate demand components are described below:C = 100 + 0.6Y (1)I = 200 (2)Now there is a boost in investment, and total investment is now 300. What is the consumption of equilibrium?
Solution
In a closed economy with no government, the equilibrium output (Y) is determined where aggregate demand equals aggregate supply. In this case, aggregate demand is the sum of consumption (C) and investment (I).
Given the consumption function C = 100 + 0.6Y and the initial investment I = 200, the aggregate demand (AD) is:
AD = C + I AD = (100 + 0.6Y) + 200 AD = 300 + 0.6Y
Now, if investment increases to 300, the new aggregate demand (AD') is:
AD' = C + I' AD' = (100 + 0.6Y) + 300 AD' = 400 + 0.6Y
In equilibrium, aggregate demand equals aggregate supply, so Y = AD'. Therefore:
Y = 400 + 0.6Y
To solve for Y, we rearrange the equation:
0.4Y = 400 Y = 400 / 0.4 Y = 1000
Substituting Y = 1000 into the consumption function:
C = 100 + 0.6*1000 C = 100 + 600 C = 700
So, the equilibrium consumption is 700.
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