Assume the economy is closed and there is no government. The aggregate demand componentsare described below:C = 100 + 0.4YI = 200 + 0.2 YWhat is the income of equilibrium?
Question
Assume the economy is closed and there is no government. The aggregate demand componentsare described below:C = 100 + 0.4YI = 200 + 0.2 YWhat is the income of equilibrium?
Solution
In a closed economy with no government, the equilibrium income 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 + 0.4Y and the investment function I = 200 + 0.2Y, aggregate demand (AD) can be expressed as:
AD = C + I AD = (100 + 0.4Y) + (200 + 0.2Y) AD = 300 + 0.6Y
In equilibrium, aggregate demand equals aggregate supply. Since we're dealing with a simple economy with no government, aggregate supply is just the total income, which we can denote as Y. Therefore, we can set AD equal to Y to find the equilibrium income:
Y = 300 + 0.6Y
To solve for Y, we can subtract 0.6Y from both sides of the equation:
Y - 0.6Y = 300 0.4Y = 300
Finally, we can solve for Y by dividing both sides of the equation by 0.4:
Y = 300 / 0.4 Y = 750
Therefore, the equilibrium income in this economy is 750.
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