Let Government purchases and taxes be 500 and 400 respectively ,investment is 200 ,and the spontaneous portion of consumption is 100 , marginal consumption trend is 0.9 ,which is the value of Y?
Question
Let Government purchases and taxes be 500 and 400 respectively ,investment is 200 ,and the spontaneous portion of consumption is 100 , marginal consumption trend is 0.9 ,which is the value of Y?
Solution
The question is asking for the value of Y, which in this context is the equilibrium level of income in an economy. This can be calculated using the formula for the equilibrium level of income in a simple Keynesian model:
Y = C + I + G
where: Y = equilibrium level of income C = consumption I = investment G = government purchases
The consumption function is given by:
C = Co + c(Y - T)
where: Co = autonomous consumption (the spontaneous portion of consumption) c = marginal propensity to consume Y = income T = taxes
Substituting the given values into the consumption function:
C = 100 + 0.9(Y - 400)
Substituting C, I, and G into the equilibrium level of income formula:
Y = [100 + 0.9(Y - 400)] + 200 + 500
Solving for Y:
Y = 800 + 0.9Y - 360
0.1Y = 440
Y = 4400
So, the equilibrium level of income (Y) is 4400.
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