Country A is a closed economy. The consumption C=150+0.5(Y-T), Government expenditure is 300, Tax is 200, I=180-1200r, (M/P)d=Y-1000r, M=1200, P=2. What is the real interest rate(r) when it is equilibrium level?A.0.2B.0.12C.0.165D.0.178
Question
Country A is a closed economy. The consumption C=150+0.5(Y-T), Government expenditure is 300, Tax is 200, I=180-1200r, (M/P)d=Y-1000r, M=1200, P=2. What is the real interest rate(r) when it is equilibrium level?A.0.2B.0.12C.0.165D.0.178
Solution
In a closed economy, the equilibrium level is achieved when the total output (Y) equals the total spending, which is the sum of consumption (C), investment (I), and government expenditure (G).
Given the consumption function C = 150 + 0.5(Y - T), where T is tax, we can substitute T = 200 to get C = 150 + 0.5(Y - 200).
The investment function is given as I = 180 - 1200r.
The government expenditure is given as G = 300.
So, the equilibrium condition Y = C + I + G becomes Y = [150 + 0.5(Y - 200)] + (180 - 1200r) + 300.
Simplify this to get Y = 0.5Y + 130 - 1200r + 480.
Rearranging terms gives 0.5Y = 610 - 1200r.
So, Y = 1220 - 2400r.
The money demand function (M/P)d = Y - 1000r is given, where M is the money supply and P is the price level. Substituting M = 1200 and P = 2, we get (1200/2) = Y - 1000r.
This simplifies to 600 = Y - 1000r.
Substitute Y from the previous equation to get 600 = 1220 - 2400r - 1000r.
This simplifies to 600 = 1220 - 3400r.
Rearranging terms gives 3400r = 620.
So, the real interest rate r = 620 / 3400 = 0.182.
Therefore, the closest answer is D. 0.178.
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