i have a college macroeconomics question due tommorow can u help??
economy decribed as follows:
C=14,000+.5(y-t)-40,000r
I=8000-20,000r
G=7000
NX=-1800
T=8000
Y=40000
1)find a numeric equation relating planned aggregate expenditure to output and the real interest rate??
2)at what value should the fed set the real interest rate to eliminate any output gap???
please let me know A.S.A.P.
Of course, I can help you with your macroeconomics questions. Let's break them down step by step.
1) To find a numeric equation relating planned aggregate expenditure (AE) to output (Y) and the real interest rate (r), we need to sum up the components of AE: consumption (C), investment (I), government spending (G), and net exports (NX). The equation for AE in this economy is given as follows:
AE = C + I + G + NX
Given the following equations:
C = 14,000 + 0.5(Y - T) - 40,000r
I = 8,000 - 20,000r
G = 7,000
NX = -1,800
We can substitute these equations into the AE equation:
AE = (14,000 + 0.5(Y - T) - 40,000r) + (8,000 - 20,000r) + 7,000 - 1,800
Simplifying further:
AE = 29,000 + 0.5(Y - T) - 60,000r
Therefore, the numeric equation relating planned aggregate expenditure to output and the real interest rate is:
AE = 29,000 + 0.5(Y - 8,000) - 60,000r
2) To eliminate any output gap, the real interest rate (r) should be set at the level where planned aggregate expenditure (AE) equals actual output (Y). In other words, we need to find the value of r that equates AE to Y in the numeric equation above.
Given that Y = 40,000, we can substitute this value into the equation:
AE = 29,000 + 0.5(40,000 - 8,000) - 60,000r
Simplifying further:
29,000 + 0.5(32,000) - 60,000r = 40,000
Rewriting the equation:
16,000 - 60,000r = 40,000 - 29,000
Simplifying:
16,000 - 60,000r = 11,000
Rearranging:
60,000r = 16,000 - 11,000
60,000r = 5,000
Dividing both sides by 60,000:
r = 5,000 / 60,000
Simplifying further:
r ≈ 0.0833
Therefore, the fed should set the real interest rate to approximately 0.0833 to eliminate any output gap.
I hope this helps!