Question #287979

ย If given the following information (Unit: RM million): Savings (S) = -500 + 0.15Yd Investment (I) = 400 - 150r Government expenditure (G) = 500 Taxes (T) = 200 + 0.1Y Money supply (Ms ) = 5000 Transaction money demand ( ๐๐ก ๐ ๐ )= 0.25Y Speculative money demand ( ๐๐ ๐ ๐ ) = 500-250r Price level (P) = 2

(a) Derive the functions of IS and LM in terms of interest rate (r) and income (Y). (b) Calculate the slope of the IS and LM curves. (c) Determine the equilibrium of interest rate and aggregate output in the economy. (d) If the autonomous consumption has increases to RM500 million, i. Calculate the new level of economic equilibrium. ii. Calculate the size of the horizontal and vertical movements that occur. iii. Sketch the changes that occurred before and after the increase in autonomous consumption and explain.

Expert's answer

i) IS Curve

Y= C+I+G

C= 500+0.75"Y^d"

Y= 500+0.75"Y^d+400-150r+500"

Y=1400+075"Y^d" -150r

"Y^d=Y-T"

=Y-(200-0.1Y)

=Y-200+0.1Y=1.1Y-200

Y=1400+0.75"(1.1Y-200)"

Y=1400+0.825Y-150-150r

0.175Y=1250-150r

**Y=7142.9-857.1r**

ii) LM Curve

Money supply equal to money demand

5000=0.25Y+500-250r

4500=0.25Y-250r

0.25Y=4500+250r

**Y=18000+1000r**

**iii) Equilibrium Interest and Output**

18000+1000r=7142.9-857.1r

1857.1r=-10857.9

r=-584.7%

Y=18000+ (-584.1"\\times1000)"

18000-584100

=-566100

iv) There is no change in the autonomous consumption hence no change in the equilibrium levels.

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