Answer to Question #208600 in Macroeconomics for Saman Khalil

Question

Consider a hypothetical economy for which you are given the following information.

C = 102 + 0.7Y

I = 150 − 100r

Ms = 300

Md = 0.25Y + 124 − 200r

Required

1. write the IS equation and explain it.
2. Find the LM equation and give its explanation
3. Find the equilibrium level of income and equilibrium level of interest
4. Find the level of of C, the level of I, the level of L(Md) when the economy is in equilibrium
5. Construct the tables of IS and LM curves. put them together on the new graph to determine the equilibrium level of income and interest rate graphically.

Answer 1

write the IS equation and explain it.

$Y = C+I$

$Y = 102+ 0.7Y+150-100r$

$Y- 0.7Y= 102+150-100r$

$0.3Y = 252-100r$ ( IS equation)

This equation comprises of the Consumption, Investment , tax and government expenditure.

In this case we are not given the tax and the government expenditure. We therefore obtain the IS using the C and I.

Find the LM equation and give its explanation

LM equation is obtained by equating money supply equation with the money demanded. Thus,

$Ms = Md$

$300=0.25Y+ 124- 200r$

$176-0.25Y = - 200r$

$200r= 0.25Y-176$

$r = \frac{Y}{800}-0.88$ ( LM equation)

Find the equilibrium level of income and equilibrium level of interest

$Y = 840- \frac{1000}{3}r$

To find Y we replace the value of r in the equation of Y.

$Y = 840- \frac{1000}{3}(\frac{Y}{800}- 0.88)$

$Y= 840- \frac{1000}{2400}Y-\frac{880}{3}$

$\frac{17}{12}Y= \frac{1640}{3}$

$Y = 385.88$

Level of C

$C= 102+ 0.7Y$

$C= 102+ 0.7(385.88)$

$C = 372.12$

Level of I

$I = 150 - 100r$

r = $\frac{385.88}{800}- 0.88$

$r = - 0.40$

$I = 150- 100( - 0.40) = 400$

$I = 400$

Level of MD

$Md = 0.25Y+ 124- 200r$

$Md = 0.25(385.88)+ 124 - 200(- 0.40)= 300.47$