We need to know which constants are subtracted from the equation:
= taxes become negative, and so does imports The system of equations now becomes:
C=800+0.6y
I = 900-50r
G=800
T = - 100
X = 350
M = -150-0.15y (make sure to subtract both parts of the equation) So all you do is add all the constants and you get:
AE=2300 +0.45y -050r Now from here we can get the IS curve:we set AE= Y
Y = 2300 +0.45y -050r group all common terms together
y-0.45y=2300-50r
0.55y=2300-50r
solving for y we get:
y=4181.82-91r What does this mean? IS is the equilibrium equation for the goods market. Every time r increase by 1%, y should increase by 91 units.Now how go we get the LM curve?We take the demand for money and we equate it to the L equation (supply of money)
M/P = L
500=0.25y-62.5r

Isolate Y on one side of the equation:
3.25y=500+62.5r
y=2000+250r

Now, we can solve for equilibrium y. This occurs when IS=LM

so we equate the two equations to each other:

4181.82-91r=2000+250r
Bring like terms together:
2181.82=341r
r= 6.4%

This is the equilibirum interest rate.

Now all we have to do is plug this r back into either the LS or Im equation
y=2000 + 250(6.4) = 3600

So our equilibirum y is now $3600

This is useful information, and can be used to give us a lot of information

We can find the trade balance at equilibirum y:

x = 350
M = 150 + 0.15(y) - plug in Y and M = 690.00
Trade balance = exports - imports = 350-690 = -340 - so there is a trade deficit

We can also calculate governement budget at equilibirum:

We can see that the tax rate is 25% from the consumption equation

t = 0.25, y=3600, T = 100 G = -800
What -800? because the goverment spend 800 and they only collect 100 in taxes

Government budget = 0.25 (3600) +100 -800 = 200$ surplus.

What if goverment spending rises to 900?
Since this changes the constant, we can just add it from the AE equation, which make it now 2400+.45y - 50r

The new IS cruve becomes 4363.63 - 91r
The LM curve will stay the same

Our new equilibirum r is

4363.63 - 91r = 2000+ 250r
2363.6=341r
r is now 6.93%

Y now becomes 2000 + 250 (6.93) = 3732.87 which is an increase from 3600.

Why does this occur?

This is due to the multiplier effect. If the goverment increases spending on the roads, the money that they spend keeps on multiplying. The governemnt will spend money on hiring workers, the workers need trucks, they need materials, they will shop, the shop keepers earn money... so the money gets multiplied.

This change is a fiscal policy, which effects the IS curve, and shifts the IS curve to the right - it causes economic expansion.

What if the supply of money increases?

this is a financial policy that will effect the LM curve.

Since there is more supply of money, the banks do not have to keep that much in their reserves, therfore, the interest rate will decrease, which will stimulate spending and cause an economic recovery. This will cause the LM curve to shift to the right.