00:03
So for the first part, we're asked to graph the is curve for r ranging from 0 to 8.
00:10
So we need to know in order to get the is curve, the equation for the is curve is given as follows.
00:27
C, which is consumption, plus i, investment, plus g, government spending.
00:36
So we have our consumption function.
00:38
So plug that in for c.
00:41
So that's 200 plus 0 .75 y minus t.
00:49
Then add your investment function, which is 200 minus 25 r.
00:58
Then government purchases are equal to 100.
01:02
We're given that taxes are also equal to 100.
01:05
So we can go ahead and plug that in for t.
01:08
So you see that we can get y in terms of r.
01:18
Now we're just going to simplify.
01:31
So we're going to distribute and combine like terms.
01:37
So this is what we end up with.
02:53
Now we need to graph the is curve.
03:02
We're going to have the interest rate r, and we're going to have income and output, which is y.
03:19
So income is on the horizontal axis, and interest rate is on the vertical axis.
03:25
So we're going to use a table.
03:35
So it's from 0 to 8, and i'm going to find y for r to go to 0, 4, and 8.
03:47
Or you can go ahead and plot all the points if you want.
03:51
So roughly it's going to look like this.
03:55
So it should be sloping downward.
04:01
Now we need to graph the lm curve.
04:08
So for this, our money demand is equal to money supply.
04:14
So we have to take our money supply and divide it by the price level.
04:28
This is equal to y minus 100r.
04:35
So m is the money supply, which is given as 1000.
04:41
Then the price level is given as 2.
04:45
So we'll plug those in.
05:00
So now we're just going to get y in terms of r.
05:04
So now we have our equation.
05:25
So plugging in our values for r into the equation, we get these values of y.
05:30
And then we can go ahead and graph the lm curve.
05:35
So when r is 0, y is 500, and we'll graph the other points.
05:43
So our lm curve looks something like this.
05:53
Find the equilibrium interest rate and equilibrium level of income.
05:57
So our equilibrium is going to be where the two curves cross.
06:04
So what we're going to do is we're going to take the two equations and we're going to set them equal.
06:15
And we can find the equilibrium output or the equilibrium interest rate because we're setting the ys equal.
06:24
So set these two equal and solve for r.
07:13
So we get r is equal to 6.
07:16
So our equilibrium interest rate is 6%.
07:19
Now we just need to plug in r into one of the formulas, and then we can solve for y.
07:38
So i'm going to use the lm curve.
07:46
So this is basically the same as how you find equilibrium for supply and demand.
07:59
So we get that it is equal to 1 ,100.
08:17
So then government purchases are raised to 150.
08:22
So this is going to go up.
08:25
And taxes will remain the same.
08:28
So how we figure this part out is we're going to basically do what we did in part a for the is curve.
08:39
We'll keep taxes at 100.
08:44
And what is changing is that this value for government purchases or spending is going to change to 150.
09:00
And if we simplify this, then we get the following for the new is curve.
09:08
So you can see here that this is a linear equation...