$1.$

Assume that the consumption function is given by

C

$=200+0\mathrm{.}5($

Y

$$

T

$),$ and the investment function is

I

$=1,000$

$200$

r

$,$ where

r

is measured in percent,

G

equals $300,$ and

T

equals $200.(20$ points$)$

a$.$

What is the numerical formula for the

IS

curve? $($

Hint:

Substitute for

C

$,$

I

$,$ and

G

in the equation

Y

$=$

C

$+$

I

$+$

G

and then write an equation for

Y

as a function of

r

$)$

b$.$

If

r

is $1$ percent, what is

I

$?$ What is

Y

$?$

c$.$

If

G

increases, does the

IS

curve s