Consider the Neoclassical model. Suppose that we assume specific functional forms

for the consumption function and the investment demand function. These are:

Ct $=$ c$1($Yt $$ Gt$)+$ c$2($Yt$+1$ Gt$+1)$ c$3$rt $(9)$

It $=$d$1$rt $+$ d$2$At$+1$ d$3$Kt $(10)$

Here, c$1>0,$ c$2>0,$ c$3>0$ and d$1>0,$ d$2>0,$ d$3>0$ are fixed parameters governing

the sensitivity of consumption and investment to different factors relevant for those

decisions.

$($a$)$ Goods market clearing implies that Yt $=$ Ct $+$ It $+$ Gt$.$ Combine the given

functional forms for consumption and investment with the resource constraint

to derive an algebraic expression for the IS curve.

$($b$)$ Use your result in $($a$)$ to derive an expression for the slope of the IS curve $($i$.$e$.$

$$Yt

$$rt $).$

$($c$)$ Suppose that the parameters are as follows: c$1=0\mathrm{.}6,$ c$2=0\mathrm{.}5,$ c$3=10,$ d$1=20,$

d$2=1,$ and d$3=0\mathrm{.}5.$ Suppose that Yt$+1=15,$ Gt $=10,$ Gt$+1=10,$ At$+1=5,$

and Kt $=15.$ Suppose that rt $=0\mathrm{.}1.$ Solve for Yt$.$

$($d$)$ Now suppose that rt is increased to rt $=0\mathrm{.}12.$ Is Yt increasing or decreasing in

response?