the economic intuition.

Question $3(16$ points$)$

Consider the Neoclassical model. Suppose that we assume specific functional forms for the consumption function and the investment demand function. These are:

$C_t=c_1(Y_t-G_t)+c_2(Y_{t+1}-G_{t+1})-c_3{r}_t$

$I_t=-d_1{r}_t+d_2{A}_{t+1}-d_3{K}_t$

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 $Y_t=C_t+I_t+G_t.$ 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$.($:$\frac{del{Y}_t}{del{r}_t}$