Suppose that we assume specific functional forms for the

consumption function and the investment demand function. These are:

Ct = c1(Yt Gt) + c2(Yt+1 Gt+1) c3rt

It = d1rt + d2At+1 + d3Kt

Here, c1 through c4 and d1 through d3 are fixed parameters governing the

sensitivity of consumption and investment to different factors relevant for

those decisions.

(a) We must have Yt = Ct + It + Gt. Use the given functions forms from above for the

consumption and investment with the resource constraint to derive an

algebraic expression for the IS curve.

(b) Derive an expression for the slope of the IS curve (i.e. Yt/rt).

(c) Suppose that the parameters are as follows: c1 = 0.6, c2 = 0.5, c3 = 10,

d1 = 20, d2 = 1, and d3 = 0.5. Suppose that Yt+1 = 15, Gt = 10, Gt+1 = 10,

At+1 = 5, and Kt = 15. Suppose that rt = 0.1. Design an Excel file to

numerically solve for Yt.

(d) Suppose instead that rt = 0.15. Solve for Yt in the Excel file.

(e) Use a range of values of rt, ranging from 0.01 to 0.2, with a gap of

0.001 between values. Solve for Yt for each value of rt. Design a plot

with rt on the vertical axis and Yt on the horizontal axis (i.e. design a plot of the IS curve). Is it downward-sloping, as you would expect?

(f) Design another version of your IS curve when At+1 = 7 instead of 5. Plot

this along with the IS curve with At+1 = 5. Explain how the higher value

of At+1 impacts the position of the IS curve.