Reference no: EM132813444
[Excel Problem] 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 function forms for the consumption and investment with the resource constraint to derive an algebraic expression for the IS curve.
(b) Use this to 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. Make an Excel file to numerically solve for Yt .
(d) Suppose instead that rt = 0.15. Solve for Yt in your Excel file. (e) Make 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 . Make a plot with rt on the vertical axis and Yt on the horizontal axis (i.e. Make a plot of the IS curve). Is it downward-sloping, as you would expect?
(f) Make 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.
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