# Question:Determine zeros, indifference curve of two levels, numerical approximation

## Question:Determine zeros, indifference curve of two levels, numerical approximation

Maple

Dear community,

I'm a taxation student and trying to figure out maple more or less successfully for a research project... My aim is to find the indifference curve of the two levels S_TEV and S_P. As its probably not easy to find the formula, I'd alternatively like to approach the indifference curve numerically.

These are the basis codes:

E := 'E'
h := 4
m := 0.035
g:= h*m
k := 0.15
a := 0.25;
F_ANR := 4*m;
r:= 0.1;
T := 'T';
ESt := piecewise
(E < 9984, 0,
E < 14926, (1008.7*(E - 9984)/10000 + 1400)*(E - 9984)/10000,
E < 58596, (206.43*(E - 14926)/10000 + 2397)*(E - 14926)/10000 + 938.24,
E < 277826, 0.42*E - 9267.53,
0.45*E - 17602.28);

Er := E + (E - ESt)*r

EStr := piecewise(Er < 9984, 0,
Er < 14926, (1008.7*(Er - 9984)/10000 + 1400)*(Er - 9984)/10000,
Er < 58596, (206.43*(Er - 14926)/10000 + 2397)*(Er - 14926)/10000 + 938.24,
Er < 277826, 0.42*Er - 9267.53,
0.45*Er - 17602.28)

srp := EStr/E

r_p := r*srp

S_P := ESt*(1 + r_p)^T

EStk := piecewise(K < 9984, 0,
K < 14926, (1008.7*(K - 9984)/10000 + 1400)*(K - 9984)/10000,
K < 58596, (206.43*(K - 14926)/10000 + 2397)*(K - 14926)/10000 + 938.24,
K < 277826, 0.42*K - 9267.53,
0.45*K - 17602.28)

r_tev := 0.29*r

K := (0.71*E*(1 + 0.71*r)^T)*0.6

stev := EStk/K
S_TEV := E*(0.29*(1 + r_tev)^T + 0.71*(0.6*stev))

plot3d([S_TEV/E, S_P/E], E = 0 .. 500000, T = 0 .. 15, color = [white, black])

The plot shows the two levels. Id like to derive the indiffernce curve from this plot (intersection of S_TEV and S_PE).
Starting with probably Diff_S := S_TEV - S_P?

Can someone please help me with finding the right codes? I'm lost.... (eg. solve function for S-TEV-S_P=0; finding the right data frame for Diff_S:=0 or almost zero dependent on E and T, i.e. dataframe of E, T and S_TEV and S_P) so that I can plot (3D) all S_TEV = S_P depending on E, T.

Id be incredibly thankful for any help. It would literally safe my thesis!
Thank you so so much in advance!!
Rebekka ﻿