In solving the following hicksian demands in this problem and so far the proceedure works great.
x1, x2, l, p1, p2, a, b, R= var('x1, x2, l, p1, p2, a, b, R')
U = x1^a*x2^b
m = p1*x1+p2*x2;
L = m+ l * (R-U);
dLdx = L.diff(x1);
dLdy = L.diff(x2);
dLdl = L.diff(l);
step1=solve([dLdx == 0, dLdy == 0, dLdl == 0], p1, p2, R)
step2=solve((p1/p2).subs(step1)==p1/p2, x1)
good2step3 = solve((U/R).subs(step2).log().log_expand()==0, x2)
good1step4=solve(step2[0].subs(good2step3).canonicalize_radical(),x1)
however I note that I dont get such a clean result for good2step3, though algebraically correct its not completely simplified. I've tried simplify_rational() and simplify_log but that ends up ruining my clean solution for x1 in good1step4.
Is there more I can do to clean up my solutions?
