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Unable to simplify variable completely

asked 2020-07-17 22:04:37 +0200

EconJohn gravatar image

updated 2020-07-20 21:16:06 +0200

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)

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?

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answered 2020-07-20 02:53:35 +0200

Juanjo gravatar image

Don't expect a clean expression from the output of solve. Instead, print (or show) the solution by substitution and apply additional methods to simplify the expressions. In this case, you can replace the last line by

good1step4 = solve(step2[0].subs(good2step3),x1)
print("x2 =", x2.subs(good2step3).canonicalize_radical())
print("x1 =", x1.subs(good1step4).canonicalize_radical())
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Asked: 2020-07-17 22:04:37 +0200

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Last updated: Jul 20 '20