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solve() doesnt solve non-linear equation correctly :-! help me out here please

Philipp
2013-10-18
2013-11-04
  • Philipp
    Philipp
    2013-10-18

    I need help on this problem: I want to maximize u with respect to c1, given IBC:

    u:(c1^(1-(1/%sigma)))/(1-(1/%sigma))+%beta*(c2^(1-(1/%sigma)))/(1-(1/%sigma));
    IBC:c1+(c2/(1+r))=y1+(y2/(1+r));
    sol:solve(IBC,c2);
    solnc2:c2,sol;
    u_c1:subst(solnc2,c2,u);
    solve(diff(u_c1,c1)=0,c1);

    The solution for c1 on my computer still is a function of c1. Where is the problem?

    Best and many thanks!
    Philipp

     
  • I think the problem ist the 1/%sigma exponent. You may want to try

    solve(''radcan(solve(diff(u_c1,c1)=0,c1)^%sigma),c1);
    

    as your last line. Is this the result you need?

     
  • Philipp
    Philipp
    2013-11-04

    Dear Albrecht,
    thank you very much for the solution to the problem, you have solved the case. The way of solving is yet not "very" nice, as the exponent in this example is only (1/%sigma); but suppose it were different, i.e. something like x^(1/%alpha)+y^(1/%beta), then the solution would get ugly I guess.
    But for the moment I like your solution proposed. Thanks