Revisions to Variable Value as Range

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edited Oct 7, 2014 at 18:28

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Thank you for the help so far!

I would like to assign +/i signs for the function and solution such as (+)(+)(-) and therefore (-).

It is working for the first evaluation, [Lambda]lowerλlower, but not for the second evaluation, [Lambda]upperλupper. I cannot see the difference - has it to do with "[Lambda]i"λi /. Solve" in both definitions?

    (* Endogenous *)
    Clear[\[Mu]Clear[μ, \[Xi]ξ, \[Beta]β, \[Gamma]γ, ri, si, rj, sj, \[Lambda]CriλCri, \[Lambda]CsiλCsi , \[Lambda]lowerλlower, \[Lambda]upperλupper, \[Lambda]lowereipλlowereip, \[Lambda]ip];λip];
    (* Exogenous *)
    Clear[ ci, yp, \[Lambda]iλi, \[Alpha]iαi, \[Epsilon]ipϵip, \[Eta]ipηip, eip];
    ri = \[Epsilon]ip*\[Lambda]iϵip*λi + (1 - \[Eta]ipηip)*(1 - \[Lambda]iλi);
    si = \[Eta]ip*ηip*(1 - \[Lambda]iλi) + (1 - \[Epsilon]ipϵip)*\[Lambda]i;*λi; 
    \[Lambda]CriλCri = (\[Epsilon]ip*\[Lambda]iϵip*λi)/(\[Epsilon]ip*\[Lambda]iϵip*λi + (1 - \[Eta]ipηip)*(1 - \[Lambda]iλi));
    \[Lambda]CsiλCsi = (\[Eta]ip*ηip*(1 - \[Lambda]iλi))/(\[Eta]ip*ηip*(1 - \[Lambda]iλi) + (1 - \[Epsilon]ipϵip)*\[Lambda]i*λi);
    \[Lambda]lowerλlower = \[Lambda]iλi /. 
    Solve[ri*(yp - eip - ci + \[Alpha]i*\[Lambda]Criαi*λCri) + si*(yp - eip + \[Alpha]i*αi*(1 - \[Lambda]CsiλCsi)) == yp + \[Alpha]i*αi*(1 - \[Lambda]iλi), {\[Lambda]iλi}];
    \[Lambda]upperλupper = \[Lambda]iλi /.Solve[ri*(yp - eip - ci + \[Alpha]i*\[Lambda]Criαi*λCri) + 
  si*(yp - eip + \[Alpha]i*αi*(1 - \[Lambda]CsiλCsi)) == yp + \[Alpha]i*\[Lambda]iαi*λi - ci, {\[Lambda]iλi} ];
    Simplify[D[\[Lambda]lowerSimplify[D[λlower, eip]]
    Simplify[Sign[D[\[Lambda]lowerSimplify[Sign[D[λlower, eip]], \[Alpha]iαi > 0 && eip > 0 && ci > 0 && 0 < \[Epsilon]ipϵip < 1 && 0 < ci < 1 && 0 < \[Eta]ipηip < 1 && \[Alpha]iαi > ci && \[Alpha]iαi > ci + eip && \[Epsilon]ipϵip + \[Eta]iηi < 1]
    Simplify[D[\[Lambda]upperSimplify[D[λupper, eip]]
    Simplify[Sign[D[\[Lambda]upperSimplify[Sign[D[λupper, eip]], \[Alpha]iαi > 0 && eip > 0 && ci > 0 && 0 < \[Epsilon]ipϵip < 1 && 0 < ci < 1 && 0 < \[Eta]ipηip < 1 && \[Alpha]iαi > ci && \[Alpha]iαi > ci + eip && \[Epsilon]ipϵip + \[Eta]iηi < 1]

Thank you for the help so far!

I would like to assign +/i signs for the function and solution such as (+)(+)(-) and therefore (-).

It is working for the first evaluation, [Lambda]lower, but not for the second evaluation, [Lambda]upper. I cannot see the difference - has it to do with "[Lambda]i /. Solve" in both definitions?

    (* Endogenous *)
    Clear[\[Mu], \[Xi], \[Beta], \[Gamma], ri, si, rj, sj, \[Lambda]Cri, \[Lambda]Csi , \[Lambda]lower, \[Lambda]upper, \[Lambda]lowereip, \[Lambda]ip];
    (* Exogenous *)
    Clear[ ci, yp, \[Lambda]i, \[Alpha]i, \[Epsilon]ip, \[Eta]ip, eip];
    ri = \[Epsilon]ip*\[Lambda]i + (1 - \[Eta]ip)*(1 - \[Lambda]i);
    si = \[Eta]ip*(1 - \[Lambda]i) + (1 - \[Epsilon]ip)*\[Lambda]i; 
    \[Lambda]Cri = (\[Epsilon]ip*\[Lambda]i)/(\[Epsilon]ip*\[Lambda]i + (1 - \[Eta]ip)*(1 - \[Lambda]i));
    \[Lambda]Csi = (\[Eta]ip*(1 - \[Lambda]i))/(\[Eta]ip*(1 - \[Lambda]i) + (1 - \[Epsilon]ip)*\[Lambda]i);
    \[Lambda]lower = \[Lambda]i /. 
    Solve[ri*(yp - eip - ci + \[Alpha]i*\[Lambda]Cri) + si*(yp - eip + \[Alpha]i*(1 - \[Lambda]Csi)) == yp + \[Alpha]i*(1 - \[Lambda]i), {\[Lambda]i}];
    \[Lambda]upper = \[Lambda]i /.Solve[ri*(yp - eip - ci + \[Alpha]i*\[Lambda]Cri) + 
  si*(yp - eip + \[Alpha]i*(1 - \[Lambda]Csi)) == yp + \[Alpha]i*\[Lambda]i - ci, {\[Lambda]i} ];
    Simplify[D[\[Lambda]lower, eip]]
    Simplify[Sign[D[\[Lambda]lower, eip]], \[Alpha]i > 0 && eip > 0 && ci > 0 && 0 < \[Epsilon]ip < 1 && 0 < ci < 1 && 0 < \[Eta]ip < 1 && \[Alpha]i > ci && \[Alpha]i > ci + eip && \[Epsilon]ip + \[Eta]i < 1]
    Simplify[D[\[Lambda]upper, eip]]
    Simplify[Sign[D[\[Lambda]upper, eip]], \[Alpha]i > 0 && eip > 0 && ci > 0 && 0 < \[Epsilon]ip < 1 && 0 < ci < 1 && 0 < \[Eta]ip < 1 && \[Alpha]i > ci && \[Alpha]i > ci + eip && \[Epsilon]ip + \[Eta]i < 1]

Thank you for the help so far!

I would like to assign +/i signs for the function and solution such as (+)(+)(-) and therefore (-).

It is working for the first evaluation, λlower, but not for the second evaluation, λupper. I cannot see the difference - has it to do with "λi /. Solve" in both definitions?

    (* Endogenous *)
    Clear[μ, ξ, β, γ, ri, si, rj, sj, λCri, λCsi , λlower, λupper, λlowereip, λip];
    (* Exogenous *)
    Clear[ ci, yp, λi, αi, ϵip, ηip, eip];
    ri = ϵip*λi + (1 - ηip)*(1 - λi);
    si = ηip*(1 - λi) + (1 - ϵip)*λi; 
    λCri = (ϵip*λi)/(ϵip*λi + (1 - ηip)*(1 - λi));
    λCsi = (ηip*(1 - λi))/(ηip*(1 - λi) + (1 - ϵip)*λi);
    λlower = λi /. 
    Solve[ri*(yp - eip - ci + αi*λCri) + si*(yp - eip + αi*(1 - λCsi)) == yp + αi*(1 - λi), {λi}];
    λupper = λi /.Solve[ri*(yp - eip - ci + αi*λCri) + 
  si*(yp - eip + αi*(1 - λCsi)) == yp + αi*λi - ci, {λi} ];
    Simplify[D[λlower, eip]]
    Simplify[Sign[D[λlower, eip]], αi > 0 && eip > 0 && ci > 0 && 0 < ϵip < 1 && 0 < ci < 1 && 0 < ηip < 1 && αi > ci && αi > ci + eip && ϵip + ηi < 1]
    Simplify[D[λupper, eip]]
    Simplify[Sign[D[λupper, eip]], αi > 0 && eip > 0 && ci > 0 && 0 < ϵip < 1 && 0 < ci < 1 && 0 < ηip < 1 && αi > ci && αi > ci + eip && ϵip + ηi < 1]

deleted 2 characters in body

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edited Oct 7, 2014 at 18:22

Tom

383
1
11

Thank you for the help so far!

A mathematical example:

0<a<1,
0<b<1,
a+b>1.
x = a(1-b)(1-a-b) < 0

I would like to assign +/i signs for the function and solution such as (+)(+)(-) and therefore (-).

It is working for the first evaluation, [Lambda]lower, but not for the second evaluation, [Lambda]upper. I cannot see the difference - has it to do with "[Lambda]i /. Solve" in both definitions?

    (* Endogenous *)
    Clear[\[Mu], \[Xi], \[Beta], \[Gamma], ri, si, rj, sj, \[Lambda]Cri, \[Lambda]Csi , \[Lambda]lower, \[Lambda]upper, \[Lambda]lowereip, \[Lambda]ip];
    (* Exogenous *)
    Clear[ ci, yp, \[Lambda]i, \[Alpha]i, \[Epsilon]ip, \[Eta]ip, eip];
    ri = \[Epsilon]ip*\[Lambda]i + (1 - \[Eta]ip)*(1 - \[Lambda]i);
    si = \[Eta]ip*(1 - \[Lambda]i) + (1 - \[Epsilon]ip)*\[Lambda]i; 
    \[Lambda]Cri = (\[Epsilon]ip*\[Lambda]i)/(\[Epsilon]ip*\[Lambda]i + (1 - \[Eta]ip)*(1 - \[Lambda]i));
    \[Lambda]Csi = (\[Eta]ip*(1 - \[Lambda]i))/(\[Eta]ip*(1 - \[Lambda]i) + (1 - \[Epsilon]ip)*\[Lambda]i);
    \[Lambda]lower = \[Lambda]i /. 
    Solve[ri*(yp - eip - ci + \[Alpha]i*\[Lambda]Cri) + si*(yp - eip + \[Alpha]i*(1 - \[Lambda]Csi)) == yp + \[Alpha]i*(1 - \[Lambda]i), {\[Lambda]i}];
    \[Lambda]upper = \[Lambda]i /.Solve[ri*(yp - eip - ci + \[Alpha]i*\[Lambda]Cri) + 
  si*(yp - eip + \[Alpha]i*(1 - \[Lambda]Csi)) == yp + \[Alpha]i*\[Lambda]i - ci, {\[Lambda]i} ];
    Simplify[D[\[Lambda]lower, eip]]
    Simplify[Sign[D[\[Lambda]lower, eip]], \[Alpha]i > 0 && eip > 0 && ci > 0 && 0 < \[Epsilon]ip < 1 && 0 < ci < 1 && 0 < \[Eta]ip < 1 && \[Alpha]i > ci && \[Alpha]i > ci + eip && \[Epsilon]ip + \[Eta]i < 1]
    Simplify[D[\[Lambda]upper, eip]]
    Simplify[Sign[D[\[Lambda]upper, eip]], \[Alpha]i > 0 && eip > 0 && ci > 0 && 0 < \[Epsilon]ip < 1 && 0 < ci < 1 && 0 < \[Eta]ip < 1 && \[Alpha]i > ci && \[Alpha]i > ci + eip && \[Epsilon]ip + \[Eta]i < 1]

Thank you for the help so far!

A mathematical example:

0<a<1,
0<b<1,
a+b>1.
x = a(1-b)(1-a-b) < 0

I would like to assign +/i signs for the function and solution such as (+)(+)(-) and therefore (-).

It is working for the first evaluation, [Lambda]lower, but not for the second evaluation, [Lambda]upper.

    (* Endogenous *)
    Clear[\[Mu], \[Xi], \[Beta], \[Gamma], ri, si, rj, sj, \[Lambda]Cri, \[Lambda]Csi , \[Lambda]lower, \[Lambda]upper, \[Lambda]lowereip, \[Lambda]ip];
    (* Exogenous *)
    Clear[ ci, yp, \[Lambda]i, \[Alpha]i, \[Epsilon]ip, \[Eta]ip, eip];
    ri = \[Epsilon]ip*\[Lambda]i + (1 - \[Eta]ip)*(1 - \[Lambda]i);
    si = \[Eta]ip*(1 - \[Lambda]i) + (1 - \[Epsilon]ip)*\[Lambda]i; 
    \[Lambda]Cri = (\[Epsilon]ip*\[Lambda]i)/(\[Epsilon]ip*\[Lambda]i + (1 - \[Eta]ip)*(1 - \[Lambda]i));
    \[Lambda]Csi = (\[Eta]ip*(1 - \[Lambda]i))/(\[Eta]ip*(1 - \[Lambda]i) + (1 - \[Epsilon]ip)*\[Lambda]i);
    \[Lambda]lower = \[Lambda]i /. 
    Solve[ri*(yp - eip - ci + \[Alpha]i*\[Lambda]Cri) + si*(yp - eip + \[Alpha]i*(1 - \[Lambda]Csi)) == yp + \[Alpha]i*(1 - \[Lambda]i), {\[Lambda]i}];
    \[Lambda]upper = \[Lambda]i /.Solve[ri*(yp - eip - ci + \[Alpha]i*\[Lambda]Cri) + 
  si*(yp - eip + \[Alpha]i*(1 - \[Lambda]Csi)) == yp + \[Alpha]i*\[Lambda]i - ci, {\[Lambda]i} ];
    Simplify[D[\[Lambda]lower, eip]]
    Simplify[Sign[D[\[Lambda]lower, eip]], \[Alpha]i > 0 && eip > 0 && ci > 0 && 0 < \[Epsilon]ip < 1 && 0 < ci < 1 && 0 < \[Eta]ip < 1 && \[Alpha]i > ci && \[Alpha]i > ci + eip && \[Epsilon]ip + \[Eta]i < 1]
    Simplify[D[\[Lambda]upper, eip]]
    Simplify[Sign[D[\[Lambda]upper, eip]], \[Alpha]i > 0 && eip > 0 && ci > 0 && 0 < \[Epsilon]ip < 1 && 0 < ci < 1 && 0 < \[Eta]ip < 1 && \[Alpha]i > ci && \[Alpha]i > ci + eip && \[Epsilon]ip + \[Eta]i < 1]

Thank you for the help so far!

I would like to assign +/i signs for the function and solution such as (+)(+)(-) and therefore (-).

It is working for the first evaluation, [Lambda]lower, but not for the second evaluation, [Lambda]upper. I cannot see the difference - has it to do with "[Lambda]i /. Solve" in both definitions?

    (* Endogenous *)
    Clear[\[Mu], \[Xi], \[Beta], \[Gamma], ri, si, rj, sj, \[Lambda]Cri, \[Lambda]Csi , \[Lambda]lower, \[Lambda]upper, \[Lambda]lowereip, \[Lambda]ip];
    (* Exogenous *)
    Clear[ ci, yp, \[Lambda]i, \[Alpha]i, \[Epsilon]ip, \[Eta]ip, eip];
    ri = \[Epsilon]ip*\[Lambda]i + (1 - \[Eta]ip)*(1 - \[Lambda]i);
    si = \[Eta]ip*(1 - \[Lambda]i) + (1 - \[Epsilon]ip)*\[Lambda]i; 
    \[Lambda]Cri = (\[Epsilon]ip*\[Lambda]i)/(\[Epsilon]ip*\[Lambda]i + (1 - \[Eta]ip)*(1 - \[Lambda]i));
    \[Lambda]Csi = (\[Eta]ip*(1 - \[Lambda]i))/(\[Eta]ip*(1 - \[Lambda]i) + (1 - \[Epsilon]ip)*\[Lambda]i);
    \[Lambda]lower = \[Lambda]i /. 
    Solve[ri*(yp - eip - ci + \[Alpha]i*\[Lambda]Cri) + si*(yp - eip + \[Alpha]i*(1 - \[Lambda]Csi)) == yp + \[Alpha]i*(1 - \[Lambda]i), {\[Lambda]i}];
    \[Lambda]upper = \[Lambda]i /.Solve[ri*(yp - eip - ci + \[Alpha]i*\[Lambda]Cri) + 
  si*(yp - eip + \[Alpha]i*(1 - \[Lambda]Csi)) == yp + \[Alpha]i*\[Lambda]i - ci, {\[Lambda]i} ];
    Simplify[D[\[Lambda]lower, eip]]
    Simplify[Sign[D[\[Lambda]lower, eip]], \[Alpha]i > 0 && eip > 0 && ci > 0 && 0 < \[Epsilon]ip < 1 && 0 < ci < 1 && 0 < \[Eta]ip < 1 && \[Alpha]i > ci && \[Alpha]i > ci + eip && \[Epsilon]ip + \[Eta]i < 1]
    Simplify[D[\[Lambda]upper, eip]]
    Simplify[Sign[D[\[Lambda]upper, eip]], \[Alpha]i > 0 && eip > 0 && ci > 0 && 0 < \[Epsilon]ip < 1 && 0 < ci < 1 && 0 < \[Eta]ip < 1 && \[Alpha]i > ci && \[Alpha]i > ci + eip && \[Epsilon]ip + \[Eta]i < 1]

added 65 characters in body

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edited Oct 6, 2014 at 21:06

Tom

383
1
11

I have used the structure for the underlying problem. Assigning signsIt is working if I evaluatefor the solution directlyfirst evaluation, [Lambda]lower, but not if I evaluatefor the variable value itselfsecond evaluation, [Lambda]upper.

    (* Endogenous *)
    Clear[\[Mu], \[Xi], \[Beta], \[Gamma], ri, si, rj, sj, \[Lambda]Cri, \[Lambda]Csi , \[Lambda]lower, \[Lambda]upper, \
    \[Lambda]lowereip, \[Lambda]ip];
    (* Exogenous *)
    Clear[ ci, yp, \[Lambda]i, \[Alpha]i, \[Epsilon]ip, \[Eta]ip, eip];
    ri = \[Epsilon]ip*\[Lambda]i + (1 - \[Eta]ip)*(1 - \[Lambda]i);
    si = \[Eta]ip*(1 - \[Lambda]i) + (1 - \[Epsilon]ip)*\[Lambda]i; 
    \[Lambda]Cri = (\[Epsilon]ip*\[Lambda]i)/(\[Epsilon]ip*\[Lambda]i + (1 - \[Eta]ip)*(1 - \[Lambda]i));
    \[Lambda]Csi = (\[Eta]ip*(1 - \[Lambda]i))/(\[Eta]ip*(1 - \[Lambda]i) + (1 - \[Epsilon]ip)*\[Lambda]i);
    \[Lambda]lower = \[Lambda]i /. 
    Solve[ri*(yp - eip - ci + \[Alpha]i*\[Lambda]Cri) + 
 si*(yp - eip + \[Alpha]i*(1 - \[Lambda]Csi)) == yp + \[Alpha]i*(1 - \[Lambda]i), {\[Lambda]i}]];
    \[Lambda]lowereip\[Lambda]upper = Simplify[D[\[Lambda]lower,\[Lambda]i eip]]
/.Solve[ri*(yp - eip - ci + \[Alpha]i*\[Lambda]Cri) + 
  si*(yp - eip + \[Alpha]i*(*1 Assigning- Sign\[Lambda]Csi)) == yp + \[Alpha]i*\[Lambda]i - notci, working{\[Lambda]i} *)];
    Simplify[Sign[\[Lambda]lowereip]Simplify[D[\[Lambda]lower, eip]]
    Simplify[Sign[D[\[Lambda]lower, eip]], \[Alpha]i > 0 && eip > 0 && ci > 0 && 0 < \[Epsilon]ip < 1 && 0 < ci < 1 && 0 < \[Eta]ip < 1 && \[Alpha]i > ci && \[Alpha]i > ci + eip && \[Epsilon]ip + \[Eta]i < 1]
 
    (* Assigning Sign - working. Note that "x" is the solution toSimplify[D[\[Lambda]upper, \[Lambda]lowereip*)eip]]
    x =Simplify[Sign[D[\[Lambda]upper, 1/(2eip]], \[Alpha]i -> ci0 (-1&& +eip \[Epsilon]ip> +0 \[Eta]ip))
&& ci > 0 Simplify[Sign[x],&& 0 < \[Epsilon]ip < 1 && 0 < ci < 1 && 0 < \[Eta]ip < 1 && \[Alpha]i > ci && \[Alpha]i > ci + eip && \[Epsilon]ip + \[Eta]i < 1]

I have used the structure for the underlying problem. Assigning signs is working if I evaluate the solution directly but not if I evaluate the variable value itself.

    (* Endogenous *)
    Clear[\[Mu], \[Xi], \[Beta], \[Gamma], ri, si, rj, sj, \[Lambda]Cri, \[Lambda]Csi , \[Lambda]lower, \[Lambda]upper, \
    \[Lambda]lowereip, \[Lambda]ip];
    (* Exogenous *)
    Clear[ ci, yp, \[Lambda]i, \[Alpha]i, \[Epsilon]ip, \[Eta]ip, eip];
    ri = \[Epsilon]ip*\[Lambda]i + (1 - \[Eta]ip)*(1 - \[Lambda]i);
    si = \[Eta]ip*(1 - \[Lambda]i) + (1 - \[Epsilon]ip)*\[Lambda]i;
    \[Lambda]Cri = (\[Epsilon]ip*\[Lambda]i)/(\[Epsilon]ip*\[Lambda]i + (1 - \[Eta]ip)*(1 - \[Lambda]i));
    \[Lambda]Csi = (\[Eta]ip*(1 - \[Lambda]i))/(\[Eta]ip*(1 - \[Lambda]i) + (1 - \[Epsilon]ip)*\[Lambda]i);
    \[Lambda]lower = Solve[ri*(yp - eip - ci + \[Alpha]i*\[Lambda]Cri) + 
 si*(yp - eip + \[Alpha]i*(1 - \[Lambda]Csi)) == yp + \[Alpha]i*(1 - \[Lambda]i), {\[Lambda]i}]
    \[Lambda]lowereip = Simplify[D[\[Lambda]lower, eip]]

    (* Assigning Sign - not working *)
    Simplify[Sign[\[Lambda]lowereip], 0 < \[Epsilon]ip < 1 && 0 < ci < 1 && 0 < \[Eta]ip < 1 && \[Alpha]i > ci && \[Alpha]i > ci + eip && \[Epsilon]ip + \[Eta]i < 1]
 
    (* Assigning Sign - working. Note that "x" is the solution to \[Lambda]lowereip*)
    x = 1/(2 \[Alpha]i - ci (-1 + \[Epsilon]ip + \[Eta]ip))
    Simplify[Sign[x], 0 < \[Epsilon]ip < 1 && 0 < ci < 1 && 0 < \[Eta]ip < 1 && \[Alpha]i > ci && \[Alpha]i > ci + eip && \[Epsilon]ip + \[Eta]i < 1]

It is working for the first evaluation, [Lambda]lower, but not for the second evaluation, [Lambda]upper.

    (* Endogenous *)
    Clear[\[Mu], \[Xi], \[Beta], \[Gamma], ri, si, rj, sj, \[Lambda]Cri, \[Lambda]Csi , \[Lambda]lower, \[Lambda]upper, \[Lambda]lowereip, \[Lambda]ip];
    (* Exogenous *)
    Clear[ ci, yp, \[Lambda]i, \[Alpha]i, \[Epsilon]ip, \[Eta]ip, eip];
    ri = \[Epsilon]ip*\[Lambda]i + (1 - \[Eta]ip)*(1 - \[Lambda]i);
    si = \[Eta]ip*(1 - \[Lambda]i) + (1 - \[Epsilon]ip)*\[Lambda]i; 
    \[Lambda]Cri = (\[Epsilon]ip*\[Lambda]i)/(\[Epsilon]ip*\[Lambda]i + (1 - \[Eta]ip)*(1 - \[Lambda]i));
    \[Lambda]Csi = (\[Eta]ip*(1 - \[Lambda]i))/(\[Eta]ip*(1 - \[Lambda]i) + (1 - \[Epsilon]ip)*\[Lambda]i);
    \[Lambda]lower = \[Lambda]i /. 
    Solve[ri*(yp - eip - ci + \[Alpha]i*\[Lambda]Cri) + si*(yp - eip + \[Alpha]i*(1 - \[Lambda]Csi)) == yp + \[Alpha]i*(1 - \[Lambda]i), {\[Lambda]i}];
    \[Lambda]upper = \[Lambda]i /.Solve[ri*(yp - eip - ci + \[Alpha]i*\[Lambda]Cri) + 
  si*(yp - eip + \[Alpha]i*(1 - \[Lambda]Csi)) == yp + \[Alpha]i*\[Lambda]i - ci, {\[Lambda]i} ];
    Simplify[D[\[Lambda]lower, eip]]
    Simplify[Sign[D[\[Lambda]lower, eip]], \[Alpha]i > 0 && eip > 0 && ci > 0 && 0 < \[Epsilon]ip < 1 && 0 < ci < 1 && 0 < \[Eta]ip < 1 && \[Alpha]i > ci && \[Alpha]i > ci + eip && \[Epsilon]ip + \[Eta]i < 1]
    Simplify[D[\[Lambda]upper, eip]]
    Simplify[Sign[D[\[Lambda]upper, eip]], \[Alpha]i > 0 && eip > 0 && ci > 0 && 0 < \[Epsilon]ip < 1 && 0 < ci < 1 && 0 < \[Eta]ip < 1 && \[Alpha]i > ci && \[Alpha]i > ci + eip && \[Epsilon]ip + \[Eta]i < 1]

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edited Oct 6, 2014 at 19:42

Tom

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edited Oct 5, 2014 at 20:10

Dr. belisarius

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asked Oct 5, 2014 at 20:06

Tom

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