Hello Rohit,

I have a follow-up question. When I plot eq1 around one of the solutions (the negative one), it seems the equation is not actually defined. Would you know why that point would be a solution if it's not on one of the equations? Please see my code and plot below:

Thank you again!

\[Beta] = 0.95
R = 1/\[Beta]
W = 10^6
A = 100
\[Phi] = 0.2
\[Lambda] = 0.1
eq1 = p - \[Phi]/R - ((1 - \[Phi]) \[Phi] (1 - \[Lambda]) \[Beta])/(((W - T p) R + \[Phi] T) R + \[Phi]*(1 - \[Phi]) T)/(R (\[Lambda]/((W - T p) R + \[Phi] T  ) + ((1 - \[Lambda]) \[Beta] R)/(((W - T p) R + \[Phi] T) R + \[Phi] (1 - \[Phi]) T)))

sol = Solve[eq1 == 0 && p == A/T, {p, T}]

Which gives 2 solutions: {p -> -0.0000199018, T -> -5.02466(10^6)}, {p -> 0.319279, T -> 313.206}. And then I plot the eq1 for T between -5.025(10^6) and 0 to see what it looks like around the negative solution T= -5.02466(10^6). The plot shows that there is no corresponding value for p when T= -5.02466(10^6).

ContourPlot[
 p - \[Phi]/R - ((1 - \[Phi]) \[Phi] (1 - \[Lambda]) \[Beta])/(((W - T p) R + \[Phi] T) R + \[Phi]*(1 - \[Phi]) T)/(R (\[Lambda]/((W - T p) R + \[Phi] T  ) + ((1 - \[Lambda]) \[Beta] R)/(((W - T p) R + \[Phi] T) R + \[Phi] (1 - \[Phi]) T))) == 0, {T, -5.025*(10^6), 0}, {p, -0.1, 0.4}]

T is the x-axis, p is the y-axis

Hi Guangye,

Define a symbol for the first equation

eq1 = p - \[Phi]/
   R + ((1 - \[Phi]) \[Phi] (1 - \[Lambda]) \[Beta])/(((W - 
            p T) R + \[Phi] T) R + \[Phi] (1 - \[Phi]) T)/(R (\
\[Lambda]/((W - 
             p T) R + \[Phi] T) + ((1 - \[Lambda]) \[Beta] R)/(((W - 
                p T) R + \[Phi] T) R + \[Phi] (1 - \[Phi]) T)))

sol = Solve[eq1 == 0 && p == A/T, {p, T}]
(* {{p -> -2.37313*10^-8, T -> -4.21384*10^9}, {p -> 0.0607204, T -> 1646.89}} *)

Verify. For eq1 both results are zero to within machine precision. For A / T the result is the two p values from the solution.

eq1 /. sol
(* {5.55112*10^-17, 0.} *)

A / T /. sol
(* {-2.37313*10^-8, 0.0607204} *)

For an exact solution

eq1r = Rationalize@eq1
solr = Solve[eq1r == 0 && p == A/T, {p, T}]

Verify as before.

Works fine for me. Try restarting the kernel. Maybe this is the problem Clear[T], not clear[T]. WL is case-sensitive.