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Basically, what you want to do is to swap the axes for one of the two plots. Usually the best way to do this is with ParametricPlot. Try this code to get a flavour of how it works:

plot1 = Plot[x^2, {x, 0, 2}, AspectRatio -> 1]
plot2 = ParametricPlot[{x^2, x}, {x, 0, 2}, AspectRatio -> 1]
Show[plot1, plot2]

With your example above, the code would be

nullPlot = Plot[Null, {x, 1, 100}, PlotRange -> {1, 100}, AspectRatio -> 1];
g1 = Plot[resp1, {p2, 1, 100}];
g2 = ParametricPlot[{resp2, p1}, {p1, 1, 100}];
Show[nullPlot, g1, g2]

the first line of which creates an empty set of axes with the relevant x,y ranges.

Also, if you want to see how your parameters affect the equilibrium you can use something like

Manipulate[plot1 = Plot[a*x^2, {x, 0, 2}, AspectRatio -> 1, PlotRange -> {0, 2}]; plot2 = ParametricPlot[{a*x^2, x}, {x, 0, 2}, AspectRatio -> 1]; Show[plot1, plot2], {a, 1, 2}]

Basically, what you want to do is to swap the axes for one of the two plots. Usually the best way to do this is with ParametricPlot. Try this code to get a flavour of how it works:

plot1 = Plot[x^2, {x, 0, 2}, AspectRatio -> 1]
plot2 = ParametricPlot[{x^2, x}, {x, 0, 2}, AspectRatio -> 1]
Show[plot1, plot2]

With your example above, the code would be

nullPlot = Plot[Null, {x, 1, 100}, PlotRange -> {1, 100}, AspectRatio -> 1];
g1 = Plot[resp1, {p2, 1, 100}];
g2 = ParametricPlot[{resp2, p1}, {p1, 1, 100}];
Show[nullPlot, g1, g2]

the first line of which creates an empty set of axes with the relevant x,y ranges.

Also, if you want to see how your parameters affect the equilibrium you can use something like

Manipulate[
    plot1 = Plot[a*x^2, {x, 0, 2}, AspectRatio -> 1, PlotRange -> {0, 2}]; 
    plot2 = ParametricPlot[{a*x^2, x}, {x, 0, 2}, AspectRatio -> 1]; 
    Show[plot1, plot2], {a, 1, 2}]

Basically, what you want to do is to swap the axes for one of the two plots. Usually the best way to do this is with ParametricPlot. Try this code to get a flavour of how it works:

plot1 = Plot[x^2, {x, 0, 2}, AspectRatio -> 1]
plot2 = ParametricPlot[{x^2, x}, {x, 0, 2}, AspectRatio -> 1]
Show[plot1, plot2]

Also, if you want to see how your parameters affect the equilibrium you can use something like

Manipulate[
     plot1 = Plot[a*x^2, {x, 0, 2}, AspectRatio -> 1, PlotRange -> {0, 2}]; 
     plot2 = ParametricPlot[{a*x^2, x}, {x, 0, 2}, AspectRatio -> 1]; 
     Show[plot1, plot2], {a, 1, 2}]

Basically, what you want to do is to swap the axes for one of the two plots. Usually the best way to do this is with ParametricPlot. Try this code to get a flavour of how it works:

plot1 = Plot[x^2, {x, 0, 2}, AspectRatio -> 1]
plot2 = ParametricPlot[{x^2, x}, {x, 0, 2}, AspectRatio -> 1]
Show[plot1, plot2]

With your example above, the code would be

nullPlot = Plot[Null, {x, 1, 100}, PlotRange -> {1, 100}, AspectRatio -> 1];
g1 = Plot[resp1, {p2, 1, 100}];
g2 = ParametricPlot[{resp2, p1}, {p1, 1, 100}];
Show[nullPlot, g1, g2]

the first line of which creates an empty set of axes with the relevant x,y ranges.

Also, if you want to see how your parameters affect the equilibrium you can use something like

Manipulate[plot1 = Plot[a*x^2, {x, 0, 2}, AspectRatio -> 1, PlotRange -> {0, 2}]; plot2 = ParametricPlot[{a*x^2, x}, {x, 0, 2}, AspectRatio -> 1]; Show[plot1, plot2], {a, 1, 2}]

Basically, what you want to do is to swap the axes for one of the two plots. Usually the best way to do this is with ParametricPlot. Try this code to get a flavour of how it works:

plot1 = Plot[x^2, {x, 0, 2}, AspectRatio -> 1]
plot2 = ParametricPlot[{x^2, x}, {x, 0, 2}, AspectRatio -> 1]
Show[plot1, plot2]

Also, if you want to see how your parameters affect the equilibrium you can use something like

Manipulate[plot1 = Plot[a*x^2, {x, 0, 2}, AspectRatio -> 1, PlotRange -> {0, 2}]; plot2 = ParametricPlot[{a*x^2, x}, {x, 0, 2}, AspectRatio -> 1]; Show[plot1, plot2], {a, 1, 2}]

Basically, what you want to do is to swap the axes for one of the two plots. Usually the best way to do this is with ParametricPlot. Try this code to get a flavour of how it works:

plot1 = Plot[x^2, {x, 0, 2}, AspectRatio -> 1]
plot2 = ParametricPlot[{x^2, x}, {x, 0, 2}, AspectRatio -> 1]
Show[plot1, plot2]

Also, if you want to see how your parameters affect the equilibrium you can use something like

Manipulate[
     plot1 = Plot[a*x^2, {x, 0, 2}, AspectRatio -> 1, PlotRange -> {0, 2}]; 
     plot2 = ParametricPlot[{a*x^2, x}, {x, 0, 2}, AspectRatio -> 1]; 
     Show[plot1, plot2], {a, 1, 2}]