Combined plots looking different from the individual ones?

[nstronko (Nathan Stronkowsky)]

Hello,

I am trying to combine two graphs that are identical in their formulas but slightly different with their parameters. Every time I try to combine them using “Show[ ]” the combined graph shows just two straight lines instead of showing the proper curves. Could it be a coding error? A size issue? I have no idea. I have attached the whole program below, plus screen shots of the specific areas and what the graphics look like.

Help is much appreciated Thank you.

Combined Graph example.pdf (15.7 KB)
Nathan Stronkowsky SSD copy.nb (229 KB)

individual graph example 1.pdf (16 KB)
individual graph example 2.pdf (16.2 KB)

[rohitnamjoshi]

Hi Nathan,

The plots being combined with Show each have a very small y range that is separated by a relatively large y value between the two plots. On a combined scale they appear as straight lines. You will have to add an offset or use a log scale, or… Really depends on what you are trying to convey by combining them.

[nstronko (Nathan Stronkowsky)]

Hi thanks for responding. How can I go about fixing it? All I want is to show the two time paths as they appear on their individual graphs but on one graph. I want to see both of them on the same time scales graph. They should look as they do (logarithmic shape) on the combined graph.

[rohitnamjoshi]

One option is to use the resource function CombinePlots. Will require some changes.

ktimepath1 =
  Plot[{Evaluate[k[t] /. solm]}, {t, 0, 200}, 
    PlotRange -> All, 
    AxesLabel -> {"t", "k"},
    PlotLegends -> {"k"},
    Frame -> True, 
    PlotStyle -> Thickness[0.01]] (* The two overlay exactly so increase thickness *)

ktimepath2 = 
  Plot[{Evaluate[k2[t] /. solm2]}, {t, 0, 200},
    PlotRange -> All, 
    AxesLabel -> {"t", "k2"},
    PlotLegends -> {"k2"}, Frame -> True, 
    FrameStyle -> Red,
    PlotStyle -> Red]

ResourceFunction["CombinePlots"][ktimepath1, ktimepath2, 
 "AxesSides" -> "TwoY",
 ImageSize -> 600]

[nstronko (Nathan Stronkowsky)]

Thats great! however it looks like they’re the same time path; one should be a bit different. Let me try what you sent me and see if I can make it work. Thank you sm!

[nstronko (Nathan Stronkowsky)]

Hey so I think your suggestion worked, however I just have an economics question about the graphs if you could maybe give your opinion.

Individually the time paths for each variable (h, k, y) have a logarithmic style graph from the beginning, but when I combined them using your suggestion using Resource Function, the time paths for h and k specifically look like the are exponential at first, then counter an inflection point after a certain point. Could this be because in the beginning of economic growth, there are positive returns to scale? It seems k and h do not possess diminishing returns in the beginning. Is that normal? Btw I am using the Mankiw Romer and Weil model of semi endogenous growth, and I am not sure if this is a phenomenon of the model, or an error in how I combined the two time paths. 

Interestingly, when I combine y (output) using your method, I do not see this which makes sense kind of? Sorry I know this is a little bit off topic, but I am just concerned that I combined the time paths in a way that messed up there individual time paths. Screenshot is below