Code:

    g1 = Manipulate[Plot[{Log[x], (x^(1-a)-1)/(1-a)}, {x, 0, 5}, PlotLegends->"Expressions"], 
    {a, 0, 0.99}, LocalizeVariables->False]

    ListAnimate[g1]

    SetDirectory[NotebookDirectory[]]
    Export["isoelastic.gif",g1]


Output (GIF):

[![enter image description here][1]][1]

As you can see, the `.gif` output does not show the animation at all (it just 'flashes'). Any ideas?


  [1]: https://i.sstatic.net/DZc6I.gif