I would like to know how to make a graph like the attached. The Figure IV is showing the changes in the evolution of the rate of technological progress (a topic in economics).

I would like to make a graph exactly like the image attached where it clearly shows the name of the x- and y-axis; the name of the functions; the 45-degree line; the transition from "theta_1" to "theta_2" with the arrows, etc. (In fact, I want to have everything the same from the graph). 

I have attached a PDF document with the definition of the functions and the figure itself. I have also attached the image of the figure on this thread. 

IMG_633.pdf

How do I create a plot like Figure I as uploaded in the PDF-document?

On Figure I, you see the plot of two income functions. The income functions are defined by equations (5), (6), (7), and (8).
Please note that:
0<a<1
0<g<1
0<"tau"<1
0<"delta"*g<1
"delta" belongs to open interval (0,1)

/Regards.

IMG_499.pdf