Expression 6: "y" equals left brace, 0 less than "x" less than "d" : "b" positive StartFraction, "a" Over "d" , EndFraction , "d" less than "x" : "b" , right bracey=0<x<d:b+ad,d<x:b
6
This represents the log change in consumption from baseline. I am aware the fraction on fraction looks really ugly, but I don't want this to be confusing. It's just the log of the ratio between the new and baseline consumption.
7
Expression 8: "y" equals left brace, 0 less than "x" less than "d" : log left parenthesis, StartFraction, "b" positive StartNestedFraction, "a" NestedOver "d" , EndNestedFraction Over "b" , EndFraction , right parenthesis , right bracey=0<x<d:logb+adb
8
Expression 9: 0 less than "y" less than left brace, 0 less than "x" less than "d" : log left parenthesis, StartFraction, "b" plus StartNestedFraction, "a" NestedOver "d" , EndNestedFraction Over "b" , EndFraction , right parenthesis , right brace0<y<0<x<d:logb+adb
9
Finally, this is the amount of value that's generated from the transfer. Notice that it increases when d increases. It's simply the area of the green above.
10
Expression 11: log left parenthesis, StartFraction, left parenthesis, "b" plus StartNestedFraction, "a" NestedOver "d" , EndNestedFraction , right parenthesis Over "b" , EndFraction , right parenthesis times "d"logb+adb·d