There has been a lot (maybe also much) commentary on my simple pedagogical exercise. To deed the give-and-take forward, allow me offering a challenge to readers: What is the dynamic Furman ratio inward such a model--that is, the ratio the wage growth to the dynamic revenue loss, which I volition telephone phone dw/dz?
Note that
dz = - d[t*f '(k)*k]
but straightaway nosotros accept into concern human relationship that k together with f '(k) volition alter amongst t.
Furman was the rootage to betoken out to me that, for Cobb-Douglas, the right respond is:
dw/dz = (1-α) / (1- α - t).
For a uppercase part together with taxation charge per unit of measurement of 1/3, nosotros instruct dw/dz = 2. Each dollar of a uppercase taxation cutting (dynamicly scored) raises payoff yesteryear ii dollars. See the derivation at Cochrane's blog. (Note that John together with I stimulate got a slightly unlike notation, together with then don't live misled yesteryear the minus sign.)
What is the full general case?
I stimulate got non worked it out, only I volition offering a conjecture: You tin write dw/dz every bit a component of the taxation rate, the uppercase share, together with the elasticity of substitution between uppercase together with labor.
You tin discovery a helpful hint inward footnote xix of mankiw/files/growth_of_nations.pdf">this paper.
Update: Eðvarð I. Erlingsson offers upward a solution.
Note that
dz = - d[t*f '(k)*k]
but straightaway nosotros accept into concern human relationship that k together with f '(k) volition alter amongst t.
Furman was the rootage to betoken out to me that, for Cobb-Douglas, the right respond is:
dw/dz = (1-α) / (1- α - t).
For a uppercase part together with taxation charge per unit of measurement of 1/3, nosotros instruct dw/dz = 2. Each dollar of a uppercase taxation cutting (dynamicly scored) raises payoff yesteryear ii dollars. See the derivation at Cochrane's blog. (Note that John together with I stimulate got a slightly unlike notation, together with then don't live misled yesteryear the minus sign.)
What is the full general case?
I stimulate got non worked it out, only I volition offering a conjecture: You tin write dw/dz every bit a component of the taxation rate, the uppercase share, together with the elasticity of substitution between uppercase together with labor.
You tin discovery a helpful hint inward footnote xix of mankiw/files/growth_of_nations.pdf">this paper.
Update: Eðvarð I. Erlingsson offers upward a solution.
