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Transcript of Double Dividend © P. Berck 2008. Sources Goulder, Parry, Burtraw. Rand 1997 Fullerton. AER 1997...
![Page 1: Double Dividend © P. Berck 2008. Sources Goulder, Parry, Burtraw. Rand 1997 Fullerton. AER 1997 Fullerton and Metcalf. NBER wp 6199 1997.](https://reader035.fdocuments.in/reader035/viewer/2022062620/551a3b5b550346a4248b58bf/html5/thumbnails/1.jpg)
Double Dividend
© P. Berck 2008
![Page 2: Double Dividend © P. Berck 2008. Sources Goulder, Parry, Burtraw. Rand 1997 Fullerton. AER 1997 Fullerton and Metcalf. NBER wp 6199 1997.](https://reader035.fdocuments.in/reader035/viewer/2022062620/551a3b5b550346a4248b58bf/html5/thumbnails/2.jpg)
Sources
• Goulder, Parry, Burtraw. Rand 1997• Fullerton. AER 1997• Fullerton and Metcalf. NBER wp 6199
1997
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Pictures
L.0
Dirty good
X.0
tl
Private mc
mc
Labor Demand
Income tax distorts labor market while externality distorts goods market
![Page 4: Double Dividend © P. Berck 2008. Sources Goulder, Parry, Burtraw. Rand 1997 Fullerton. AER 1997 Fullerton and Metcalf. NBER wp 6199 1997.](https://reader035.fdocuments.in/reader035/viewer/2022062620/551a3b5b550346a4248b58bf/html5/thumbnails/4.jpg)
GPB Model
• 3 Goods• Dirty X• Clean Y• Leisure H
• Dirty good externality • PPF: T=X+Y+H• Producer prices are all 1. • T – H is labor
• Taxes• tX for X
• tl for T-H, labor
• Gov’t revenue• TR= tl(T-H) + txX
• Given back to consumer lump sum.• Is constant
![Page 5: Double Dividend © P. Berck 2008. Sources Goulder, Parry, Burtraw. Rand 1997 Fullerton. AER 1997 Fullerton and Metcalf. NBER wp 6199 1997.](https://reader035.fdocuments.in/reader035/viewer/2022062620/551a3b5b550346a4248b58bf/html5/thumbnails/5.jpg)
Consumer Problem
• Consumer problem max U(X,Y,H) • s.t. (1+tx)X + Y =(1-tl)(T-H) + TR
• good X costs more than good Y• labor (T-H) is taxed at rate tl
• foc: Ux=(1+tx) l; UY= l; UH=(1-tl) l l is marginal utility of income• Demands are X(tx,tl), Y(), H().
• Write X(t), Y(t), H(t) for short.
![Page 6: Double Dividend © P. Berck 2008. Sources Goulder, Parry, Burtraw. Rand 1997 Fullerton. AER 1997 Fullerton and Metcalf. NBER wp 6199 1997.](https://reader035.fdocuments.in/reader035/viewer/2022062620/551a3b5b550346a4248b58bf/html5/thumbnails/6.jpg)
Consumer prices for Goods
• Approx 1/(1-tl) as 1+tl
• Budget constraint is then• (1+tl)(1+tx)X + (1+tl) Y =(T-H) + TR (1+tl)
• So is equivalent to a tax on both goods and a subsidy on TR
• (not appealing, but shows that Y really isn’t “untaxed”.
![Page 7: Double Dividend © P. Berck 2008. Sources Goulder, Parry, Burtraw. Rand 1997 Fullerton. AER 1997 Fullerton and Metcalf. NBER wp 6199 1997.](https://reader035.fdocuments.in/reader035/viewer/2022062620/551a3b5b550346a4248b58bf/html5/thumbnails/7.jpg)
More setup
• Gov Rev Constraint + Budget imply PPF• just substitute for TR in budget
• Demands Equations satisfy Budget by construction
• So only one equation remains• TR= tl(T-H(t)) + txX(t)
• Taking the total derivative and rearranging give
![Page 8: Double Dividend © P. Berck 2008. Sources Goulder, Parry, Burtraw. Rand 1997 Fullerton. AER 1997 Fullerton and Metcalf. NBER wp 6199 1997.](https://reader035.fdocuments.in/reader035/viewer/2022062620/551a3b5b550346a4248b58bf/html5/thumbnails/8.jpg)
Effect of tax increase on x
x ll x x
xl
x
dX Hx t t
dt dt tHdt T H tt
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Social Problem
• U() + V(Q(X))• utility plus negative contribution from dirty
good.• V doesn’t enter into consumer choice
because it is aggregate X, not individual X that impairs breathing
![Page 10: Double Dividend © P. Berck 2008. Sources Goulder, Parry, Burtraw. Rand 1997 Fullerton. AER 1997 Fullerton and Metcalf. NBER wp 6199 1997.](https://reader035.fdocuments.in/reader035/viewer/2022062620/551a3b5b550346a4248b58bf/html5/thumbnails/10.jpg)
Change in utility
• D = 1/ l V’ Qx
• Num of M is (1+t) – 1 times lost hours; partial equilib welfare loss
• Denom is partial equilib increase in tax rev from increase in labor tax
ll
ll
Htt
MH
T H tt
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Intermediate Steps
'xx
dUU V Q
dt
'x x Y Hx x x x
dU dX dY dHU V Q U U
dt dt dt dt
Now substitute: l (1+tx) for Ux and so on.And D l for V’Qx (and note the sign reversal! My error, their error?And totally differentiate the ppf to get: dY/dtx = - dH/dtx- dX/dtx
Putting this together with the definition of M gives the final expression on The next slide
![Page 12: Double Dividend © P. Berck 2008. Sources Goulder, Parry, Burtraw. Rand 1997 Fullerton. AER 1997 Fullerton and Metcalf. NBER wp 6199 1997.](https://reader035.fdocuments.in/reader035/viewer/2022062620/551a3b5b550346a4248b58bf/html5/thumbnails/12.jpg)
1
(1 )
xx x
xx
lx
dU dXD t
dt dt
dXM X t
dt
HM t
t
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Comments
• Empirical applications are via CGE’s, which have lots of other things in them.
• When one raises a tax on labor it is equivalent to taxing both goods, to tx is the difference in the tax rate between the two goods with tl normalized to one.
• A standard doesn’t have the revenue recycling effect, cause there is no revenue.
• The pigouvian tax is probably not the right tax, though one can argue for too low or too high, depending on parameters. Goulder says too high.
![Page 14: Double Dividend © P. Berck 2008. Sources Goulder, Parry, Burtraw. Rand 1997 Fullerton. AER 1997 Fullerton and Metcalf. NBER wp 6199 1997.](https://reader035.fdocuments.in/reader035/viewer/2022062620/551a3b5b550346a4248b58bf/html5/thumbnails/14.jpg)
The Dual
• DM notation.• PPF: p’y = 0
• (sign of work is negative, of goods positive)• Simple version has p fixed
• Budget: q’x = 0• gov’t budget: R= p’z = (q-p)’x
• Treat z as fixed
• 3 equations
![Page 15: Double Dividend © P. Berck 2008. Sources Goulder, Parry, Burtraw. Rand 1997 Fullerton. AER 1997 Fullerton and Metcalf. NBER wp 6199 1997.](https://reader035.fdocuments.in/reader035/viewer/2022062620/551a3b5b550346a4248b58bf/html5/thumbnails/15.jpg)
Down to one eq.
• R = (q-p)’x• Let x = x(q-p) = x(t), the demand equation.• x(t) always satisfies x(t)’q = 0.
• R = t’x(t)
![Page 16: Double Dividend © P. Berck 2008. Sources Goulder, Parry, Burtraw. Rand 1997 Fullerton. AER 1997 Fullerton and Metcalf. NBER wp 6199 1997.](https://reader035.fdocuments.in/reader035/viewer/2022062620/551a3b5b550346a4248b58bf/html5/thumbnails/16.jpg)
Feasible tax Variation
'
'j i
i
j
t xdt t
t xdtt
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• W = V(q) – Dxi(q)• Indirect utility less damage• a is the marginal util of income• dV/dt = dV/dq = - a x by Roy’s identity
What happens when only taxes i and j are perturbed. Like tax on dirt up and labor down.
![Page 18: Double Dividend © P. Berck 2008. Sources Goulder, Parry, Burtraw. Rand 1997 Fullerton. AER 1997 Fullerton and Metcalf. NBER wp 6199 1997.](https://reader035.fdocuments.in/reader035/viewer/2022062620/551a3b5b550346a4248b58bf/html5/thumbnails/18.jpg)
• Double dividend means first term is non-zero and original tax system is nonoptimal.
[ ] ( )j i i ii j
i i i j
dt x x dtV x x D
dt t t dt
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• t = q-p• p is constant, so can write • q(t) = q(t+p) as the demand system• q(t) satisfies budget constraint by
construction
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1 Equation left
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Direct Approach
• Form the indirect utility function• IN(X(t),Y(t),H(t))= IN(t)
• Use Roy’s identity to get• dIN/dtx = -aX –aH dtl/dtx
• Adding the Pigou term• dU/dtx = -aX –aH dtl/dtx + V’Qx dX/dtx
• Here the dwl in X market decreases by aX dX; in labor market by –aH dtl/dtx dX.