Presentation8 Taxes Labor Leisurejpd48/Presentation8_Taxes_Labor_Leisure.pdf ·...
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Macroeconomics Taxes on the Labor – Leisure Choice ECON 321
Transcript of Presentation8 Taxes Labor Leisurejpd48/Presentation8_Taxes_Labor_Leisure.pdf ·...
Macroeconomics+Taxes+on+the+Labor+–+Leisure+Choice+
ECON+321+
TAXES+
(1) Lump+Sum+Tax+
y+=+c+=+wl+++x+F+T+
(2) Wage+(income+tax)+
+++++y+=+c+=+(1Fτw)wl+++x+
(3) ConsumpJon+tax++
(1) y+=+(1+τc)c+=+wl+++x+
Lump+Sum+Tax:+Everyone+Pays+the+Same+
c+
l++++++++++l2+
c2+
+Pure+Income Effect: Income +++c+#; h #; l +
+++++++l1+
c1+
c+=+wl+x+++
c+=+wl+x+FT++
x++F+T+
x+
parallel+shiN+
Tax+on+Wages+
c+
l++++++++++l*+
c*+
Income Effect: # # τ +++c+#; h #; l %
Substitution Effect: # τ +++c+#; h #; l +
Overall+Effect: + + + τ +++c+#; h ?#; l ? ++
c+=+wl+x++
c+=+(1Fτ)wl+x++
The+subsJtuJon+effect+dominates+in+the+short+run+as+shown+here.+
Labor+Supply+and+Demand+
wR+
L+
LD+
LS+
wR+(mkt+clearing)+
+++++++(1Fτ)wR+
wRf+(paid+by+firms)+
Government+tax+revenue+
ConsumpJon+Tax:+Two+Income+Effects+and+On+SubsJtuJon+Effect+
c+
l++++++++++l1+
c1+
c+=+wl+x+++
where++++++++++++++++acts+like+a+wage+tax+and+++++++++++like+a+wealth+tax.+
++(x)/(1+τc)++
x+
€
(1+τc)c = wl + x
c =wl
(1+τc)+
x(1+τc)
€
w(1+τc)
€
(1+τc)
Taxes+Example+
• U+=+c+++αln(h)+s.t.+:+c+=+wl+++x ++
1+=+l+++h+
Maxl+U+=+wl+++x+++αln(1Fl)+
dU/dl+=+w+–+α/(1Fl)+=+0++
Which+is+marginal+benefit+and+which+is+marginal+cost?+
l*+=+(wFα)/w+
Taxes+Example+
+dU/dl+=+w+–+α/(1Fl)+=+0+++
+l*+=+(wFα)/w+
(wFα)++SubsJtuJon+effect+
(w)+ +Income+effect+
dl*/dw+>+0,+which+tells+us+the+subsJtuJon+effect+dominates.+
+c*+=+w+++x+–+α+
+h*+=+α/w+
With+a+Wage+Tax+
!c!=!(1&τ)wl+x! + +; +V+=+Transfers+=+τwl!+c!=!(1&τ)wl+x!+!V,+
– However+the+consumer+does+not+choose+τ+and+V.+
• U!=!(1&τ)wl+x!+!V!+!αln(1Fl)++du/dl+=+(1&τ)w!–!α/(1Fl)+=+0+
+l*+=+[(1&τ)w!–!α]/[(1&τ)w]!– A!distor8onary!tax!breaks!up!what!we!earn!versus!what!we!get.+
With+a+Wage+Tax+
+l*+=+[(1&τ)w!–!α]/[(1&τ)w]!dl*/dτ+<+0,+showing+a+dominate+subsJtuJon+effect.+
+c*+=+(1&τ)w!–!α!+!x!+!V!+h*+=+α/[(1&τ)w]!
How+do+UJliJes+compare?+U+=+c*+++αln(h*)+
example+with+w+=+2,+x+=+1,+α+=+½,+τ+=+¼+UNO+TAX+=+1.81+;+UTAX+=+1.62++So+we+work+less+and+earn+less,+decreasing+the+amount+of+tax+revenue+that+might+have+been+thought+possible+with+no+changes+to+labor+supply.+
Labor+Supply+and+Demand+
wR+
L+
LD+
LS+
wR+(mkt+clearing)+
+++++++(1Fτ)wR+
wRf+(paid+by+firms)+
Government+tax+revenue+
L’S+
We+see+the+supply+curve+gets+steeper+(more+inelasJc)+represenJng+the+subsJtuJon+effect+away+from+labor+supplied,+which+decreases+the+tax+revenues+possible+from+the+wage+tax.+
Labor+Demand+
• Y+=+AKαL1Fα+
• π+=+PyAKαL1Fα+–+wL+–+rK+– where+Py+is+the+price+of+the+output+good.+– r+is+the+rental+rate+of+capital.+
• MaxL+π+=+PyAKαL1Fα+–+wL+–+rK+
– Suppose+K+is+fixed+in+the+short+run.+
• dπ/dL+=+(1Fα)PyAKαLFα+–+w+=+0+marginal+revenue+ marginal+cost+
Labor+Demand+
• dπ/dL+=+(1Fα)PyAKαLFα+–+w+=+0++LD*+=+K[(1Fα)PyA/w]
1/α+
++ ++ + #Here+all+the+workers+are+the+same+ + ++ + +(homogenous)+RepresentaJve+Agent+ ++ + +(worker)+
U+=+c+++3+ln(h)++s.t.+:+ +c+=+y+=+wl+
+ + + +h+=+1Fl+
Labor+Demand+
• Maxl++++++U+=+wl+++3+ln+(1Fl)+
FOC+:+w+–+3/(1Fl)+=+0+
+ + +l+=+LS*+=+(wF3)/w+
• So+we+have+LD+and+LS+we+can+find!w.+Lets+say++++K+=+1,+A+=+1,+Py+=+1,+α+=+1/2+
LD++=+LS++
(wF3)/w+=+K[(1Fα)PyA/w]1/α+
Labor+Demand+
• LD++=+LS+++(wF3)/w+=+K[(1Fα)PyA/w]
1/α+
+(wF3)/w+=+1[(1/2)(1)(1)/w]2++
+(wF3)/w+=+1/(4w2)+
+4w2+F12w+F1+=+0+
USE+QUADRATIC+:++
w+=+[Fb(+/F)(b2F4ac)1/2]/(2a)+
w*+=+[12(+/F)(144F16)1/2]/8+=+(3.08+,+(F))+LS+=+(3.08+–+3)/3.08+=+0.26+=+LD+
With+Wage+Taxes+
• c!=!(1&τ)wl!;!τ!=!.5!!Maxl!U!=!(1/2)wl!+!3!ln(1&l)!!dU/dl!=!(1/2)w!–!3/(1&l)!=!0!!l*!=!LS!=!(w&6)/w!!LS=!LD ! ! !; !(w&6)/w!=!K[(1Fα)PyA/w]1/α+
! !Again+Lets+say:+K+=+1,+A+=+1,+Py+=+1,+α+=+½+!4w2!–!24w!–!1!=!0!+w+=+[24(+/F)(576+16)1/2]/8++!w*!=!6.04,!which+is+higher+than+the+pretax+wage!of+3.02.+!LS=!LD!=!(w&6)/w!=!.04/6!=!.06666…..+
CompeJJve+Equilibrium+
• A+CompeJJve+Equilibrium+(C.E.)+:+is+a+set+of+quanJJes+and+prices,+given+exogenous+variables+and+parameters,+such+that+consumers+maximize+uJlity,+and+firms+maximize+profit,+both+subject+to+their+constraints+and+taking+all+prices+as+given,+such+that,+all+markets+clear.+
• QuanJJes:+C,+LS,+LD,+Y+
CompeJJve+Equilibrium+
• QuanJJes +:+ +C,+LS,+LD,+Y+• Prices+ + +: +w ++
• Exogenous +: +A,+PY,+α,+K,+τ+
• Taken+prices+(wages)+as+given+(since+each+person+is+not+large+enough+to+affect+prices),+markets+clear+(Supply+=+Demand+in+all+markets).+
Pareto+OpJmal+
• Pareto+OpJmal:+is+an+allocaJon+of+goods+is+Pareto+OpJmal+if+there+is+no+way+to+rearrange+the+allocaJon+such+that+at+least+one+agent+is+bever+off+without+making+any+other+agent+worse+off.+
– example:++• Everyone+has+one+cookie:++ + ++Pareto+OpJmal? +YES+
• One+person+has+all+the+cookies:++Pareto+OpJmal? +???+
Pareto+OpJmal+
• Pareto+OpJmal+isn’t+about+distribuJon,+but+rather+efficiency…i.e.+there+are+no+wasted+cookies.+
First+Fundamental+Welfare+Theorem+
• The+First+Fundamental+Welfare+Theorem:+states+that+under+certain+condiJons,+a+compeJJve+equilibrium+is+Pareto+OpJmal.+– Adam+Smith,+laissezFfaire,+the+invisible+hand.+
– Gov’t+not+necessary+for+this+outcome.+
• CondiJons+(Only+Role+for+Gov’t)+1. All+agents+are+price+takers.+2. All+markets+are+complete.+(no+externaliJes)+
3. No+distorJons+of+incenJves+(i.e.+wage+tax)+
