601-tls-5nov09pdf

601-tls-5nov09pdf - A Note on Taxes and Labour Supply...

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Assume a person can choose her hours of work. How ine cient are taxes on earnings? Suppose W isthewagerate , P is the price of consumption, T is the time endow- ment, l is time spent at leisure, n T l is time at work, and c is consumption. With no taxes her budget constraint is Wl + Pc = WT. With a proportional tax on earnings ( W ( T l )) at rate t this becomes (1 t ) Wl + Pc =(1 t ) WT. To keep the calculations manageable assume she has Cobb-Douglas preferences: U = l a c 1 a , 0 <a< 1 . From our earlier work with CD utility functions we know l = a (1 t ) WT (1 t ) W = aT c =( 1 a ) (1 t ) WT P V ((1 t ) W, P, (1 t ) WT )= a a (1 a ) 1 a ((1 t ) W ) a P (1 a ) (1 t ) WT e ( W, P, U )= a a (1 a ) (1 a ) W a P 1 a U. Tax revenue is tWn = tW ( T l )= tW ( T aT )=(1 a )
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601-tls-5nov09pdf - A Note on Taxes and Labour Supply...

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