Public Economics Tax distorsions
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1 Public Economics Tax distorsions I. Ortuño 2015 Public Economics () distorsions / 15
2 Distorsions AGZ 2.1. and Stiglitz. pg 488, and notes in Aula Global Public Economics () distorsions / 15
3 Distorsions Why do taxes create ine ciencies? Competitive Equilibrium -> E cient allocation of resources (FFTWE). Consumers and produces -> same prices Tax-> consumer s price diiferent from producer s price Public Economics () distorsions / 15
4 Basic Model Consumption goods x and y. Leisure h.labor l = 1 h Public Economics () distorsions / 15
5 Basic Model Consumption goods x and y. Leisure h.labor l = 1 Utility: U(x, y, h) h Public Economics () distorsions / 15
6 Basic Model Consumption goods x and y. Leisure h.labor l = 1 Utility: U(x, y, h) Prices (constant): p x, p y. Wage: w (Frontier of production possibilities-> linear function. In the notes we have a more general model) h Public Economics () distorsions / 15
7 Basic Model Consumption goods x and y. Leisure h.labor l = 1 Utility: U(x, y, h) Prices (constant): p x, p y. Wage: w (Frontier of production possibilities-> linear function. In the notes we have a more general model) Tax function: T (x, y, l) h Public Economics () distorsions / 15
8 Basic Model Consumption goods x and y. Leisure h.labor l = 1 Utility: U(x, y, h) Prices (constant): p x, p y. Wage: w (Frontier of production possibilities-> linear function. In the notes we have a more general model) Tax function: T (x, y, l) The agent solves: Max x,y,l U(x, y, 1 l) s.t. p x l + p y y = wl T (x, y, l) h Public Economics () distorsions / 15
9 Basic Model Consumption goods x and y. Leisure h.labor l = 1 Utility: U(x, y, h) Prices (constant): p x, p y. Wage: w (Frontier of production possibilities-> linear function. In the notes we have a more general model) Tax function: T (x, y, l) The agent solves: Max x,y,l U(x, y, 1 l) s.t. p x l + p y y = wl T (x, y, l) Comment: Where is the tax revenue? h Public Economics () distorsions / 15
10 Basic Model Consumption goods x and y. Leisure h.labor l = 1 Utility: U(x, y, h) Prices (constant): p x, p y. Wage: w (Frontier of production possibilities-> linear function. In the notes we have a more general model) Tax function: T (x, y, l) The agent solves: Max x,y,l U(x, y, 1 l) s.t. p x l + p y y = wl T (x, y, l) Comment: Where is the tax revenue? We obtain the same results if such revenue is included h Public Economics () distorsions / 15
11 Basic model FFTWE -> Pareto e cient conditions (draw a gure to see it) RMS xy = p x p y = RMT xy (1) RMS hx = w p x = RMT hx (2) RMS hy = w p y = RMT hy (3) Public Economics () distorsions / 15
12 Lump-sum tax A lump-sum tax is T (x, y, l) = T Public Economics () distorsions / 15
13 Lump-sum tax A lump-sum tax is T (x, y, l) = T The above conditions are satis ed Public Economics () distorsions / 15
14 Lump-sum tax A lump-sum tax is T (x, y, l) = T The above conditions are satis ed This is an e cient tax. Public Economics () distorsions / 15
15 Excise tax T (x, y, l) = t x p x x Public Economics () distorsions / 15
16 Excise tax T (x, y, l) = t x p x x Budget constraint: (1 + t x )p x x + p y y = wl Public Economics () distorsions / 15
17 Excise tax T (x, y, l) = t x p x x Budget constraint: The new equiluibrium is given by: (1 + t x )p x x + p y y = wl RMS xy = p x (1 + t x ) 6= p x = RMT xy p y p y w RMS hx = p x (1 + t x ) 6= w = RMT hx p x Public Economics () distorsions / 15
18 Excise tax It doesn t a ect the marginal cost of production. It creates a distorsion on consumption The consumer will reduce x and increase y and h. Public Economics () distorsions / 15
19 Tax on consumption T (x, y, l) = t c (p x x + p y y) Public Economics () distorsions / 15
20 Tax on consumption T (x, y, l) = t c (p x x + p y y) The new budget constraint: (1 + t c )(p x x + p y y) = wl Public Economics () distorsions / 15
21 Tax on consumption T (x, y, l) = t c (p x x + p y y) The new budget constraint: (1 + t c )(p x x + p y y) = wl The equilibrium is given by (1) and RMS hx = RMS hy = w 6= w = RMT hx (1 + t c )p x p x w 6= w = RMT hy (1 + t c )p y p y Public Economics () distorsions / 15
22 Tax on consumption T (x, y, l) = t c (p x x + p y y) The new budget constraint: (1 + t c )(p x x + p y y) = wl The equilibrium is given by (1) and RMS hx = RMS hy = w 6= w = RMT hx (1 + t c )p x p x w 6= w = RMT hy (1 + t c )p y p y Leisure is not taxed -> taxation creates a welfare ine ciency Public Economics () distorsions / 15
23 A tax on labour income T (x, y, l) = t w wl Public Economics () distorsions / 15
24 A tax on labour income T (x, y, l) = t w wl The budget constraint: p x x + p y y = (1 t w )wl Public Economics () distorsions / 15
25 A tax on labour income T (x, y, l) = t w wl The budget constraint: p x x + p y y = (1 t w )wl The new equilibrium is given by (1) and RMS hx = w(1 p x t w ) RMS hy = w(1 p y t w ) 6= w p x = RMT hx 6= w p y = RMT hy Public Economics () distorsions / 15
26 A tax on labour income T (x, y, l) = t w wl The budget constraint: p x x + p y y = (1 t w )wl The new equilibrium is given by (1) and RMS hx = w(1 p x t w ) RMS hy = w(1 p y t w ) 6= w p x = RMT hx 6= w p y = RMT hy This is equivalent to a general tax on consumption. Public Economics () distorsions / 15
27 A tax on labour income T (x, y, l) = t w wl The budget constraint: p x x + p y y = (1 t w )wl The new equilibrium is given by (1) and RMS hx = w(1 p x t w ) RMS hy = w(1 p y t w ) 6= w p x = RMT hx 6= w p y = RMT hy This is equivalent to a general tax on consumption. Only labor income; no savings -> t c is equivalent to t w = t c /(1 + t c ) Public Economics () distorsions / 15
28 Production ine ciencies Two production sectors x and y. Public Economics () distorsions / 15
29 Production ine ciencies Two production sectors x and y. L i, K i : labor and capital in sector i, i = x, y. Public Economics () distorsions / 15
30 Production ine ciencies Two production sectors x and y. L i, K i : labor and capital in sector i, i = x, y. Perfect competiton without taxation: factor price= marginal productivity Public Economics () distorsions / 15
31 Production ine ciencies Two production sectors x and y. L i, K i : labor and capital in sector i, i = x, y. Perfect competiton without taxation: factor price= marginal productivity The equilibrium condition with e cient allocation of capital and labor: RMTS x KL = r w = RMTS y KL Public Economics () distorsions / 15
32 Production ine ciencies Suppose a tax on wages on sector x, t wx, (the tax is paid by the rms in sector x) RMTS x KL = r w(1 + t wx ) 6= r w = RMTS y KL Public Economics () distorsions / 15
33 Production ine ciencies Suppose a tax on wages on sector x, t wx, (the tax is paid by the rms in sector x) RMTS x KL = -> ine ecient allocation r w(1 + t wx ) 6= r w = RMTS y KL Public Economics () distorsions / 15
34 Production ine ciencies Suppose a tax on wages on sector x, t wx, (the tax is paid by the rms in sector x) RMTS x KL = -> ine ecient allocation What about a general tax on wages? r w(1 + t wx ) 6= r w = RMTS y KL Public Economics () distorsions / 15
35 Production ine ciencies Suppose a tax on wages on sector x, t wx, (the tax is paid by the rms in sector x) RMTS x KL = -> ine ecient allocation What about a general tax on wages? r w(1 + t wx ) 6= r w = RMTS y KL No ine cienies in production (make sure you see it). Public Economics () distorsions / 15
36 Production ine ciencies Suppose a tax on wages on sector x, t wx, (the tax is paid by the rms in sector x) RMTS x KL = -> ine ecient allocation What about a general tax on wages? r w(1 + t wx ) 6= r w = RMTS y KL No ine cienies in production (make sure you see it). But we still have distorsions in comsumption Public Economics () distorsions / 15
37 Notes in "aula global" Two consumption goods,x and y. One production factor l. Two rms X s = F k (l x ) Y s = F y (l y ) Fixed labor supplu l Consumer U(x, y) Frontier of possibilities of production: y = T (x) MRT (x, y) MRS(x, y) Public Economics () distorsions / 15
38 Notes in "aula global" One can prove the following Theorem If the allocation f(x D, y D ), (x S, l x ), (y S, l y )g is e cient,then l x + l y = l x D = x S y D = y S MRS x,y (x D, y D ) = MRT x,y (x S, y S ) Theorem If [(p x, p y, w ), f(x D, y D ), (x S, l x ), (y S, l y )g] is a competitive equilibrium, then the allocation f(x D, y D ), (x S, l x ), (y S, l y )g is e cient. Public Economics () distorsions / 15
39 Public Economics () distorsions / 15
G + V = w wl + a r(assets) + c C + f (firms earnings) where w represents the tax rate on wages. and f represents the tax rate on rms earnings
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