Question

Consider a household facing the following problem: mgx U(c.h) = { ine+(1 – žin(1 – 1) subject to c=wh, where c denotes consumption, h hours worked and w is the wage.

a. Describe the trade-off that the household faces and solve for hours worked, i.e. labour supply.

b. Suppose that the government introduces a proportional tax, T, on labour income so that the budget constraint becomes c = (1 - T)wh. The tax revenue will be used to finance the restoration of old castles in the south of Sweden. How is the individual's labour supply affected? Motivate your answer mathematically

c.  Suppose instead that the tax revenue is returned to households as a lump-sum transfer. Specify the government’s budget constraint and explain how labour supply is affected by the tax.

d.  Maintaining the assumptions in question c, suppose that the tax rate is set to τ = 0.3. Compute labour supply.

e.  Suppose that the tax rate is lowered from 0.3 to 0.2. Compute the change in labour supply in percentage terms.

Answer 1

со / incl-u) е : а Сі-т)ѕи b. [c.) с + The budget constraint :. 3 w - Marx U.2 Lac + 32 cm (1-2) c with (1-2) wh. Man U = 2 ln (1-4)wh + 3 3 Kana" + 3 Luci-) du 1 2 1 Ci-) + 3 5 1-к) с (-3) = 0 dh Б (-) N 9. 1) ғ|Р 3. 1- S I-h и 5 h 1 г 235 The labour spp. does not depend on the 9 Thas wages. hеlоt tому or decreare any 4 ш will not wages чол. The consumption will reduce will reduce due to labour tax rate imposition Pro) labom supply LA twages

(%) с. Эх % the at .к. мике. .. The government's budget constraint G = TWh олти маі "4 Now the individual's budget constraint С: (- дали ) + (отра. h) -(1-т ) + 6 6. То с. 1-т) htt: w° Wh. Thus the budget constraint and utility function и алты а, ра "IN WIN Р И. Optimal ho tax rate. а) 름 :. It doesnt depend on :. Latour fr is fixed at *e 2

(e) The latour 3) Prg doesn't depend on depend on the tax rate. It is fixed at И+ г لما ta2 Labour supply Thus nt к. | Р