Question

1. The production function for Belgium is given by Y = AKIN and K 25. 4 = 9 is given. The labor supply curve is given by N, = 100(1 - 1) where we is the before-tax real wage, and (1 - T) is the afte rate. The labor income is given by the product of the real wage and the equilibrium employment level. (a) Write down the equation of the labor demand curve. Draw the labor demand curve. Then, draw the labor supply curve (with after-tax wage on the vertical axis). Draw the pictures as accurately as you can (using the above information) (b) How does labor supply respond to an increase in the tax rate ?! (c) Assumer=0. Compute the i. equilibrium real wage, ii. equilibrium employment, and iii. equilibrium pre-tax labor income (pre-tax wage times total em- ployment) of all workers. (d) Does a beneficial productivity shock (K is still fixed at 25) help or hurt the pre-tax labor income of all workers in Belgium? Explain. (e) Assume r=0.6. Compute the i. equilibrium real wage, ii. equilibrium employment, and iii. equilibrium after-tax labor income of all workers. (f) Why does employment fall when rise? (g) Will a minimum wage of min = 2 increase the total after-tax income of all employed workers if t = 0.6? Explain. Show all steps. (h) Will a minimum wage of min = 2 increase the total after-tax income of all employed workers if t = 0? Explain.

Answer 1

. a) Labor demand: MPN: (1-7) w 05, 9(25)??..NYEW or, 45 NYO 2w og nyeshadow b) The labor demana and supply is depicted in figure - Labor supply: Ng = 100 [c1-) W] care sa : -2009 [61-y)w] <o :. ONS 27 Then as J rises Ns decreases. c) Assuming y = 0; N3 = 100 w² Nd. 22:52 W2 Equilibrium: NS = Na a 100 W2 22.5 ay wt. ( Or, 12 2205 is :W315 (ii) (15) N = 225 Total income = 337.5

A. d) The beneficial productivity shock n rise in A rise in parameter a increases labor demand. A rise in demand increases wage rate and employment. Hence, help the pre tase labor income by increasing in rame. 22.5 72 es Assuming y = 0.6 Nos. 190[0:4w]? Nd=52205 ] Equilibrium: ns. Nd. 2,100 [0:4w.jº. or, [w]". [225]" ar, W2 = 5625 12. .. w: 2:37 (ii) :. N = 89.87 (m) :. Total income = 852 . f) As parent tax rate rises labor supply decreases , to keep the employment the firm increases wage rate nence decreaseas employment. g) with whin =2, N=1 2215] = 126 5625 1. After tax income: (1.) When N= 101.25

Then, with a minimum wage, the after-tax income of the worker rises with a tax rate of 0.6.

h)

With w_min=2, the market wage rate is 1.5 with t=0.6. Then the minimum wage is not binding and total income remains the same.