Question

In: Economics

In an economy, the supply of labour is given by S = 10 + 200Wn, where...

In an economy, the supply of labour is given by S = 10 + 200Wn, where S is the quantity supplied of labour (hours of work), and Wn is the after-tax wage rate (net wage). Assume that the before-tax wage rate is fixed at $10.

a) Find the quantity supplied of labour and the total tax revenue at the following tax rates: 15%, 30%, 50%, 70%, and 80%.

b) Calculate the net wage elasticity of labour supply at each of the tax rates. Is the tax revenue positively or negatively related to the net wage elasticity? (1.5 marks)

c) What does the relationship between the tax rate and the tax revenue resemble? What is the tax rate that generates the highest level of tax revenue? (1.5 marks).

Solutions

Expert Solution

S=10+200Wn or

S=10+200(10-taxrate*10). (Just put the value of Wn=10-tax rate*10)

tax revenue = tax rate*labor supplied at that tax rate

Ansa) labor supplied at 15%

S=10+200(10-0.15*10)=1710

Tax revenue =0.15*1710=256.500

Labor supplied at 30%

S=10+200(10-0.3*10)=1410

Tax revenue =0.3*1410=423

Labor supplied at 50%

S=10+200(10-0.5*10)=1010

Tax revenue =0.5*1010=505

Labor supplied at 70%

S=10+200(10-0.7*10)=610

Tax revenue =0.7*610=427

Labor supplied at 80%

S=10+200(10-0.8*10)=410

Tax revenue =0.8*410=328

Ans b) Net wage elasticity of labor supply= percentage change in labor supply/percentage change in net wage

Net wage elasticity = (dS/S)/(dWn/Wn)=dS/dWn * Wn/S

dS/dWn=200( from labor supply equation)

Net wage elasticityat 15%=200*Wn/S=200*8.5/1710=0.9941

Net wage elasticity at 30%=200*Wn/S=200*7/1410=0.9929

Net wage elasticity at 50%=200*Wn/S=200*5/1010=0.9901

Net wage elasticity at 70%=200*Wn/S=200*3/610=0.9836

Net wage elasticity at 80%=200*Wn/S=200*2/410=0.9756

Note : There is an error in question part b .The question should be is tax rate positively or negatively related to net wage elasticity & answer is negatively.Higher the tax rate lower the net wage elasticity

Ans c) Tax revenue declines as tax rate increases from 50%onwards and Tax revenue increases as tax rate increase from 15% to 50%.50% generates highest tax revenue (evident from part a)

Rahul Sunny answered 9 months ago
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