In economics, when a tax is imposed where do i subtract the tax from? the demand or supply side?

Question

Given - Demand: Wd = 30 - 0.04L

Supply: Ws = 0.05L - 15

Question - Suppose the government imposes a payroll tax $9 per labor unit on the employer. Calculate the new equilibrium wage and employment level.

Answer 1

♦ Current equilibrium:

30-0.04L=0.05L-15

0.09L=45

L=500

W=10

♦ New equilibrium:

Wd-9=30-0.04L

Wd=30+9-0.04L=39-0.04L

39-0.04L=0.05L-15

0.09L=54

L=54*100/9=600

W=39-0.04*600=15

♦ Answ: New equilibrium L=600 and W=15

Answer 2

Answer to your basic question is that you can do one of the two things here:

either, (a) substract from the price in the demand equation the tax ( that is write Wd-t instead of just Wd in the demand equation), the reason being that the demand for labor at the pre-tax wage rate of Wd will be the same as the demand for labor at the post tax price - a firm will find that the marginal cost of labor has increased by t at all levels of employment and his demand curve will shift down to the left.,

or, (b) add t to the price variable in the supply equation: instead of just Ws , use Ws+t. the reason being that from the point of view of the workers since his net post tax earnings rate remains Ws, he will now be quoting the same supply of labor at post tax wage rate of Ws+t as he was earlier offering

to supply the tax free wage of Ws.

But do not do both.

Just check for the equivalence of (a) and (b) below.

With (a) your new demand equation is Wd-9 = 30 - 0.04L.or Wd= 39 - 0.04L

For equilibrium you need Wd=Ws. . That is ,

39 - 0.04L = Wd = Ws= 0.05L - 15,

or, 0.09L= 54 or L = 54/ 0.9= 5400/9= 600 and

W=Ws= Wd= 39 - 0.04L = 39 - 0.04*600 = 39-24=15

Now under (b), the supply equation will be Ws+9=0.05L -15, or, Ws= 0.05L -24

Ws=Wd equlibrium will require

30 - 0.04L =Wd=Ws= 0.05L -24, ie, 0.09L= 54 and so L is again = to 5400/9=600 and W= Ws=Wd=30 - 0.04L=30-0.04*600 = 30- 24=6 So, add the tax element now to get post tax W = 6+9=15.

You may get confused with this equivalence. Therefore better to remember the the method (a): replace the wage (price) variable W (in other cases P) with (W-tax per unit),in other case (P-tax per unit), keep the supply equation in tact and solve for the wage and employment or the price and quantity as the case may be.