Question

6. Who should pay the tax? The following graph shows the labor market for research assistants in the fictional country of Universalia. The equilibrium wage is $10 per hour, and the equilibrium number of research assistants is 200. Suppose the government has decided to institute a $2-per-hour payroll tax on research assistants and is trying to determine whether the tax should be levied on the employer, the workers, or both (such that half the tax is collected from each side). Use the graph input tool to evaluate these three proposals. Entering a number into the Tax Levied on Employers field (initially set at zero dollars per hour) shifts the demand curve down by the amount you enter, and entering a number into the Tex Levied on Workers field (initially set at zero dollars per hour) shifts the supply curve up by the amount you enter. To determine the before-tax wage for each tax proposal, adjust the amount in the Wage field until the quantity of labor supplied equals the quantity of labor demanded. You will not be graded on any changes you make to this graph. Note: Once you enter a value in a white field, the graph and any corresponding amounts in each grey field will change accordingly. Graph Input Tool ? Market for Research Assistants 20 18 4 Supply 16 Wage (Dollars per hour) Labor Demanded (Number of workers) 320 Labor Supplied (Number of workers) 80 14 12 Demand Shifter Supply Shifter WAGE (Dollars per hour) 10 0 0 Tax Levied on Employers (Dollars per hour) Tax Levied on Workers (Dollars per hour) Demand 4 2 0 0 40 80 120 160 200 240 280 320 380 400 LABOR (Number of workers)

Answer 1

I don't have access to the graphing tool therefore,first of all we have to derive the demand function.

P = 20 - mQ

When P = 0, Q = 400

0 = 20 - m × 400

=> 400m = 20

=> m = 0.05

Thus,the demand curve is

P = 20 - 0.05Q

Similarly, deriving the supply curve

P = mQ

When P = 10, Q = 200

10 = 200m

=> m = 0.05

Supply curve is,

P = 0.05Q

1st case when the tax is imposed on employers then the demand curve would shift to its left.

P - 2 = 20 - 0.05Q

P = 18 - 0.05Q

Equate it to original supply curve

18 - 0.05Q = 0.05Q

=> 0.05Q + 0.05Q = 18

=> 0.1Q = 18

=> Q = 180

Price received by suppliers, P = 0.05 × 180 = $ 9

Price paid by buyers, P = 20 - 0.05 × 180 = $ 11

Case 2. When a tax of $ 2 is imposed on employers then the supply curve would shift to its left. After tax the price received by suppliers would shift by $ 2 that is new price would be P - 2.

P - 2 = 0.05Q

New Supply curve, P = 2 + 0.05Q

Now equate it to demand curve

2 + 0.05Q = 20 - 0.05Q

=> 0.05Q + 0.05Q = 20 - 2

=> 0.1Q = 18

=> Q = 180

P = 20 - 0.05 × 180 = $ 11

Price received by suppliers, P = 0.05 × 180 = $ 9

Case 3. When $ 1 tax is imposed on both workers and employers then the demand and supply curve would shift by $ 1

P - 1 = 20 - 0.05Q

=> P = 19 - 0.05Q

New supply curve

P - 1 = 0.05Q

=> P = 1 + 0.05Q

Equate demand and supply

19 - 0.05Q = 1 + 0.05Q

=> 0.1Q = 18

=> Q = 180

Employers pay, P = $ 11

Workers receive, P = $ 9

Quantity of Labour Hired Tax Proposal Employers Workers 2 0 0 2 1 180 After tax paid After tax wage by employers received by workers 11 9 11 9 11 9 180 1 180

Suppose the government doesn't want to discourage employers from hiring research assistants and, therefore, wants to minimize the share of the tax paid by the employers. Of the three tax proposals, which is best for accomplishing this goal?

None of the proposals is better than the others

From the above table, we can see that the equilibrium quantity of labor, the amount employers pay per hour after the tax, and the amount workers receive are all independent of who pays the tax. Therefore, it doesn't matter which tax proposal the government implements because none of the proposals is better than the others.

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