Question

Consider the market for labor is segmented into the market for low skilled labor and the market for high skilled labor. If the low skilled labor market is given by the following function: labor demand: w = 35 – 0.005L; and labor supply is 4000. If the high skilled labor market is given by the following functions: labor demand: w = 400 – 2L, and the labor supply function is given by w = 160 + 1.2L. The hourly wage in both is given by w, and L is the number of workers.

(a) Show both numerically and with corresponding graphs (for the two markets) the equilibrium wages and number of workers in the low skilled labor market and the high skilled labor market. (4 points)

(b) Suppose the government needing to provide some basic services decided to place a tax on labor income and chooses a progressive tax structure where it taxes the low income earners at a rate of $3 per labor hour, and the high income earners at rate of $112 per labor hour. Compute the total revenues the government will get from this tax scheme and the deadweight loss associated with this. (4 points)

(c) Suppose instead the government decides to use a flat tax of 24% of the equilibrium wage for labor in all markets. Again compute the total revenues to the government and the deadweight loss associated with this. (4 points)

(d) Discuss the efficiency and equity attributes of both policies. In general if the government wanted to focus on minimizing the deadweight loss from taxation, what should be the optimal labor income tax policy providing tax revenues in the same range as in (b) and (c) above? Are there any problems with this policy? Explain. (2 points)

(e) What if the government decides to focus more on reducing income inequality through its tax policy and tries to tax only the high income earners, what are the two revenue generation problems with this policy? Explain. (2 points)

Answer 1

a)

Show both numerically and with corresponding graphs (for the two markets) the equilibrium wages and number of workers in the low skilled labor market and the high skilled labor market.

Low skilled labor
labor demand: w = 35 – 0.005L, and the labor supply is given by 4000

Here since labor supply is constant at 4000 let us find at what wage rate demand equals supply. So at W = $15, labor demand = 4000

High skilled labor
labor demand: w = 400 – 2L, and the labor supply function is given by w = 160 + 1.2L
labor demand: w = 400 – 2L = labor supply: w = 160 + 1.2L
w = 400 – 2L = 160 + 1.2L
240 = 3.2L
L = 240/3.2 = 75
W = 400-2*75 = 250

b)

Suppose the government needing to provide some basic services decided to place a tax on labor income and chooses a progressive tax structure where it taxes the low income earners at a rate of $3 per labor hour, and the high income earners at rate of $112 per labor hour. Compute the total revenues the government will get from this tax scheme and the deadweight loss associated with this.

For Low income, at rate of $3 per labor hour, the wage would be 15+3=18
At 18, the labor demand would be 3400,
The government revenue is
the area of square
= l*b
=3400*3
=10200

deadweight loss = 900= ½*600*3

For high income, at rate of $112 per labor hour, the wage would be 250+112=362
At 362, the labor demand would be 19,
The government revenue is
the area of trapezoid
= (a+b)/2*h
=(67+90)/2*19
=1491.5

deadweight loss = 5012= ½*179*56

c)

Suppose instead the government decides to use a flat tax of 24% of the equilibrium wage for labor in all markets. Again compute the total revenues to the government and the deadweight loss associated with this.

Low skilled labor
labor demand: w = 35 – 0.005L, and the labor supply is given by 4000

Here since labor supply is constant at 4000 let us find at what wage rate demand equals supply. So at W = $15, labor demand = 4000

Now government uses flat rate of 24% of equilibrium wage 15 is $3.6, for $18.6
total revenues to the government: Area of rectangle = 3280*3.6 = 11808
deadweight loss: area of triangle DWL = ½*3280*3.6 = 1296

High skilled labor

labor demand: w = 400 – 2L, and the labor supply function is given by w = 160 + 1.2L
labor demand: w = 400 – 2L = labor supply: w = 160 + 1.2L
w = 400 – 2L = 160 + 1.2L
240 = 3.2L
L = 240/3.2 = 75
W = 400-2*75 = 250
Now government uses flat rate of 24% of equilibrium wage 250 is $60, for $210
total revenues to the government: Area of rectangle = 60*45 = 2700
deadweight loss: area of triangle DWL = ½*214*45 = 4815

d)

Generally taxing would help governments to revenue when high skilled labor where marginal utility for consumption would be less compared to taxing low skilled labor whose marginal utility is less.

The optimal labor income tax policy would be where the ratio of marginal utility of individual from income and MR is the marginal revenue from taxing would equal for both rich and poor. With a flat rate, it would increase the inequality of income of rich and poor.

e)

If only high income earners are taxed the two revenue generation problems would be
a)

People would report less income and try to avoid income tax which would reduce the tax revenue for the government

b)

It would discourage high skilled workers to earn more and their by it would reduce tax revenue for the government.