High School Graduate

Seminar 8

1. 
   Suppose that the person earns $7000 if he is college graduate, and $5000 if he is high school drop out. Moreover, suppose that person should give up 2 years of labor market participation to get a college education, while the person can only participate to labor market for 15 years after high school graduation. The tuition for college is $1000 Use 0.1 as the interest rate.
   

1. 
   Show the conditions under which it is optimal for the person to get college education.
   

High School Graduate:

College Graduate. :

He will get College education iff :

In other terms:

2. 
   How change in variables affect the decision?
   

As the wage difference increases, person become more likely to attend college given all other parameters.

As the tuition increases it, person become less likely to attend college given all other parameters.

As time in college decreases, person become more likely to attend college given all other parameters.

As time in labor market increases, person become more likely to attend college given all other parameters.

As interest rate rises , person become less likely to attend college given all other parameters.

2-Suppose that the person attends the labor market and stays there forever. (It has infinite life time). He decides to get one more year education which will increase the yearly salary with g < 1. Show that when g (marginal rate of return) of education is greater than r (discount rate), he should get an education. The salary level without additional education is $7000.

The left hand side is the gain from education and right hand is the loss.
By adding to both sides we get the following:

Which can be written as

Or

Which is equal to

3-Suppose that there are two types of labor according to their skill set; skilled labor and unskilled labor. The proportion of unskilled labor in population is p. Skilled labor person has a VMP_S , greater than the unskilled labor’s VMP_U . Cost of education differs between skilled and unskilled labor. The cost of education for the skilled labor is c_s and unskilled labor is c_u while c_s > c_u.

1. 
   Find the pooling wage level? Show that there is an incentive to get education for skilled labor.
   

E(W) = P. VMP_U + (1-P) VMP_S (Pooling wage level)
VMP_S > E(W) since VMP_S > VMP_U

2. 
   Show the conditions under which the separating equilibrium occurs?
   

Incentive to get X_s much education for skilled labor:

VMP_S – X_s.c_s > VMP_U (1)

Incentive to get X_u much education for unskilled labor:

VMP_S – X_u. c_u > VMP_U (2)

Solving (1) :

X_s. <

Solving (2) :

X_U <

X_s > X_U since
Therefore if are different enough we can always find separating equilibrium in the discrete space, and find for any in Real space.

(Think about 11.85 and 11.65 for the upper bounds for X_s and X_u , if the education is non-divisible , the separating equilibrium fails in the discrete space since skilled cant distinguish itself from unskilled in its feasible(incentive) region).

iii) Use numerical values for those variables and solve ii..

VMP_{High Skill} = $100, VMP_{Low Skill} = $50
ρ_{Low Skill} = 0.6
Cost per Signal_{High Skill} = $4, Cost per Signal_{Low Skill} = $8

High Skill will take courses up to:

Net Wage courses > No courses
$100 - $4*X > $50
12.5 > X
Low Skill will take courses up to:
Net Wage course > No courses
$100 - $8*X > $50
6.25 > X
X = 7
Net Wage_{High Skill} = $100 – 7*$4 = $72 > $50 Takes 7 courses.
Net Wage_{Low Skill} = $100 – 7*$8 = $44 < $50 Takes 0 courses.
4- Suppose that W= 6+2L^S is the labor supply function, and there is only one buyer in the market. Suppose that the production function for the firm is q=30L- 2L²

1. 
   Calculate wage, employment and profit level for perfectly discriminating monopsony case?
   

VMP_L = 30-4L

Profit max condition: VMP_L= W, however in the perfectly discriminating monopsony case, firm is not price taker and uses labor supply function to extract labor by offering them reservation wages. (so each cost of increasing employment corresponds to marginal factor cost, thus labor supply curve and MFC are same)

Therefore;

30-4L* = 6+2L* , Solving for L* gives

L* = 4, W= 14,

Profit:

= = 48

ii)Calculate wage, employment and profit level for perfectly non-discriminating monopsony case?

In non-discriminating monopsony case the firm can not distinguish labor according to their reservation wage. Therefore, it offers same equilibrium wage level to all labor.

The equilibrium wage is found by equalizing VMP to MFC

MFC is different than labor supply curve since each additional employment rises the cost more than the cost implied by the labor supply curve.

TFC= W*L= (6+2L)*L

MFC= 6+4L

VMP = MFC

30-4L* = 6+4L

Solving for L* = 3, W=18

Profit level

Compared to perfectly discriminating case, L* decreased, W increased, profit decreased.