Question

Skill premium in the Heckscher-Ohlin Model

Suppose that we are within Heckscher-Ohlin model with perfect competition. There are two goods (computers and shoes), and two factors of production: Skilled labor (H) and unskilled labor (L). The country has 10 skilled workers and 20 unskilled workers. Each factor is mobile across industries. The production function in the computer industry is given by: Y_C = L_C^1/3 H_C^2/3. The production function in the shoe industry is given by: Y_S = L_S^2/3 H_S^1/3. Denote by s the wage of skilled workers and by w the wage of unskilled workers.

a) Which industry is more intensive in skilled labor?

b) Show that the skill intensity in the computer industry satisfies: H_C/L_C = 2 (s/w)^-1

c) Show that the skill intensity in the shoe industry satisfies: H_S/L_S = ½ (s/w)^-1

d) Half of the unskilled workers work in each industry initially. What is the skill premium then?

e) The computer industry now hires 75% of the unskilled workers. What is the skill premium?

Answer 1

a) The weightage of H in the production function of computer industry is (2/3). The weightage of H in shoe industry is (1/3). Thus more skilled labourers are used in computer industry than in shoe industry. Computer industry is skilled intensive.

b) Y= L_c^(1/3)H_c^(2/3)

Differentiating, we get,

dY= (1/3)L_c^(-2/3)H_c^(2/3) dLc + (2/3) H_c^(-1/3)L_c^(1/3)dHc

0=(1/3)L_c^(-2/3)H_c^(2/3) dLc + (2/3) H_c^(-1/3)L_c^(1/3)dHc

Thus, (1/3)L_c^(-2/3)H_c^(2/3) dLc = - (2/3) H_c^(-1/3)L_c^(1/3)dHc

(H_c/L_c)= 2(-dH_c/dL_c)....... (1)

Now, we know the Cost function is

Cost in computer industry = sH_c + wL_c

dCost= s dH_c + w dL_c

dCost= 0

thus -(dH_c/dL_c)= w/s..... (2)

Putting (2) in (1), we get

(H_c/L_c)= 2(s/w)^-1.....(A)

c) Y=H_s^(1/3)L_s^(2/3)

Differentiating, we get,

dY= (1/3) H_s^(-2/3)L_s^(2/3)dH_s + (2/3)Ls^(-1/3)H_s^(1/3)dL_s

0= (1/3) H_s^(-2/3)L_s^(2/3)dH_s + (2/3)Ls^(-1/3)H_s^(1/3)dL_s

(1/3) H_s^(-2/3)L_s^(2/3)dH_s = - (2/3)Ls^(-1/3)H_s^(1/3)dL_s

2(H_s/L_s)= - dH_s/dL_s ....... (3)

Now, we know the Cost function is

Cost in shoe industry = sH_s + wL_s

dCost= s dH_s + w dL_s

dCost= 0

thus -(dH_s/dL_s)= w/s..... (4)

Putting (4) in (3), we get,

H_s/L_s = ½ (s/w)^-1............ (B)

d) Total number of unskilled workers present : 20.

(1/2) of the unskilled workers work in each industry initially ie each industry has 10 unskilled workers.

Skill premium is the ratio of wage rate of skilled labourers to wage rate of unskilled labourers.

From equation A and B, we get

s/w= L_s/(2H_s)= (2L_c/H_c)

L_c= L_s= 10

(10/2H_s)= (20/H_c)

H_c= 4H_s

H_c+H_s= 10 (given)

5H_s=10

H_s=2, H_c=8

s/w = 10/ 4 = 2.5

Skill premium= 2.5

e) Lc= 0.75 x 20 (given)

Lc= 15, Ls= 5

From equation A and B, we get

L_s/(2H_s)= (2L_c/H_c)

5/(2H_s)= (30/H_c)

H_c= 12H_s

If we consider labour to be infinitely divisible for our simplicity,

H_c+ H_s= 10

13H_s=10

H_s= (10/13)

H_c= (120/13)

s/w= L_s/(2H_s)= (2L_c/H_c) = 3.25

The skill premium is 3.25.