Question

Heckscher-Ohlin model

Country A produces cellphone (C) and food (F) with capital and labor. Both sectors are perfect competitive. Capital (K) and labor (L) are not substitutable with each other. Thus, unit capital requirement and unit labor requirement are fixed. ??? = 3, ??? = 1, ??? = 2, ??? = 4, where ??? is the number of units of K-capital required to produce and unit of C-cellphone.

a. Which sector is relatively capital intensive? Which sector is relatively labor intensive?

b. Suppose that the world price of cellphone is 16 and food is 12. Assume that Country A produces both foods. What are the free trade wage rate w and rental rate r? What is the share of revenue that goes to capital in each sector?

c. Suppose the world price of cellphone increases to 26, while the food price is still 12. What are the new wage rate w and rental rate r? What theorem may help you predict this result?

d. Suppose country A has 100 units capital and 150 units of labor. How many cellphone and food will it produce?

e. Suppose that the relative demand curve of this country is :

（Qc/Qf）=（Pc/Pf）-1

Country A’s endowment of capital and labor is as described in question d. If country A is in autarky (i.e. no trade). What is the autarky equilibrium relative price ?? ? What is the

relative factor price w/r in equilibrium?

datas are enough and all info provided

Answer 1

aKC = 3

aKF=1

aLC=2

aLF= 4

a) K/L required to produce C = aKC/aLC =3/2

K/L required to produce F = aKF/aLF =1/4

since aKC/aLC > aKF/aLF i.e. 3/2 > 1/4 , C is more capital intensive as it requires more capital per unit of labor to produce another unit of C and F is labor intensive as it requires more labour per unit of capital (4/1 > 2/3).

b) Due to perfect competition in both markets, each sector earns a zero profit. which means that price = cost

thus, Pc = akc.r + alc.w and Pf = akf.r+alf.w

16 = 3r+2w ............ [1]

12 = r+4w.................[2]

solving [1] and [2] for w and r,

from [2] r = 12-4w, put this in [1]

16 = 3(12-4w) + 2w = 36 – 12w + 2w = 36 – 10w

16 = 36-10w

10w = 36-16 = 20

w = 20/10 = 2

r = 12-4w = 12-4.2 = 12-8 = 4

thus wages = 2,

rent = 4

rent gets 4:(2+4) share which is to say that 4/6 of revenue

(c) P'c = 26

then w' and r' can be found as follows

P'c = akc.r' + alc.w' and Pf = akf.r'+alf.w'

26 = 3r'+2w' ............ [3]

12 = r'+4w'.................[4]

solving [3] and [4] for w' and r',

from [4] r' = 12-4w', put this in [1]

26 = 3(12-4w') + 2w' = 36 – 12w' + 2w' = 36 – 10w'

26 = 36-10w'

10w' = 36-26 = 10

w' = 10/10 = 1

r' = 12-4w' = 12-4.1 = 12-4 = 8

thus wages = 1, wages decreased

rent = 8 rent increased

Stolper-Samuelson theorem states that an increase in the price of a good which is C will lead to an increase in the price of the factor used intensively in the industry (here k) and a decrease in the price of the other factor (here L).

D) K = 100 and L = 150

let qc and qf be the production levels, then,

akc.qc+ akf.qf = K and alc.qc + alf.qf = L

thus we have,

3.qc + 1.qf =100 (for k )........ A

and 2.qc + 4qf =150 (for L).........B

solving from A we get, qf = 100 - 3qc... put this in B

we get, 2qc + 4(100-3qc) = 150

2qc +400 - 12qc = 150

-10qc = 150-400

-10qc = -250

10qc = 250

qc = 25

putting back in A, qf = 100 - 3.25 = 100-75 = 25

so produce 25 units of C and 25 units of F

(e) relative demand curve : qc/qf = ( pc/pf)^-1

this can be written as qc/qf = pf/pc also. or as qc.pc = qf.pf

in autarky, since given that K = 100 and L = 150 (endowments), qc = 25 = qf is produced, then qc/qf = 25/25 = 1

then the autarky price pf/pc = qc/qf = 1

relative price in autarky will be 1. since pc/pf = 1, we can say that pc = pf.

in that case

Pc = akc.r + alc.w = Pf = akf.r+alf.w

3r+2w = r+4w.

3r-r = 4w-2w

2r = 2w

r = w

r/w = 1 or w/r = 1, that is relative factor prices and relative good prices amount to 1.