economics assignment

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

ECO 364 - International Trade Lecture 4: The Specific Factors Model

ECO 364 - International Trade Fall 2018 Specific Factors Model 1

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Motivation

I So far, we have studied models that tell us trade is always good

I but why are so many people opposed to trade?

ECO 364 - International Trade Fall 2018 Specific Factors Model 2

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Overview

I Key idea:

I there are always gains from trade in the aggregate I but these gains may not be distributed evenly across different groups I in particular, some groups may gain while some groups may lose

I To study this, extend Ricardian model with an additional factor of production

I call this factor capital, which will be specific to sectors I model will allow us to study how trade affects incomes for different factors

ECO 364 - International Trade Fall 2018 Specific Factors Model 3

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Overview

(1) (2) (3) (4)

exchange Ricardian specific Hecksher-Ohlin

economy model factors model model

# countries 2 2 2 2

# goods 2 2 2 2

# factors - 1 2 2

factors mobile no yes 1 yes, 1 no yesacross sectors?

ECO 364 - International Trade Fall 2018 Specific Factors Model 4

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Demand Production Market Clearing Equilibrium Example

Closed Economy Model

I First consider a single country “Home”

I omit H superscripts here for brevity

I Two sectors (goods): 1 and 2

I both goods produced using labor and capital I labor is mobile across the two sectors I two types of capital, specific to each sector I market structure is perfect competition

I Factor endowments:

I L̄ units of labor I K̄1 units of sector 1 capital I K̄2 units of sector 2 capital

I Households in Home:

I consuming C1, C2 of the two goods yields utility U (C1,C2) I U has standard properties of a utility function

ECO 364 - International Trade Fall 2018 Specific Factors Model 5

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Demand Production Market Clearing Equilibrium Example

Household Income

I Household income I now depends on whether it is a worker or capital owner:

I =

 wL̄ , for workers

r1K̄1 , for sector 1 capital owners

r2K̄2 , for sector 2 capital owners

I Factor prices

I w : wage paid to workers I r1: rental rate of sector 1 capital I r2: rental rate of sector 2 capital

I Since labor is assumed to be mobile across sectors, there will be a common wage

I Since capital is immobile, there can be different rental rates

ECO 364 - International Trade Fall 2018 Specific Factors Model 6

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Demand Production Market Clearing Equilibrium Example

Budget Set

I Household’s budget constraint:

p1C1 + p2C2 ≤ I

where p1, p2 are the prices of goods 1 and 2, with relative price pr ≡ p1/p2

ECO 364 - International Trade Fall 2018 Specific Factors Model 7

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Demand Production Market Clearing Equilibrium Example

Utility Maximization

I Given prices, household chooses consumption to maximize utility:

max C1,C2

U (C1,C2)

s.t. p1C1 + p2C2 ≤ I

I First-order conditions imply:

MRS ≡ U1/U2 = p1/p2

ECO 364 - International Trade Fall 2018 Specific Factors Model 8

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Demand Production Market Clearing Equilibrium Example

Relative Demand

I As before, different relative prices pr induce different choices of C1, C2 I As good 1 becomes more expensive relative to good 2...

I consumption of good 1 relative to good 2 decreases

I Relative demand curve:

ECO 364 - International Trade Fall 2018 Specific Factors Model 9

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Demand Production Market Clearing Equilibrium Example

Production

I Production technology available to firms in Home for producing good i ∈ {1, 2}

Xi = F (Ki , Li )

where F is a production function that has standard properties

I In contrast with the Ricardian model, marginal products are not constant:

aLi ≡ FL (Ki , Li ) aKi ≡ FK (Ki , Li )

I In particular, there are diminishing returns to each factor

ECO 364 - International Trade Fall 2018 Specific Factors Model 10

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Demand Production Market Clearing Equilibrium Example

Marginal Products

I Holding capital inputs constant, output grows by less as labor input is increased

ECO 364 - International Trade Fall 2018 Specific Factors Model 11

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Demand Production Market Clearing Equilibrium Example

Marginal Products

I Holding capital inputs constant, output grows by less as labor input is increased

I The slope of the curve measures the marginal product of labor, aLi

ECO 364 - International Trade Fall 2018 Specific Factors Model 12

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Demand Production Market Clearing Equilibrium Example

Marginal Products

I Holding capital inputs constant, output grows by less as labor input is increased

I The slope of the curve measures the marginal product of labor, aLi I As labor input increases, marginal product of labor falls as capital is fixed

I Same is true for marginal product of capital, aKi

ECO 364 - International Trade Fall 2018 Specific Factors Model 13

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Demand Production Market Clearing Equilibrium Example

Production Possibilities Frontier

I How much of each good can be produced given the available technology?

I Home’s production possibilities frontier (PPF):

I As before, the slope of the PPF is the ratio of MPLs

I except that now, MPLs are no longer constant

ECO 364 - International Trade Fall 2018 Specific Factors Model 14

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Demand Production Market Clearing Equilibrium Example

Profit Maximization

I Market structure is assumed to be perfect competition

I firms take prices as given and choose factor inputs to maximize profits

I Formally, profit-maximization problem for a firm producing good i is:

max Ki ,Li {pi F (Ki , Li )− ri Ki − wLi}

I First-order conditions imply that factors are paid their marginal revenue product:

w = pi FL (Ki , Li ) = pi aLi

ri = pi FK (Ki , Li ) = pi aKi

ECO 364 - International Trade Fall 2018 Specific Factors Model 15

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Demand Production Market Clearing Equilibrium Example

Profit Maximization

I Real incomes are equal to marginal products of each factor:

w/pi = aLi

ri/pi = aKi

I Since w is common across sectors, MRPLs must be equal:

p1aL1 = p2aL2

I Therefore, the relative goods price is equal to the inverse of relative MPLs:

p1

p2 =

aL2

aL1

I Same as in Ricardian model, except that marginal products are not constant

ECO 364 - International Trade Fall 2018 Specific Factors Model 16

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Demand Production Market Clearing Equilibrium Example

Market Clearing

I Capital market clearing requires:

K1 = K̄1

K2 = K̄2

I Labor market clearing requires:

L1 + L2 = L̄

I Goods market clearing requires:

C1 = X1

C2 = X2

I Market clearing will determine factor and goods prices

ECO 364 - International Trade Fall 2018 Specific Factors Model 17

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Demand Production Market Clearing Equilibrium Example

Determination of Wages

I First take goods prices p1, p2 as given

I As L1 increases, marginal product of labor in sector 1 falls

ECO 364 - International Trade Fall 2018 Specific Factors Model 18

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Demand Production Market Clearing Equilibrium Example

Determination of Wages

I First take goods prices p1, p2 as given

I As L1 increases, marginal product of labor in sector 1 falls

I As L2 increases, marginal product of labor in sector 2 falls

ECO 364 - International Trade Fall 2018 Specific Factors Model 19

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Demand Production Market Clearing Equilibrium Example

Determination of Wages

I In equilibrium, labor allocation must be such that MPL is equal across sectors

I This determines the wage rate

ECO 364 - International Trade Fall 2018 Specific Factors Model 20

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Demand Production Market Clearing Equilibrium Example

Determination of Rental Rates

I The equilibrium allocation of labor also determines capital rental rates

I As L1 increases, marginal product of capital in sector 1 rises

ECO 364 - International Trade Fall 2018 Specific Factors Model 21

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Demand Production Market Clearing Equilibrium Example

Determination of Rental Rates

I The equilibrium allocation of labor also determines capital rental rates

I As L1 increases, marginal product of capital in sector 1 rises

I As L2 increases, marginal product of capital in sector 2 rises

ECO 364 - International Trade Fall 2018 Specific Factors Model 22

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Demand Production Market Clearing Equilibrium Example

Determination of Rental Rates

I Since capital is specific to sectors, equilibrium rental rates can differ

ECO 364 - International Trade Fall 2018 Specific Factors Model 23

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Demand Production Market Clearing Equilibrium Example

Relative Supply

I Now suppose that p1 increases

ECO 364 - International Trade Fall 2018 Specific Factors Model 24

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Demand Production Market Clearing Equilibrium Example

Relative Supply

I Now suppose that p1 increases

I MRPL in sector 1 rises

I More labor is allocated to sector 1

ECO 364 - International Trade Fall 2018 Specific Factors Model 25

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Demand Production Market Clearing Equilibrium Example

Relative Supply

I Similarly, suppose that p2 falls

I MRPL in sector 2 falls

I More labor is again allocated to sector 1

ECO 364 - International Trade Fall 2018 Specific Factors Model 26

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Demand Production Market Clearing Equilibrium Example

Relative Supply

I Therefore as relative price p1/p2 increases, relative supply X1/X2 increases

ECO 364 - International Trade Fall 2018 Specific Factors Model 27

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Demand Production Market Clearing Equilibrium Example

Determination of relative goods price

I Goods market clearing requires that relative demand equals relative supply

I This determines the relative goods price pr

ECO 364 - International Trade Fall 2018 Specific Factors Model 28

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Demand Production Market Clearing Equilibrium Example

Equilibrium

I Once the relative goods price is determined, so are:

I relative MPL aL2/aL1 I equilibrium production X1, X2 I equilibrium consumption C1, C2

ECO 364 - International Trade Fall 2018 Specific Factors Model 29

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Demand Production Market Clearing Equilibrium Example

Example

I As an example, solve the model with the following functional forms

I Cobb-Douglas utility with symmetric weights:

U (C1,C2) = (C1C2) 1/2

I Cobb-Douglas production function with labor share λ:

F (K , L) = K 1−λLλ

ECO 364 - International Trade Fall 2018 Specific Factors Model 30

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Demand Production Market Clearing Equilibrium Example

Example

Step 1: solve for relative demand

I Household’s utility maximization problem:

max C1,C2

(C1C2) 1/2

s.t. p1C1 + p2C2 ≤ I

I From first-order conditions, relative demand is:

C1

C2 =

p2

p1 (1)

I Intuition: higher goods prices → lower demand

ECO 364 - International Trade Fall 2018 Specific Factors Model 31

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Demand Production Market Clearing Equilibrium Example

Example

Step 2: solve for relative supply

I Production function: X1 = K

1−λ 1 L

λ 1

I Therefore relative supply depends on relative labor allocation:

X1

X2 =

( K̄1

K̄2

)1−λ ( L1

L2

)λ (2)

where capital market clearing Ki = K̄i has been imposed

I Intuition: more inputs → more output

ECO 364 - International Trade Fall 2018 Specific Factors Model 32

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Demand Production Market Clearing Equilibrium Example

Example

I To solve for labor allocation, look at firm’s profit maximization problem

max Ki ,Li

{ pi K

1−λ i L

λ i − ri Ki − wLi

} I First-order conditions for profit maximization in sector 1 are:

∂L1 : λp1 ( K̄1/L1

)1−λ = w (3)

∂K1 : (1− λ) p1 ( L1/K̄1

)λ = r1 (4)

I First-order conditions for profit maximization in sector 2 are:

∂L2 : λp2 ( K̄2/L2

)1−λ = w (5)

∂K2 : (1− λ) p2 ( L2/K̄2

)λ = r2 (6)

I Intuition: higher factor prices → lower factor demand

ECO 364 - International Trade Fall 2018 Specific Factors Model 33

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Demand Production Market Clearing Equilibrium Example

Example

I Equating (3) and (5) implies that relative labor allocation is:

L1

L2 =

K̄1

K̄2

( p1

p2

) 1 1−λ

(7)

I Intuition: higher goods prices → more labor allocated I Substituting (7) into (2) gives relative supply as:

X1

X2 =

K̄1

K̄2

( p1

p2

) λ 1−λ

I Intuition: higher goods prices → more output

ECO 364 - International Trade Fall 2018 Specific Factors Model 34

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Demand Production Market Clearing Equilibrium Example

Example

Step 3: equate relative demand and relative supply to determine p2/p1

I From step 1, relative demand is:

C1

C2 =

p2

p1

I From step 2, relative supply is:

X1

X2 =

K̄1

K̄2

( p1

p2

) λ 1−λ

I Therefore the relative goods price is:

p1

p2 =

( K̄2

K̄1

)1−λ I Intuition: more capital → good is less scarce, lower prices

ECO 364 - International Trade Fall 2018 Specific Factors Model 35

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Demand Production Market Clearing Equilibrium Example

Example

Step 4: solve for all other variables

I Once the relative goods price is known, can recover all other variables

I From (7), relative labor allocation is:

L1

L2 =

K̄1

K̄2

( p1

p2

) 1 1−λ

= 1

I Therefore from labor market clearing, can solve for labor allocation:

L1 = L2 = 1

2 L̄

ECO 364 - International Trade Fall 2018 Specific Factors Model 36

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Demand Production Market Clearing Equilibrium Example

Example

I Once labor allocation is known, can solve for output and consumption:

C1 = X1 = K̄ 1−λ 1

( L̄/2 )λ

C2 = X2 = K̄ 1−λ 2

( L̄/2 )λ

I Once output is known, can solve for welfare:

U = K̄ 1−λ

2 1 K̄

1−λ 2

2

( L̄/2 )λ

ECO 364 - International Trade Fall 2018 Specific Factors Model 37

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Demand Production Market Clearing Equilibrium Example

Example

I From firm’s first-order conditions, can solve for factor prices I Real wages:

w

p1 = λ

( 2K̄1/L̄

)1−λ w

p2 = λ

( 2K̄2/L̄

)1−λ I Real capital income for sector 1 capital:

r1

p1 = (1− λ)

( L̄/2K̄1

)λ r1

p2 = (1− λ)

( L̄/2K̄2

)λ ( K̄2/K̄1

) I Real capital income for sector 2 capital:

r2

p1 = (1− λ)

( L̄/2K̄1

)λ ( K̄1/K̄2

) r2

p2 = (1− λ)

( L̄/2K̄2

)λ ECO 364 - International Trade Fall 2018 Specific Factors Model 38

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

The pattern of trade Factor prices Welfare Summary

Small Open Economy

I Now suppose that Home can trade at world prices pW1 , p W 2

I i.e. as in previous lectures, assume that Home is a small open economy

I For concreteness, suppose that pWr > p H r

I the case with pWr < p H r will follow a similar but opposite logic

I Study the following questions:

I what will the pattern of trade be? I how will trade affect factor prices? I how will trade affect welfare?

ECO 364 - International Trade Fall 2018 Specific Factors Model 39

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

The pattern of trade Factor prices Welfare Summary

The pattern of trade

I Recall that in autarky, equilibrium is characterized as above

ECO 364 - International Trade Fall 2018 Specific Factors Model 40

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

The pattern of trade Factor prices Welfare Summary

The pattern of trade

I Since p1 relative to p2 is now higher, production occurs at point A:

I output of X1 increases I output of X2 decreases

ECO 364 - International Trade Fall 2018 Specific Factors Model 41

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

The pattern of trade Factor prices Welfare Summary

The pattern of trade

I The ability to trade at world prices also changes the household’s budget set

ECO 364 - International Trade Fall 2018 Specific Factors Model 42

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

The pattern of trade Factor prices Welfare Summary

The pattern of trade

I The ability to trade at world prices also changes the household’s budget set

I Consumption therefore occurs at point B, with higher utility in the aggregate

ECO 364 - International Trade Fall 2018 Specific Factors Model 43

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

The pattern of trade Factor prices Welfare Summary

The pattern of trade

I Since pHr < p W r , Home has a comparative advantage in good 1, and hence:

I Home exports good 1 I Home imports good 2

ECO 364 - International Trade Fall 2018 Specific Factors Model 44

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

The pattern of trade Factor prices Welfare Summary

Factor prices

I How does trade affect factor incomes?

I Recall that in autarky, factor prices are determined as above

ECO 364 - International Trade Fall 2018 Specific Factors Model 45

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

The pattern of trade Factor prices Welfare Summary

Factor prices

I Now suppose that pW1 > p H 1 and p

W 2 = p

H 2 (only relative price matters)

ECO 364 - International Trade Fall 2018 Specific Factors Model 46

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

The pattern of trade Factor prices Welfare Summary

Factor prices

I Now suppose that pW1 > p H 1 and p

W 2 = p

H 2 (only relative price matters)

I Marginal revenue product of good 1 increases

ECO 364 - International Trade Fall 2018 Specific Factors Model 47

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

The pattern of trade Factor prices Welfare Summary

Factor prices

I Now suppose that pW1 > p H 1 and p

W 2 = p

H 2 (only relative price matters)

I Marginal revenue product of labor for good 1 increases

I Hence more labor is allocated to sector 1

ECO 364 - International Trade Fall 2018 Specific Factors Model 48

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

The pattern of trade Factor prices Welfare Summary

Factor prices

I Now suppose that pW1 > p H 1 and p

W 2 = p

H 2 (only relative price matters)

I Marginal revenue product of labor for good 1 increases

I Hence more labor is allocated to sector 1

I The wage increases from w to ŵ , but by less than the change in p1

ECO 364 - International Trade Fall 2018 Specific Factors Model 49

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

The pattern of trade Factor prices Welfare Summary

Factor prices

I What about capital rental rates?

ECO 364 - International Trade Fall 2018 Specific Factors Model 50

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

The pattern of trade Factor prices Welfare Summary

Factor prices

I Since pW1 > p H 1 , marginal revenue product of capital for good 1 also increases

ECO 364 - International Trade Fall 2018 Specific Factors Model 51

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

The pattern of trade Factor prices Welfare Summary

Factor prices

I Since pW1 > p H 1 , marginal revenue product of capital for good 1 also increases

I In addition, more labor is allocated to sector 1

ECO 364 - International Trade Fall 2018 Specific Factors Model 52

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

The pattern of trade Factor prices Welfare Summary

Factor prices

I Since pW1 > p H 1 , marginal revenue product of capital for good 1 also increases

I In addition, more labor is allocated to sector 1

I Hence, the rental rate r1 increases to r̂1, and by more than the change in p1

ECO 364 - International Trade Fall 2018 Specific Factors Model 53

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

The pattern of trade Factor prices Welfare Summary

Factor prices

I Since pW1 > p H 1 , marginal revenue product of capital for good 1 also increases

I In addition, more labor is allocated to sector 1

I Hence, the rental rate r1 increases to r̂1,and by more than the change in p1 I But the rental rate r2 decreases to r̂2

ECO 364 - International Trade Fall 2018 Specific Factors Model 54

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

The pattern of trade Factor prices Welfare Summary

Welfare

I In summary, if pW1 > p H 1 and p

W 2 = p

H 2 , then factor prices change in the

following way:

I the wage w rises, but by less than the increase in p1 I the rental rate r1 rises, and by more than the increase in p1 I the rental rate r2 falls

I What does this imply for real incomes and hence welfare?

ECO 364 - International Trade Fall 2018 Specific Factors Model 55

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

The pattern of trade Factor prices Welfare Summary

The wage w rises by less than the increase in p1

I The real wage in terms of good 1 decreases:

ŵ

pW1 <

w

pH1

I Recall that in sector 1: w = p1FL(K̄1, L1)

ECO 364 - International Trade Fall 2018 Specific Factors Model 56

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

The pattern of trade Factor prices Welfare Summary

The wage w rises by less than the increase in p1

I The real wage in terms of good 1 decreases:

ŵ

pW1 <

w

pH1

I Recall that in sector 1: w ↑

= p1 ↑

FL(K̄1, L1)

I Intuition:

I as p1 rises, MRPL in sector 1 rises

ECO 364 - International Trade Fall 2018 Specific Factors Model 57

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

The pattern of trade Factor prices Welfare Summary

The wage w rises by less than the increase in p1

I The real wage in terms of good 1 decreases:

ŵ

pW1 <

w

pH1

I Recall that in sector 1: w ↑↓

= p1 ↑

FL(K̄1, L1 ↑

)

I Intuition:

I as p1 rises, MRPL in sector 1 rises I but more workers enter sector 1, causing MRPL to fall

ECO 364 - International Trade Fall 2018 Specific Factors Model 58

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

The pattern of trade Factor prices Welfare Summary

The wage w rises by less than the increase in p1

I The real wage in terms of good 2 increases:

ŵ

pW2 >

w

pH2

I Recall that in sector 2: w = p2FL(K̄2, L2)

ECO 364 - International Trade Fall 2018 Specific Factors Model 59

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

The pattern of trade Factor prices Welfare Summary

The wage w rises by less than the increase in p1

I The real wage in terms of good 2 increases:

ŵ

pW2 >

w

pH2

I Recall that in sector 2: w ↑

= p2FL(K̄2, L2 ↓

)

I Intuition: as p1 rises, workers leave sector 2, causing MRPL to rise

I Therefore the overall effect of trade on welfare for workers is ambiguous

I In particular, it depends on preferences for good 1 versus good 2

ECO 364 - International Trade Fall 2018 Specific Factors Model 60

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

The pattern of trade Factor prices Welfare Summary

The rental rate r1 rises by more than the increase in p1

I The real rental rate in terms of good 1 increases:

r̂1

pW1 >

r1

pH1

I Recall that in sector 1: r1 = p1FK (K̄1, L1)

ECO 364 - International Trade Fall 2018 Specific Factors Model 61

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

The pattern of trade Factor prices Welfare Summary

The rental rate r1 rises by more than the increase in p1

I The real rental rate in terms of good 1 increases:

r̂1

pW1 >

r1

pH1

I Recall that in sector 1: r1 ↑

= p1 ↑

FK (K̄1, L1)

I Intuition:

I as p1 rises, MRPK in sector 1 rises

ECO 364 - International Trade Fall 2018 Specific Factors Model 62

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

The pattern of trade Factor prices Welfare Summary

The rental rate r1 rises by more than the increase in p1

I The real rental rate in terms of good 1 increases:

r̂1

pW1 >

r1

pH1

I Recall that in sector 1: r1 ↑↑

= p1 ↑

FK (K̄1, L1 ↑

)

I Intuition:

I as p1 rises, MRPK in sector 1 rises I and more workers enter sector 1, causing MRPK to rise further

ECO 364 - International Trade Fall 2018 Specific Factors Model 63

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

The pattern of trade Factor prices Welfare Summary

The rental rate r1 rises by more than the increase in p1

I The real rental rate in terms of good 2 increases:

r̂1

pW2 >

r1

pH2

I Intuition: MRPK in sector 1 is higher

I Therefore the effect of trade on welfare for owners of sector 1 capital is positive

ECO 364 - International Trade Fall 2018 Specific Factors Model 64

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

The pattern of trade Factor prices Welfare Summary

The rental rate r2 falls

I The real rental rate in terms of good 1 decreases:

r̂2

pW1 <

r2

pH1

I Recall that in sector 2: r2 = p2FK (K̄2, L2)

ECO 364 - International Trade Fall 2018 Specific Factors Model 65

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

The pattern of trade Factor prices Welfare Summary

The rental rate r2 falls

I The real rental rate in terms of good 1 decreases:

r̂2

pW1 <

r2

pH1

I Recall that in sector 2: r2 ↓

= p2FK (K̄2, L2 ↓

)

I Intuition:

I as p1 rises, workers leave sector 2, causing MRPK in sector 2 to fall I and good 1 has become more expensive

ECO 364 - International Trade Fall 2018 Specific Factors Model 66

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

The pattern of trade Factor prices Welfare Summary

The rental rate r2 falls

I The real rental rate in terms of good 2 decreases:

r̂2

pW2 <

r2

pH2

I Intuition: MRPK in sector 2 is lower

I Therefore the effect of trade on welfare for owners of sector 2 capital is negative

ECO 364 - International Trade Fall 2018 Specific Factors Model 67

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

The pattern of trade Factor prices Welfare Summary

Summary

I When Home opens to trade at prices pWr > p H r , we now know the following

I What will the pattern of trade be?

I Home exports good 1 (its comparative advantage good) I Home imports good 2

I How will trade affect factor prices?

I the wage w will rise I the rental rate r1 will rise I the rental rate r2 will fall

I How will trade affect welfare?

I aggregate welfare increases I effect on workers is ambiguous I effect on owners of sector 1 capital is positive I effect on owners of sector 2 capital is negative

ECO 364 - International Trade Fall 2018 Specific Factors Model 68

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

The pattern of trade Factor prices Welfare Summary

Summary

I Trade therefore has distributional consequences

I unlike the models we have studied before

I What is the solution?

I no trade? I or policies to redistribute the aggregate gains from trade?

ECO 364 - International Trade Fall 2018 Specific Factors Model 69

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Two-country Model

I As with previous trade models, we can introduce a second country Foreign

I Foreign might differ from Home in terms of:

I production technologies I factor endowments

I Both of these will lead to differences in comparative advantage

I Therefore if Home and Foreign are allowed to trade:

I trade will occur, as dictated by comparative advantage I both countries will gain from trade in the aggregate I effect on welfare for workers in both countries will be ambiguous I effect on welfare for some capital owners will be positive I effect on welfare for some capital owners will be negative

I Home and Foreign’s import demand and export supply will determine pWr

ECO 364 - International Trade Fall 2018 Specific Factors Model 70

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Two-country Model

I Trade patterns are determined by comparative advantage, as before

I Mechanisms by which trade affects income distributions are the same as before

I Hence we do not really learn anything new from the full two-country model!

ECO 364 - International Trade Fall 2018 Specific Factors Model 71

Overview Closed Economy Model

Small Open Economy Model Two-country Model

Summary

Summary

I Studied trade in economies with specific factors of production

I Same general results from the exchange economy and Ricardian models apply:

I countries export goods in which they have a comparative advantage I trade increases aggregate welfare

I However, with specific factors, trade creates both winners and losers

I highlights that the welfare effects of trade can be complicated I suggests the importance of redistributive policies

I Next lecture: the Heckscher-Ohlin model

I assumes that capital is also mobile across sectors I will allow us to see how differences in factor endowments can be a source

of comparative advantage

ECO 364 - International Trade Fall 2018 Specific Factors Model 72