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Chapter 2: Gains from Trade. Keith Head Sauder School of Business. Objectives of this chapter. Illustrate the gains from trade based on exploiting comparative advantage Show how productivity, wages, competitive advantage, and exchange rates relate to each other.

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Chapter 2: Gains from Trade

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chapter 2 gains from trade

Chapter 2: Gains from Trade

Keith Head

Sauder School of Business

objectives of this chapter
Objectives of this chapter
  • Illustrate the gains from trade based on exploiting comparative advantage
  • Show how productivity, wages, competitive advantage, and exchange rates relate to each other.
  • Illustrate the gains from trade based on exploiting plant-level scale economies.
your assignment
Your assignment:
  • Decide the number of workers in each of two factories (Korea & Thailand) to allocate to each of two activities (molding soles & stitching uppers).
  • Maximize corporate shoe output
shoe terms
Shoe terms



  • 450 workers in Thai factory
  • 300 workers in Korean factory
  • In the short run, you cannot add or subtract workers, or move them between plants.
  • One sole and one upper needed for each finished shoe.
  • Transport costs are negligible
compute total shoe output for
Compute total shoe output for
  • Plan A: (self-sufficient factories): Each country combines workers to produce completed shoes. There is no trade.
  • Plan B:
    • Thailand produces only uppers,
    • Korea produces soles and uppers.
  • Plan C:
    • Korea produces only uppers,
    • Thailand produces soles and uppers.
plan a self sufficient factories
Plan A (self-sufficient factories):
  • Thailand: U=S  10Lu = 20(450-Lu)

Lu= 300, Ls = 150, output = 3000

  • Korea: U=S  15Lu = 45(300-Lu)

Lu= 225 Ls = 75, output = 3375

  • Combined output = 6375 shoes

6375/750 = 8.5 shoes per worker

plan b thailand specializes in uppers
Plan B: Thailand specializes in uppers
  • Thailand: Lu =450  4500 uppers
  • Korea: U=S  4500 +15Lu =45(300-Lu)

Lu = 150  2250 U, Ls =150 6750S

  • Combined output: 6750 shoes
    • 4500 shoes stitched in Thailand using soles imported from Korea
    • PLUS 2250 finished shoes made in Korea

Productivity: 9 shoes per worker

plan c korea specializes in uppers
Plan C: Korea specializes in Uppers
  • Korea: Lu = 300  4500 uppers
  • Thailand: U=S  4500+10Lu=20(450-Lu)

Lu = 150  1500 U, Ls=300  6000 S

  • Combined output: 6000 shoes
    • 4500 shoes stitched in Korea using soles imported from Thailand
    • PLUS 1500 finished shoes made in Thailand

Productivity: 6000/750 = 8 shoes/worker

plan b increases shoe output by 6
Plan B increases shoe output by 6%
  • Firm-level productivity rises 8.5 to 9 shoes per day
  • Output growth:

(6750-6375)/6375 = .06

  • No new machinery, no new skills, no extra effort.
  • Trade is like a new technology!
specialization is not enough
Specialization is not enough
  • Plan C, involves specialization but it lowers output by 6% relative to Plan A.
  • Specialization based on comparative advantage yields gains from trade.
  • Comparative advantage = low opportunity costs.
  • CA gains = matching process
opportunity cost calculations
Opportunity cost calculations
  • Opportunity cost of uppers in foregone soles
    • Thailand: 20 S/ 10 U = 2 S/U
    • Korea: 45S/15U = 3 S/U
  • Opportunity cost of soles in foregone uppers
    • Thailand: 10 U/ 20 S = 0.5 U/S
    • Korea: 15U/45S = 0.33 U/S
  • Korea has lower opportunity cost of seouls!
beyond guess check general method
Beyond “Guess &Check”: general method
  • Determine comparative advantage via opportunity cost calculation (T->U, K->S)
  • Check if complete specialization is possible: compare [prody in CA task] X [factory size] for each factory
    • T: 10 X 450=4500, K: 45 X 300 = 13500
    • So, Thai factory is “too small” (it needs 1350 or more)
  • If no, then the “too small” factory fully specializes in its CA task but the “too big” factory will partially specialize
    • Supply from too small + non-CA supply from too big = CA supply from too big
    • 10 X 450 + 15 X L = 45 (300-L)
long run decisions
Long run decisions
  • The level of employment is only fixed in each plant in the short run.
  • When employment is a decision variable, not a sunk cost, then wages and productivity matter.
calculate the critical wages
Calculate the critical wages

If wages were equal, Korea’s factory would be the low cost source for both uppers and soles. (Why? AA)

  • How low would Thai wages have to be justify operating the plant? (doing what?)
  • How low would the wage in Thailand have to be to justify shutting the Korean plant?

Draw the Korean relative wage line.

competitive advantage
Competitive advantage
  • A factory has a competitive advantage in a task when it can provide an equivalent product at a lower monetary cost than alternatives.
  • Competitive advantage here corresponds to lower unit labour costs.
  • Unit labour costs are given by wages divided by productivity.
unit labour costs in baht unit
Unit Labour Costs (in baht/unit)

WK = wages in Korea (won/worker)

WT= wages in Thailand (baht/worker)

e = exchange rate (baht/won)

thai plant gains competitive advantage
Thai plant gains competitive advantage
  • in uppers when Korea pays 50% more than the Thai wage
    • e WK/15 > WT/10
    • eWK/WT > 1.5
  • in soles when Korea pays 2.25 times the Thai wage
    • e WK/45 > WT/20
    • eWK/WT > 2.25
competitive advantage equilibrium exchange rates
Competitive Advantage & Equilibrium Exchange Rates
  • Suppose that unions or government fix the local currency values of wages at WK = 100 Won/day and WT = 200 Baht/day.
  • What values of e (in Baht/Won) would be consistent with equilibrium (green zone)?
  • How would the e range change if Thai productivity doubled in all activities?
exchange rate zones
Exchange rate zones
  • Recall the green zone for the relative wage:

1.5 <eWk/Wt <2.25

  • Now set Wk/Wt =100/200 =1/2,

1.5 <e (1/2) <2.25

  • To simplify, just multiply everywhere by 2, we get


  • If productivity in Thailand doubles, then we need to divide 1.5 and 2.25 by two, so the new range is


  • Substitute in Wk/Wt= 100/200 =1/2 as before and multiply by 2 across the board, to get


  • Baht/Won must decline…won depreciates, baht appreciates
lessons from the shoe story
Lessons from the Shoe Story
  • Making sense of the 1997-8 Asian exchange rate crisis.
  • Average levels of productivity in the traded goods sector determine wages.
    • Low wage countries are also low-productivity
    • Rising productivity leads to appreciation
  • Low wage countries do not “steal” all industries—only the ones where their productivity gap is less than the wage gap.
shoe story ii returns to scale
Shoe Story II: Returns to Scale
  • Comparative advantage is not the only way to obtain gains from trade.
  • Plant-level economies of scale (PLEoS) are important in many industries.
  • To illustrate the gains from exploiting PLEoS through trade, we revise the story to exclude comparative advantage and absolute advantage.
indivisible overhead
Indivisible Overhead
  • Factory workers are supported by services of non-production employees, also known as “overhead”
    • Accounting
    • Logistics and input procurement
    • Machinery maintenance
  • Some minimum number of overhead workers are required for any positive level of production.
new example
New example
  • 300 workers at each factory
  • Let overhead be 30 workers per “product” (soles or uppers) per plant.
  • A factory that produces both products (that is, a factory that is not fully specialized) has overhead of 30+30= 60, leaving 300-60=240 workers for production.
  • A factory that specializes has 300-30=270 workers for production.
plan a vs plan b revisited
Plan A vs Plan B revisited
  • Plan A (self-sufficiency):
    • Sole output in each factory: (240/2)*10 = 1200
    • Upper output in each factory: (240/2)*10 = 1200
    • Combined output = 1200+1200=2400 shoes
revisiting plan b
Revisiting Plan B
  • Plan B (full specialization, KS,TU):
    • Sole output in Korea: 270*10 = 2700
    • Upper output in Thailand: 270*10 =2700
    • Combined output = 2700 shoes (11% gain!)
pleos gains are different from ca gains
PLEoS gains are different from CA gains

Plan C (full specialization KU and TS) is just as good (2700 shoes) as plan B

  • No such thing as specializing in the “wrong” thing in this case.
  • The key for PLEoS is to avoid duplicative overhead, rather than to “match” products with skills (as in the CA case)
pleos vs ca cont d
PLEoS vs CA (cont’d)
  • In the long run, only one plant stays open (whichever has lower ULC)
  • Under PLEoS, increases in total production increase productivity, whether or not factories are specialized.
  • Under CA, changing scale of plants doesn’t help unless you change the mix of activities done in each.
  • Under CA, observe larger plant to be less productive.
gains from trade summary
Gains from Trade Summary
  • When relative productivities of two tasks (uppers, soles) differ across locations, there are CA gains.
  • When there is indivisible overhead (or other PLEoS), concentrating activities in one location helps.
  • Next question: what is the ultimate source of opportunity costs diffs?