Chapter 2: Gains from Trade

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Chapter 2 Gains from Trade

• Keith Head
• Sauder School of Business

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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.

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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

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Shoe terms
Upper
Sole
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Assumptions

• 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

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Productivity Matrix
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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.

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Plan A (self-sufficient factories)

• Thailand US ? 10Lu 20(450-Lu)
• Lu 300, Ls 150, output 3000
• Korea US ? 15Lu 45(300-Lu)
• Lu 225 Ls 75, output 3375
• Combined output 6375 shoes
• 6375/750 8.5 shoes per worker

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Plan B Thailand specializes in uppers

• Thailand Lu 450 ? 4500 uppers
• Korea US ? 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

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Plan C Korea specializes in Uppers

• Korea Lu 300 ? 4500 uppers
• Thailand US ? 450010Lu20(450-Lu)
• Lu 150 ? 1500 U, Ls300 ? 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

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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!

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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

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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!

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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 4504500, 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)

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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.

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Calculate the critical wages

• If wages were equal, Koreas 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.

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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.

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Unit Labour Costs (in baht/unit)
WK wages in Korea (won/worker) WT wages in
Thailand (baht/worker)
e exchange rate (baht/won)
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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

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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?

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Exchange rate zones

• Recall the green zone for the relative wage
• 1.5
• Now set Wk/Wt 100/200 1/2,
• 1.5
• To simplify, just multiply everywhere by 2, we
  get
• 3
• If productivity in Thailand doubles, then we need
  to divide 1.5 and 2.25 by two, so the new range
  is
• .75
• Substitute in Wk/Wt 100/200 1/2 as before and
  multiply by 2 across the board, to get
• 1.5
• Baht/Won must declinewon depreciates, baht
  appreciates

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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
  industriesonly the ones where their productivity
  gap is less than the wage gap.

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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.

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New Productivity Matrix
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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.

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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 3030 60, leaving 300-60240 workers
  for production.
• A factory that specializes has 300-30270 workers
  for production.

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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 120012002400 shoes

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Revisiting Plan B

• Plan B (full specialization, K?S,T?U)
• Sole output in Korea 27010 2700
• Upper output in Thailand 27010 2700
• Combined output 2700 shoes (11 gain!)

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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)

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PLEoS vs CA (contd)

• 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 doesnt help
  unless you change the mix of activities done in
  each.
• Under CA, observe larger plant to be less
  productive.

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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?