Chapter 2: Gains from Trade

Keith HeadSauder 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.

• Illustrate the gains from trade based on exploiting plant-level scale economies.

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

Sole

Upper

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

Productivity Matrix

Factory:

Activity:

Uppers Soles

Korea 15 45

Thailand 10 20

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):

• 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 shoes6375/750 = 8.5 shoes per worker

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

• 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%

• 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

• 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 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

• 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

• 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 wagesIf 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

• 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)

Factory

Activity:

Uppers Soles

Korea eWK/15 e WK/45

Thailand

WT/10 WT/20

WK = wages in Korea (won/worker)WT= wages in Thailand (baht/worker)

e = exchange rate (baht/won)

Thai plant gains competitive advantage

• in uppers when Korea pays 50% more than the Thai wagee WK/15 > WT/10

eWK/WT > 1.5

• in soles when Korea pays 2.25 times the Thai wagee WK/45 > WT/20

eWK/WT > 2.25

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• 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 3<e<4.5. • If productivity in Thailand doubles, then we need to

divide 1.5 and 2.25 by two, so the new range is .75<eWk/Wt<1.125.• Substitute in Wk/Wt= 100/200 =1/2 as before and

multiply by 2 across the board, to get 1.5<e<2.25 • Baht/Won must decline…won depreciates, baht

appreciates

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

• 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.

New Productivity Matrix

Factory:

Activity:

Uppers Soles

Korea 10 10

Thailand 10 10

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• 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 (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

• Plan B (full specialization, KS,TU):– 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

Plan C (full specialization KU and TS) 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)

• 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

• 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?