27.04.2023 Labor Productivity#

why does Trade exist?

Ricardian Model#

Comparative Advantages in Productivity of Labor

Opportunity Cost: Cost of next best Alternative

Comparative Advantage: Country with lower Opportunity Costs of Product

Example:

  • US: same resources can produce 10mil Roses and 100k computers

  • Colombia: same resources \(\to\) 10mil Roses and 30k computers

Colombia = lower opportunity cost of computers => comp. Advantage in Roses

without Trade

Roses

Computers

US

5mil Roses

15k Computers

Colombia

5 mil Roses

50k Computers

with Trade

US

10 mil Roses

0

Colombia

0

100 k Computers

=> 35k Computers more

One Factor Economy#

Assumptions#

  • labor = only factor of Production

  • labor prod. varies across countries

  • supply of labor = constant in country

  • two goods: wine and cheese

  • competition means wages = productivity

  • two countries: home and foreign

Model Definition#

  • \(a_L\): unit labor requirement = labor needed for one product

    • \(a_{LC}\) = hours needed for cheese in home country

    • \(a_{LW}\) = same for wine

  • L: labor supply in home country

  • total Production: \(Q\)

    • \(Q_C\) = total pounds of cheese produced (home)

    • \(Q_W\) = same for wine

Production Possibilities#

= maximum amount of goods given resources (L) $\( a_{LC} \ Q_C+ a_{LW} \ Q_w \le L \)$

  • Maximum home Cheese: \(Q_C = \frac{L}{a_{LC}}\) with \(Q_W = 0\)

  • Maximum home Wine: \(Q_w = \frac{L}{a_{LW}}\)

img

opportunity cost: \(\frac{a_{LC}}{a_{LW}} = const.\)

Opportunity Cost of Cheese to Wine: \(Q_C = \frac{L}{a_{LC}}- \frac{a_{LW} Q_W}{a_{LC}}\)

Wages#

  • P = Prices: \(P_C, P_W\)

Competition: Wages = Price and Productivity

  • Wage of Cheese Makers: \(w_C = \frac{P_C}{a_{LC}}\)

  • Wage if Wine makers; \(w_w = \frac{P_W}{a_{WC}}\)

Workers choose industry with higher wage

  • if cheese price exceeds the Opportunity cost

    • \(\frac{P_C}{P_W} > \frac{a_{LC}}{a_{LW}}\)

    • then wage in cheese higher

    • then everybody into cheese industry

    • = specialization

  • if prices equal opportunity cost:

    • wages same everywhere

Trade#

  • „*“ = foreign country

  • absolute advantage: \(a_{LC} < a^*_{LC}\)

  • comparative advantage: \(\frac{a_{LC}}{a_{WC}} < \frac{a_{LC}^*}{a_{WC}^*}\)

    • cheese comp. advantage of home

    • more cheese in home: would reduce less wine production than foreign

PPF foreign

PPF home

img

img

in the absence of trade:

  • relative price of cheese to wine = higher in Foreign

  • profitable to ship cheese from Home to Foreign

Equilibrium#

Relative Supply of Cheese $\( RS = \frac{Q_C + Q_C^*}{Q_W+ Q_W^*} \)$

Sitations

relative price of cheese equals o.c $\( \frac{P_C}{P_W} = \frac{a_{LC}}{a_{WC}} < \frac{a_{LC}^*}{a_{LW}^*} \)$

  • workers home, indifferent

  • workers foreing only wine

\[ \frac{a_{LC}}{a_{WC}} < \frac{P_C}{P_W} < \frac{a_{LC}^*}{a_{LW}^*} \]

  • Home workers = only cheese

  • foreign workers = only wine

\[ \frac{a_{LC}}{a_{WC}} < \frac{a_{LC}^*}{a_{LW}^*} < \frac{P_C}{P_W} \]

  • no wine produced

  • only cheese

Result

img

Exercise II#

Foreign Trade Theory:

Free Trade

Protectionism

Dismantling of Trade Barriers

Governmental Influence to promote industries

Harmony

efficient allocation

Types of Protectionism:

  • Import restrictions

    • tariffs

    • trade barriers: quotas, bans, complications

  • Export Promotions

    • subsidies / dumping

Gravitational Model#

How much do people trade with each other?

\[ T_ij = \frac{A \times Y_i \times Y_j}{D_{ij}} \]

  • A = constant term

  • D = Distance

  • Y = GDP of respective country

Implications:

  • big economies trade more

  • A can change!