# Lecture 3a: Specific-factor Model

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Lecture 3a:Specific-factor ModelThibault FALLYC181 – International TradeSpring 2018

CHAPTER 2: Ricardian model: Only one factor of production: labor Labor is mobile across sectors Everyone gains from tradeThe next model relaxes these assumptions: CHAPTER 3: But what if: We have more than one factor of production? What if these factors are NOT mobile across sectors? Then there may be losers and winners!(unequal effects of globalization)

CHAPTER 3: Road map: Setting up the specific factor model Change in production and employment Aggregate gains from trade Effect on labor wages Effect on returns to K and Land

1 Setup of Factor-Specific ModelSetup Two countries: Home and Foreign. Two sectors: Manufacturing and Agriculture Manufacturing uses labor and capital Agriculture uses labor and land.

1 Setup of Factor-Specific ModelSetup Two countries: Home and Foreign. Two sectors: Manufacturing and Agriculture Manufacturing uses labor and capital Agriculture uses labor and land. Diminishing returns for labor in each industry:The marginal product of labor declines if theamount of labor used in the industry increases.

1 Setup of Factor-Specific ModelAlternative interpretationNOTE:We can also use the same model and interpret “capital”and “land” as fixed labor:Capital: equivalent to Labor that is stuck in manufacturingLand: equivalent to Labor that is stuck in AgricultureLabor: Labor that is mobile across industries Three types of labor depending on its mobility(for the lecture, we’ll keep talking about capital and land as it’s easier to follow)

1 Setup of Factor-Specific ModelProduction function with Constant Returns to Scale: Manufacturing output: Y F ( K , L)such that: F ( K , L) F ( K , L)

1 Setup of Factor-Specific ModelProduction function with Constant Returns to Scale: Manufacturing output: Y F ( K , L)such that: F ( K , L) F ( K , L) This implies decreasing returns to scale if we focuson one input:F ( K , L) F ( K , L) F ( K , L ) F ( K , L ) In each industry: MPL 0 L

1 Setup of Factor-Specific ModelDiminishing returns for labor in each industry:(same for Agriculture: MPL decreases with production)

1 Setup of Factor-Specific ModelExample of production function: Manufactures:YM aM K 1/ 3 LM Agriculture: YA a AT1/ 3LA2/32/3

1 Setup of Factor-Specific ModelExample of production function: Manufactures:YM aM K 1/ 3 LM Agriculture: YA a AT1/ 3LA2/32/3 Marginal product of Labor: MPL in Manufactures: MPLM 21/ 3aM K LM 321/ 3 MPL in Agriculture: MPLA a A T LA 3

1 Setup of Factor-Specific ModelExample of production function: Manufactures:YM aM K 1/ 3 LM Agriculture: YA a AT1/ 3LA2/32/3 Marginal product of Labor:21/ 3 MPL aKL MPL in Manufactures:MMM3Increases with K LM2 MPL in Agriculture: MPLA a A T LA 1/ 33Increases with T LA

1 Setup of Factor-Specific ModelExample of production function: Manufactures:YM aM K 1/ 3 LM Agriculture: YA a AT1/ 3LA2/32/3 Marginal product of Capital and Land:1 MPK in Manufactures: MPK aM LM K 2 / 331 MPT in Agriculture: MPT a A LA T 2 / 33

1 Setup of Factor-Specific ModelExample of production function: Manufactures:YM aM K 1/ 3 LM Agriculture: YA a AT1/ 3LA2/32/3 Marginal product of Capital and Land:1 MPK in Manufactures: MPK aM LM K 2 / 33Decreases with K LM1 MPT in Agriculture: MPT a A LA T 2 / 33Decreases with T LA

A)Production Possibility Frontier:How does it look likeB)in this case?C)D)

A)Production Possibility Frontier:How does it look likeB)in this case?C)D)

Slope of PPF reflects the opportunity cost of manuf. output:If one worker moves from A to B(i.e. from Ag to Manufacturing):Change in QA - MPLAChange in QM MPLMPPF

Slope of PPF reflects the opportunity cost of manuf. output:If one worker moves from A to B(i.e. from Ag to Manufacturing):Why does the slope increase?PPF

Slope of PPF reflects the opportunity cost of manuf. output:If one worker moves from A to B:Why does the slope increase?MPLA increases and MPLM decreasesPPF

1 Setup of Factor-Specific ModelSlope of PPFWhy does the slope increase from point A to B? Slope equals MPLA/MPLM As LA decreases, MPLA increases As LM increases, MPLM decreases Hence the ratio increases!

1 Setup of Factor-Specific ModelLabor market and relative prices Labor is mobile across sectors Hence wages are equalized:W PM MPLMW PA MPL A And should be the same across sectors. Hence:PMPA MPL AMPLM Slope of the PPF

1 Setup of Factor-Specific ModelEquilibrium in Autarky:Autarky Equilibrium:tangency between PPF andindifference curve

1 Setup of Factor-Specific ModelEquilibrium in Autarky:Autarky Equilibrium:tangency between PPF andindifference curveIn contrast to Ricardian model,preferences affect equilibriumrelative price!

CHAPTER 3: Road map: Setting up the specific factor model Change in production and employment Aggregate gains from trade Effect on labor wages Effect on returns to K and Land

2 Effect of Trade on productionThe Foreign Country Let us assume that Home has a comparative advantagein manufacturing Equivalent to assuming that the Home no-trade relativeprice of manufacturing is lower than Foreign rel. price:(PM /PA) (P*M /P*A).New world price?

2 Effect of Trade on productionThe Foreign Country Let us assume that Home has a comparative advantagein manufacturing Equivalent to assuming that the Home no-trade relativeprice of manufacturing is lower than Foreign rel. price:(PM /PA) (P*M /P*A).New world price:(PM /PA) (PM /PA)W (P*M /P*A).Effect on production?

2 Effect of Trade on productionNew relative price

2 Effect of Trade on productionNew relative priceNew production mix

2 Effect of Trade on productionQuantitative example:In the next example with Cobb-Douglas production,I would like to show you: How to link ratio of MPL to employment How to link ratio of MPL to prices How to link employment to prices

2 Effect of Trade on productionQuantitative example: Manufactures:YM aM K 1/ 3 LM Agriculture: YA a AT1/ 3LA2/32/3Marginal product of Labor:21/ 3 MPL in Manufactures: MPLM aM K LM 32 MPL in Agriculture: MPLA a A T LA 1/ 33

2 Effect of Trade on productionQuantitative example: Manufactures:YM aM K 1/ 3 LM Agriculture: YA a AT1/ 3LA2/32/3Marginal product of Labor:21/ 3 MPL in Manufactures: MPLM aM K LM 32 MPL in Agriculture: MPLA a A T LA 1/ 331/ 3 Slope of PPF:MPL Aa ATSlope 1/ 3MPLM aM K LM LA1/ 3

2 Effect of Trade on productionQuantitative example:1/ 3MPL Aa AT Slope of PPF: Slope MPLM aM K 1 / 3Constant term x LM LA1/ 3 Employment ratio

2 Effect of Trade on productionQuantitative example: LMMPL Aa AT Slope of PPF: Slope 1/ 3 MPLM aM K LAPM At equilibrium: Slope PALA How does a change in prices affectsLM?1/ 31/ 3

2 Effect of Trade on productionQuantitative example: LMMPL Aa AT Slope of PPF: Slope 1/ 3 MPLM aM K LAPM At equilibrium: Slope PALA How does a change in prices affectsLM?1/ 31/ 3PMa AT PA aM K 1 / 3 LM LA1/ 3 LAa T PA LM a K PM 3A3M1/ 3 3

Clicker question:If the relative price of manufacturing goods increasesby 1%, relative employment in manufacturing LM LAincreases by:a) A negative percentage, i.e. decreases!!b) Increases by 1%c) Increases by 0.33%d) Increases by 3%

Answer:

Answer:If the relative price of manufacturing goods increasesby 1%, relative employment in manufacturing LM LAincreases by:d) Increases by 3%

Some useful algebra Quantifying changes with exponents, etc.: SupposeZ a X If X increases by 1% then Z increases by β %. If Z increases by 1% then X increases by 1/β %. SupposeZ X .Y If X increases by x % If Y increases by y % Then Z increases by: x y %.

CHAPTER 3: Road map: Setting up the specific factor model Change in production and employment Aggregate gains from trade Effect on labor wages Effect on returns to K and Land

3 Gains from TradeOverall Gains from Trade? We start by looking at the average consumer

3 Gains from TradeSupply side:New relative priceNew production mix

3 Gains from TradeDemand side:New equilibrium consumptionNew budget line

Clicker Q:Trade for theHome country is ?503015025 30a) XM 5, MA 20;40b) XM 20, MA 20;c) XM 15, MA 35; d) XM 20, MA 15;

3 Gains from TradeOverall Gains from TradeSo far, things are not very different from Ricardo:New world price:(PM /PA) (PM /PA)W (P*M /P*A). Manufacturing goods are exported, Agricultural goods are imported For an average consumer, Home is better off with trade.

3 Gains from TradeGains for everyone? When there are gains from trade on average, it does notimply that everyone gains from trade The interesting part of the model is to examine whathappens to the return to each factor:1) Labor wage2) Rental rate of Capital and LandDo workers gain? Do land and capital owner gain?

CHAPTER 3 – Next lecture (part 2): Setting up the specific factor model Change in production and employment Aggregate gains from trade Effect on labor wages? Effect on returns to Capital and Land?

Alternative interpretation NOTE: We can also use the same model and interpret "capital" and "land" as fixed labor: Capital: equivalent to Labor that is stuck in manufacturing Land: equivalent to Labor that is stuck in Agriculture Labor: Labor that is mobile across industries Three types of labor depending on its mobility

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