Specific factor endowments and trade I

Transcription

1 Specific factor endowments and trade I Part A: Basics and autarky Robert Stehrer The Vienna Institute for International Economic Studies - wiiw May 28, 2018

2 1 Ricardo model assumed only one factor of production (labour) 2 Other factors: land, capital, etc. 3 Allows discussion if gains from trade are unevenly distributed, or if even their are loosers 4 2 and more factor models: 1 Specific factors model (Ricardo-Viner model) 2 Heckscher-Ohlin model (discussed later)

3 1 Mobile factor (labour) l can move across sectors 2 Immobile factors: k i with i = 1, 2 is fixed for each sector 3 Full employment assumptions for all factors 1 For mobile factor it has to hold that l = l 1 + l 2 4 Labour mobility equilibrates wages across sectors, i.e. w 1 = w 2 = w 5 Requires derivation of labour demand equations

4 1 Production characterised by standard production function with x i = f i (k i, l i ) 1 Constant returns to scale: λf i(k i, l i) = f i(λk i, λl i) 2 Marginal products are positive and decreasing f i k i > 0 and f i l i > 0 2 f i k i k i < 0 2 f i l i k i > 0 and and f i l i l i < 0 2 f i k i l i > 0

5 Production function and marginal productivity 1 More inputs produce more output 2 The more of a factor is already employed, the less an additional unit contributes to output x i x i = f(k i, li) x i = f(k i, l i) 0 l i

6 Example: Cobb-Douglas Production technology in sector i (assuming Cobb-Douglas technology): 1 Total factor productivity: ϕ i 2 Constant returns to scale 3 Marginal productivity of labour x i = ϕ i k γi i l1 γi i MPL i = ϕ i (1 γ i )k γi i l γi i = ϕ i (1 γ i ) 1 Increasing in TFP and capital 2 Decreasing in labour 4 Marginal productivity of capital ( MPK i = ϕ i γ i k γi 1 ki i l 1 γi i = ϕ i γ i 1 Increasing in TFP and labour 2 Decreasing in capital l i ( ki l i ) γi 1 ) γi = ϕ i (1 γ i )κ γi = ϕ i γ i κ γi 1 i

7 Example: CES Production technology in sector i: x i = ϕ i ( γki k φ i + γ lil φ i ) 1 φ with γ ki + γ li = 1 1 Total factor productivity: ϕ i 2 Constant returns to scale 3 Marginal productivity of labour MPL i = 1 φ ϕ i( γki k φ i + γ lil φ i 1 Increasing in TFP and capital 2 Decreasing in labour ) 1 φ 1 φγ li l φ 1 γ li l φ 1 i i = x i ( γki k φ i + γ lil φ i )

8 Transformation curve (PPF) x 2 = f(k 2, l 2) x 2 l 2 x 1 l 1 x 1 = f(k 1, l 1)

9 Transformation curve (PPF) x 2 = f(k 2, l 2) x 2 l 2 x 1 l 1 x 1 = f(k 1, l 1)

10 Transformation curve (PPF) x 2 = f(k 2, l 2) x 2 l 2 x 1 l 1 x 1 = f(k 1, l 1)

11 Marginal rate of transformation x 2 MRT = x 2 x 1 MRT = x 2 x 1 x 1

12 Interpretation of MRT Production of x 1 more output in industry 1 requires additional labour input in this industry of l 1 a l1 x 1. Being at the PPF this additionally required labour in sector 1 is only available when reducing production and therefore labour demand in sector 2, i.e. l 2 a l2 x 2. As l 1 = l 2 one gets a l1 x 1 = a l2 x 2 x2 a l1 x 1 a l2 The more of x 1 is already produced, the more labourers are needed to produce an additional unit of good 1 (due to the declining marginal productivity of labour). Therefore, the more of good 2 has to be foregone, to provide the additional workers for producing the additional unit of good 1. Thus, the MRT is increasing (in absolute terms) the larger is x 1 (the slope becomes steeper). The MRT is interpreted as the opportunity costs of good 1 in terms of good 2

13 1 Represented by SWF or representative consumers 1 Standard properties (e.g. homogenous,... ) 2 Functional forms: e.g. Cobb-Douglas, CES,...

14 Equilibrium Equilibrium relative price determined by technology, endowment and demand conditions x 2 MRT = MRS = p 1 p 2 p 1 p 2 x 1

15 Firm behaviour 1 Full employment assumption 2 Prices p i given 1 Relative price p 1/p 2 is determined by MRT=MRS 2 Set p 2 = 1 as numeraire 3 Then level of p 1 is determined as well 3 Profit-maximisation MPL i = w p i p i MPL i = w 4 Labour mobility p 1 MPL 1 = p 2 MPL 2 p 1 p 2 = MPL 2 MPL 1

16 Equilibrium at given prices p i p 1 MPL 1 p 2 MPL 2 w 0 l 1 l

17 1 Determines w and l i with l 1 + l 2 = l 2 With FE assumption (of fixed factors) also MPK i is determined 3 Determines factor income of fixed factors 4 Total income: MPK i = r i p i p i MPK i = r i y = wl + r 1 k 1 + r 2 k 2 = p 1 x 1 + p 2 x 2

18 Autarkic equilibrium in specific factors model 1 : Mobile factor l i = 200; Fixed factors k i = : Cobb-Douglas demand with α i = Production function: Cobb-Douglas with γ i = 0.5 and ϕ i = 1 4 Numeraire: p 2 = 1 Sector 1 Sector 2 Economy Prices p i 1 1 Factor prices / income w i r i Factor demand l i k i Consumption/Production x i Total income (nominal) GDP 200 Price index P 1 Total income (real) GDP/P 200 Factor income (real) w i r i Utility level U 100

19 Increase in fixed factor Increase in k 1 x 2 = f(k 2, l 2) x 2 l 2 x 1 l 1 x 1 = f(k 1 x 1 = f(k 1, l, l1) 1)

20 Equilibrium Increase in fixed factor x 2 MRT = MRS = p 1 p 2 p 1 p 2 p 1 p 2 x 1 Good 1 becomes relatively cheaper, i.e. p 1 /p 2 decreases (Note: p 2 is numeraire)

21 Labour market implications Increase in fixed factor p 1 MPL 1 = w p 2 MPL 2 = w w w 0 l

22 Increase in fixed factor Autarkic equilibrium in specific factors model 1 : Mobile factor l i = 200; Fixed factors k 1 = 110 and k 2 = : Cobb-Douglas demand with α i = Production function: Cobb-Douglas with γ i = 0.5 and ϕ i = 1 4 Numeraire: p 2 = 1 Sector 1 Sector 2 Economy Prices p i Factor prices / income w i r i Factor demand l i k i Consumption/Production x i Total income (nominal) GDP 200 Price index P 0.98 Total income (real) GDP/P Factor income (real) w i r i Utility level U

23 Increase in fixed factor Increase in fixed factor of industry 1 1 Price of this industry declines (relatively) 2 Demand (and supply) for this industry increases 3 Labour shifts to industry 1 4 Nominal and real wage (of workers) increases 5 Capital intensity in industry 1 increases 1 MPK 1 decreases; real return to capital decreases (r 1 decreases stronger than p 1) 6 Capital intensity in industry 2 increases 1 MPK 2 decreases; real return to capital decreases (r 2 decreases) 2 NOTE: in previous slide factor return divided by the price index was shown!