Technology and trade I

Transcription

1 Technology and trade I Part A: Basics and autarky Robert Stehrer The Vienna Institute for International Economic Studies - wiiw March 20, 2017

2 The first industrial revolution Historical background : Assumptions Der italienische Abbe Lancelotti in einer Schrift, die 1636 zu Venedig erschien, erzählt: Anton Müller aus Danzig habe vor ungefähr 50 Jahren [L. schrieb 1629] eine sehr künstliche Maschine in Danzig gesehen, die 4-6 Gewebe auf einmal verfertigte; weil aber der Stadtrat besorgt habe, diese Erfindung möchte eine Masse Arbeiter zu Bettlern machen, so habe er die Erfindung unterdrückt und den Erfinder heimlich ersticken oder ersäufen lassen. (Karl Marx, Das Kapital, Band I).

3 David Ricardo, Historical background : Assumptions David Ricardo (1817), On the Principles of Political Economy and Taxation, London: John Murray; Chapter 7 On Foreign Trade Chapter 23 On Machinery 1 Ricardo argued that Portugal was technologically advanced in both sectors (cloth and wine production). Nonetheless he advised that Great Britain should have free trade with Portugal as both countries would be better off. 2 Further, free trade would limit the power of the landowners ( landlords ) and thus reduce land rents. This would provide resources for the industrial sector characterised by higher productivity growth, technical progress and innovation. 3 Adjustments in the value of money

4 : Assumptions Historical background : Assumptions 1 Two industries 2 Production technology is fixed 3 One factor of production (fixed labour endowment) h 1 Mobile across sectors 2 Immobile between countries 4 Presentation of model: 1 Autarkic equilibrium 2 Small country assumption 3 Two trading economies 4 Generalisations (more sectors, countries, etc.)

5 Endowments and Technology Production technology in sector i: 1 x i... (gross) output 2 ϕ i... (total factor) productivity 3 l i... labour input. 4 Properties: x i = ϕ i l i 1 Labour productivity ( output per unit of input ) ϕ i = x i l i 2 The marginal product of labour ( additional output per unit of additional input ) MPL i = dxi = ϕ i dl i is constant and equal to labour productivity 3 Constant returns to scale as λx i = λ(ϕ il i) = ϕ(λl i)

6 Labour demand equation: l i = 1 x i = a li x i ϕ i where a li is labour input per unit of (gross) output. Endowment: 1 Fixed and given by h (in number of persons employed, hours worked,...) 2 Workers are assumed to be fully mobile across sectors. 3 Assume full employment Full employment (FE) condition (Resource constraint): h = a l1 x 1 + a l2 x 2 = l 1 + l 2

7 Reformulating the full employment condition expresses output in sector 2 as a function of output in sector 1: x 2 = 1 a l2 h a l1 a l2 x 1 = 1 a l2 h 1/a l2 1/a l1 x 1 = ϕ 2 h ϕ 2 ϕ 1 x 1 which is referred to as production possibility frontier (PPF) or transformation curve. The slope of the PPF is given by x 2 x 1 = dx 2 dx 1 = a l1 a l2 = ϕ 2 ϕ 1 and referred to as marginal rate of transformation (MRT)

8 Numerical example Let labour endowment be h = 100 and labour productivity given by ϕ 1 = 0.25 and ϕ 2 = 0.5. Labour input coefficients are therefore a l1 = 4 and a l2 = 2. The resource constraint is given by 100 = 4x 1 + 2x 2 and the PPF is The slope of the PPF is given by x 2 = x1 dx 2 = 2 dx 1 Production of one unit more of good 1 requires 4 units of labour. Therefore, production in sector 2 has to be reduced by 2 units, freeing 4 units of labour.

9 Production possibility frontier x 2 ϕ 2h = 50 Interpretation of slope: 1 x 1 = 1 l 1 = 4 2 l 2 = 4 x 2 = 2 3 Slope: x 2 x 1 = 2 1 = 4 2 = a l1 a l2 x 1 = 1 x 2 = 2 ϕ 1h = 25 x 1

10 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 larger the labour input coefficient in sector 1 as compared to 2 (or, analogously, the lower is productivity in sector 1 as compared to sector 2), the more labour has to be freed in sector 2 implying a larger reduction in output in this sector. Graphically, this is reflected in a steeper slope of the PPF. The MRT is interpreted as the opportunity costs of good 1 in terms of good 2

11 Nominal wage rate is given by w (expressed in local currency) 1 Note: This is the nominal wage rate 2 w is equalized across sectors due to the assumption of full mobility of workers across sectors Pre-multiplying the resource constraint by the wage rate gives wh = wa l1 x 1 + wa l2 x 2 1 y = wh is total factor income Corresponds to a country s GDP according to income definition of National Accounts 2 c i = wa li x i is total costs of production in industry i Unit costs (average costs) are AC i = wa li Marginal costs are MC i = wa li

12 As in a perfectly competitive economy p i = AVC i = MC i (zero-profit condition) the above equation can be written as y = p 1 x 1 + p 2 x 2 1 Total income equals total value of final goods production The rhs is GDP according to production definition of National Accounts 2 Ricardo argued with the labour cost theory of prices : p i = a li w Income earners (i.e. workers h receiving nominal wage w) spend income on goods i facing prices p i. Therefore above equation can be interpreted as budget constraint. Rewriting yields x 2 = 1 p 2 y p 1 p 2 x 1 = 1 wa l2 wh wa l1 wa l2 x 1 = 1 a l2 h a l1 a l2 x 1 = ϕ 2 h ϕ 2 ϕ 1 x 1 1 The level of nominal wages does not matter (as wages and prices are proportional) E.g. real income (in terms of good i is y/p i = wh/wa li = hϕ i) 2 Graphically, the resource and budget constraint are identical

13 Numerical example (contd.) Let the wage rate (expressed in local currency) be w = 2. Total income is then y = = 200 and prices are p 1 = 2 4 = 8 and p 2 = 2 2 = 4. The budget constraint is given by 200 = 8x 1 + 4x 2 or x 2 = x1 The slope of the budget line is given by dx 2 = 2 dx 1 Expenditures for one unit more of good 1 require 8 units of NCU. Therefore, expenditures for good of sector 2 has to be reduced by 2 units, providing 2 4 = 8 NCUs..

14 Budget constraint x 2 y/p 2 = 50 Interpretation of slope: 1 x 1 = 1 y = 8$ 2 y = 8$ x 2 = 2 3 Slope: x 2 x 1 = 2 1 = 8$ 4$ = p1 p 2 x 1 = 1 x 2 = 2 y/p 1 = 25 x 1

15 Interpretation of slope of budget constraint Affording x 1 more of output in industry 1 requires additional expenditure of y = p 1 x 1. Being at the budget constraint this additionally required income is only available when reducing expenditures on goods from sector 2, i.e. y = p 2 x 2. Therefore, p 1 x 1 = p 2 x 2 x2 = p1 = a l1 x 1 p 2 a l2 The larger the price (i.e. the labour input coefficient) in sector 1 as compared to 2, the more expenditures on sector 2 products has to be reduced. Graphically, this is reflected in a steeper slope of the budget constraint. The slope of the budget constraint is therefore interpreted as the opportunity costs of good 1 in terms of good 2

16 Demand of products i depends on income levels y and prices p i, i.e. x i = f(y, p 1, p 2 ) 1 All income is spent (i.e. no savings) 2 Derived from rational consumer behaviour assumptions (preferences, utility function) 1 should satisfy certain regularity conditions (ensuring uniqueness of decision) 2 Expressed as Social Welfare Function (SWF) or representative consumer (due to aggregation problems) 3 Yielding indifference curves bulging towards origin (as preferences are convex)

17 Consumer preferences are represented by SWF or utility function u = u(x 1, x 2 ) with u x i > 0, u xix i < 0 and u xix j > 0 1 Marginal utility (MU i ): Increase in consumption of good i increases u by MU i 2 Positive but decreasing marginal utilities Marginal rate of substitution of u(x 1, x 2 ) du = u x 1 dx 1 + u x 2 dx 2 = 0 u x 1 dx 1 = u x 2 dx 2 yields u x 1 MRS = dx 2 = = MU 1 dx u 1 MU x 2 2

18 Indifference curve: Representing goods combination (x 1, x 2 ) which gives same level of utility to consumer x 2 Interpretation of slope: 1 x 1 = 1 u MU 1 2 u MU 2 x 2 3 Slope: x 2 x 1 = MU1 MU 2 x 1 = 1 x 2 u x 1

19 Interpretation of slope of MRS The slope at a certain point of an indifference curve (i.e. the tangency line) expresses how much of good 2 one is willing to give up to get one unit more of good 1 and stay at the same level of utility. One unit more of good 1 provides additional utility of U MU 1 x 1. To stay at the same level of utility one has to give up consumption of good 2 by U MU 2 x 2. As U = U one gets MU 1 x 1 = MU 2 x 2 x2 dx2 = MU1 x 1 dx 1 MU 2 The larger the marginal utility of good 1 (i.e. the less is consumed) as compared to good 2, the more has to be given up from good 2 to satisfy this condition (also note that this means larger consumption of good 2 and therefore lower marginal utilities). Therefore the slope of the tangency on the indifference curve is larger the more of good 2 and the less of good 1 is actually consumed. The slope of the tangency is therefore interpreted as the opportunity costs of good 1 in terms of good 2

20 Maximisation of social welfare (or utility) function max u(x 1, x 2 ) under constraint y = p 1 x 1 + p 2 x 2 Lagrangian optimisation L = u(x 1, x 2 ) + λ(y p 1 x 1 p 2 x 2 ) Condition for optimality L x 1 = L x 2 = L λ u λp 1 = 0 x 1 u λp 2 = 0 x 2 = y p 1x 1 p 2x 2 = 0 u/ x 1 u/ x 2 = MU 1 MU 2 = p 1 p 2 Assumptions concerning second derivatives of u guarantee that this is a maximum (negative (semi-)definiteness of bordered Hessian considering leading principal minors) [see advanced Microeconomics or Optimisation]

21 Optimal (utility maximising) consumption bundle x 2 y/p 2 Optimum: Marginal rate of substitution (MRS) equals relative price MRS = MU 1 MU 2 = p 1 p 2 y/p 1 u > u u x 1

22 (Walrasian) General equilibrium Existence of set of prices such that 1 Labour supply equals labour demand (FE-condition) h = a l1 x 1 + a l2 x 2 2 Goods demand equals goods supply (for all industries i) x d i = ϕ il i = ϕ ia l1 x i = x i 3 Zero-profit condition (perfectly competitive markets) 4 Welfare maximisation p i = AC i

23 Graphical representation of general equilibrium x 2 ϕ 2 l = y/p 2 Production point = Consumption point x 2 dx 2 dx 1 = MRT = MRS = p1 p 2 x 1 ϕ 1 l = y/p 1 x 1

24 1 Cobb-Douglas demand system u = x α1 1 xα2 2 with α 1 + α 2 = 1; α i > 0 with (uncompensated) demand derived as x i = α i y p i Alternatively (affine transformation): u = ( x 1 ) α1 ( x2 α 1 2 Constant elasticity of substitution (CES) demand system with α 2 ) α2 u = ( α 1 ρ 1 x ρ 1 + α1 ρ 2 x ρ 2) 1/ρ with < ρ 1 and ρ 0 α i p 1 σ i x i = α 1 p 1 σ 1 + α 2 p 1 σ 2 }{{} Share spent on good i y p i with σ = 1/(1 ρ) 3 Proper price index should satisfy y = p H u y p H = u

25 Properties of Cobb-Douglas demand system 1 Income elasticity ε im = 1: If income increases by 1%, demand for product i increases by ε im = 1% (homothetic demand) 2 Own price elasticity: ε ii = 1 If price of product i increases by 1%, demand for product i decreases by 1% 3 Cross-price elasticity: ε ij = 0 If price of product j increases by 1%, demand for product i changes by 0% 4 Elasticity of substitution: σ = 1 5 Special case of CES with ρ 0 (or σ 1) 6 Proper price index (derived from Hicksian (compensated) demand): P = p α 1 1 pα 2 2 [Note: This is derived from u = (x 1/α 1) α 1 (x 2/α 2) α 2 ]

26 Properties of CES demand system 1 Income elasticity ε im = 1 If income increases by 1%, demand for product i increases by ε im = 1% (homothetic demand) 2 Own price elasticity: ε ii = < 1 if σ > 1 If price of product i increases by 1%, demand for product i decreases by ε ii % > 1 3 Cross-price elasticity: ε ij = > 0 if σ > 1 If price of product j increases by 1%, demand for product i increases by ε ij% > 0 4 Elasticity of substitution: σ = 1 1 ρ > 1 (curvature) 5 Special cases: 1 σ 0 ρ : Perfect complements (Leontief preferences) 2 σ 1 ρ 0: Cobb-Douglas case 3 σ > 1 0 < ρ < 1: Goods are substitutes 4 σ ρ 1: Perfect substitutes 6 Proper price index (derived from Hicksian (compensated) demand): [ ] P = α 1p 1 σ 1 + α 2p 1 σ 1 1 σ 2

27 Numerical example ( ) x1 0.5 ( ) x Let the SWF given by u = The budget constraint was given by 200 = 8x 1 + 4x 2. The demand system which can be derived yields ( 1 Utility level: u = x 1 = = 12.5 and x2 = = 25 ) 0.5 ( ) 0.5 = Price index: p H = (8 0.5 )(4 0.5 ) = Therefore: = Let the SWF given by u = (0.5 1 ρ x ρ ρ x ρ 2 ) ρ 1, with ρ = 0.5 and (therefore) σ = 2. The budget constraint was given by 200 = 8x 1 + 4x 2. The demand system which can be derived yields x 1 = = and x 2 = = Note: Demand in CES with σ > 1 reacts more sensitive to differences in relative prices 1 Utility level: u = (0.5 1 ρ ρ ρ ρ ) 1 ρ = Price index: p H = Therefore: = 37.5

28 Changes in income and prices 1 Change in income level: 1 Impacts proportionally on consumption of both goods (income elasticity is 1 for both functional forms) 2 Homothetic preferences 2 Change in price of good i has two effects: 1 Substitution effect: the good which is becoming (relatively) cheaper is consumed more, the other less 2 (Real) Income effect: impacts proportionally on both goods 3 Cobb-Douglas demand: 1 For good j substitution and income effect mutually cancels out: ε ij = 0 2 Share of income spent on both goods is constant α i 4 CES demand: 1 Substitution effect is stronger than income effect (for σ > 1): ε ji > 0 2 Share of income spent on goods changes α ip 1 σ i α 1p 1 σ 1 + α 2p 1 σ 2

29 What happens if supply of labour increases (decreases) 2... (labour) productivity grows in both sectors (balanced growth) 3... (labour) productivity grows in sector i

30 x 2 x 2 x 2 Population growth x 1 x 1 Balanced productivity growth Cobb-Douglas case CES case Sector biased productivity growth x 1

31 with Cobb-Douglas demand Benchmark Scenario 1 Scenario 2 Scenario 3 Labour h Productivity ϕ ϕ Wage rate w Prices p p Nominal income y = wh Demand/Output x x Price index P Utility u = y/p Real wage w/p Change in % Benchmark Scenario 1 Scenario 2 Scenario 3 Labour h 10.0 Productivity ϕ ϕ Wage rate w Prices p p Nominal income y = wh 10.0 Demand/Output x x Price index P Utility u = y/p Real wage w/p

32 with CES demand Benchmark Scenario 1 Scenario 2 Scenario 3 Labour h Productivity ϕ ϕ Wage rate w Prices p p Nominal income y = wh Demand/Output x x Price index P Utility u = y/p Real wage w/p Change in % Benchmark Scenario 1 Scenario 2 Scenario 3 Labour h 10.0 Productivity ϕ ϕ Wage rate w Prices p p Nominal income y = wh 10.0 Demand/Output x x Price index P Utility u = y/p Real wage w/p

33 Comparison of scenarios 1 1 and 2: 1 Welfare effect (real income effect) is equal for CD or CES demand 2 In both cases homothetic preferences 2 Scenario 3: 1 Welfare effect (real income effect) when assuming CES demand is larger 2 Stronger substitution effect towards relatively cheaper product is stronger implying larger real income effect 3 Scenario 1 versus 2 and 3: 1 Population growth (Scenario 1): 1 GDP/capita remains constant 2 GDP level is growing (full employment assumption) 2 Productivity growth ( 2 and 3): 1 GDP level is increasing 2 Real income per worker (w/p ) is increasing