ECON2915 Economic Growth Lecture 13 : Summing up Andreas Moxnes - PowerPoint PPT Presentation

ECON2915 Economic Growth Lecture 13 : Summing up Andreas Moxnes University of Oslo Fall 2016 1 / 27

The Solow model Y = F ( K , L ) Y = C + I ˙ K = I − D I = γ Y 0 < γ < 1 D = δ K 0 < δ < 1 n = ˙ L / L 2 / 27

Assumptions F ( zK , zL ) = zF ( K , L ) ′ ′ K ( K , L ) > 0 L ( K , L ) > 0 F F ′′ ′′ F KK ( K , L ) < 0 F LL ( K , L ) < 0 3 / 27

Intensive form Start with production function Y = F ( K , L ) L = 1 � K � � K � Y L , L LF ( K , L ) = F = F L , 1 L Define y ≡ Y / L and k ≡ K / L . Then y = F ( k , 1 ) = f ( k ) 4 / 27

Capital accumulation Let’s rewrite ˙ K to intensive form: KL − K ˙ ˙ k = ∂ ( K / L ) L ˙ = L 2 ∂ t ˙ ˙ K L − K L = L L = γ Y − δ K − kn L = γ f ( k ) − ( δ + n ) k . 5 / 27

Steady state Steady state defined by ˙ k = 0: γ f ( k ) − ( δ + n ) k = 0 γ f ( k ) = ( δ + n ) k . Investment per worker (LHS) = depreciation + dilution of capital per worker (RHS). 6 / 27

Steady state Higher n − → Steeper slope of ( n + δ ) k − → SS k ↓ and y ↓ . Intuition: Less capital/worker − → lower productivity. Note: We have growth in Y but not y . 7 / 27

Cobb-Douglas case We get f ( k ) = Ak α . Hence γ Ak α = ( n + δ ) k k α − 1 = n + δ γ A � γ A � 1 / ( 1 − α ) k ss = . n + δ Insert k ss into the production function: � α / ( 1 − α ) � γ y ss = Ak α = A 1 / ( 1 − α ) n + δ 8 / 27

Extensions Human capital. ◮ Production function Y = AK α ( hL ) 1 − α ⇐ ⇒ y = Ak α h 1 − α ◮ Capital accumulation equation as before ˙ k = γ f ( k ) − ( δ + n ) k . ◮ Hence steady state is γ Ak α h 1 − α = ( δ + n ) k k 1 − α = h 1 − α γ A δ + n � γ A � 1 / ( 1 − α ) k SS = h . δ + n Growth in productivity A . 9 / 27

Development accounting Production function (intensive form, with human capital) y = Ak α h 1 − α If we know y , k and h , then we can back out productivity A : y A = k α h 1 − α If α is the same across countries, then we can decompose differences in output per capita into Productivity differences 1 Differences in factors of production. 2 Appears that (1) is (slightly) more important than (2). 10 / 27

Growth accounting Production function (intensive form, with human capital) y = Ak α h 1 − α Growth rates: y = ˆ A + α ˆ k +( 1 − α )ˆ ˆ h ⇐ ⇒ ˆ y − α ˆ k − ( 1 − α )ˆ A = ˆ h Productivity growth = output growth - growth in inputs. Appears that ˆ A is more important than growth in inputs in explaining growth. 11 / 27

What is A? Technology ◮ Knowledge about the use of inputs into production. ◮ Affected by patents, R&D, cross-country spillovers, incentives to innovate. Efficiency ◮ How effective we are at utilizing the inputs. ◮ Affected by incentives, trade, competition, institutions, management, misallocation (across firms and/or industries), culture, etc. 12 / 27

Decomposing efficiency and technology Assume productivity is A = T × E , where T is technology and E is efficiency. Technology growth rate g and i G years behind. Then T t , j = T t , i × ( 1 + g ) G T t , i = ( 1 + g ) − G T t , j And relative productivity A i = ( 1 + g ) − G × E i A j E j Recall: Differences in A ’s way too big to be explained by T − → differences in efficiency must be dominant souce of productivity differences. 13 / 27

Comparative advantage Simplest version: Constant relative productivity differences : The Ricardian model. Output per farmer (ton): Rice Cocoa America 2/3 2/3 Nigeria 1 3 14 / 27

The production possibility frontier 130 mill farmers in Nigeria and 390 mill in America, L N = 130, L A = 390. 15 / 27

Autarky: RS/RD curve in Nigeria P R / P C = 3 because otherwise only one good would be produced. A farmer can produce 1 ton of rice - his income is p R . A farmer can produce 3 tons of cocoa - his income is 3 P C . 16 / 27

Trade: RS/RD curves 17 / 27

Gains from trade : Nigeria 18 / 27

Specific Factors Allows us to analyze the short-run impact of trade on different groups in the economy. 19 / 27

Winners and losers Factors specific to the export sector are unambiguously hurt by the tariff. Factors specific to the import-competing sector unambiguously benefit from the tariff. Mobile factors (labor) could go either way. 20 / 27

The Heckscher-Ohlin model Allows us to analyze the long-run impacts. Thee main theorems: ◮ Rybczynski theorem. ◮ Stolper Samuelson theorem. ◮ Heckscher-Ohlin theorem. 21 / 27

Rybczynski theorem → Unskilled labor constraint shifts out − → Q A up, Q P down . L U ↑ − 22 / 27

Stolper Samuelseon P P / P A ↑ − → Plastics curve shifts out − → real skilled wages ↑ . Intuition: P P / P A ↑ generates profits in the Plastics industry − → Wages → w U ↓ . w S must go up. But that generates negative profits in Apparel − 23 / 27

Heckscher-Ohlin theorem High rel. supply Q A / Q P in China (bc L U / L S high). Low rel. supply Q A / Q P in US (bc L U / L S low). Countries export the good that is intensive in the factor in which it is abundant. 24 / 27

Infant industry protection In the presence of no externalities (but possibly learning by doing), IIP leads to welfare losses. In the presence of externalitities, IIP can be welfare improving. ◮ Credit market failures ◮ Agglomeration externalities. Empirical evidence currently weak in either direction. 25 / 27

Learning by doing A tariff on x will raise the domestic price on x − → industry x profitable. LBD can lead to expansion of x over time. But if workers/firms can anticipate LBD effects, they would choose x even in the absence of tariffs. ◮ Tariff cannot be welfare improving. 26 / 27

Agglomeration externalities Imagine industry x has AE and industry y has not. Market outcome may be too little x (because the market price of x is too low). Free trade may result in even less x production if the country is not very competitive. A tariff on x will raise the domestic price on x − → raise x output (closer to socially optimal level). 27 / 27