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

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The Solow model

Y = F (K,L) Y = C +I ˙ K = I −D I = γY 0 < γ < 1 D = δK 0 < δ < 1 n = ˙ L/L

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Assumptions

F (zK,zL) = zF (K,L) F

′

K (K,L) > 0

F

′

L (K,L) > 0

F

′′

KK (K,L) < 0

F

′′

LL (K,L) < 0

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Intensive form

Start with production function Y = F (K,L) Y L = 1 LF (K,L) = F K L , L L

• = F

K L ,1

• Define y ≡ Y /L and k ≡ K/L. Then

y = F (k,1) = f (k)

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Capital accumulation

Let’s rewrite ˙ K to intensive form: ˙ k = ∂ (K/L) ∂t = ˙ KL−K ˙ L L2 = ˙ K L − K L ˙ L L = γY −δK L −kn = γf (k)−(δ +n)k.

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Steady state

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

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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.

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Cobb-Douglas case

We get f (k) = Akα. Hence γAkα = (n +δ)k kα−1 = n +δ γA kss = γA n +δ 1/(1−α) . Insert kss into the production function: yss = Akα = A1/(1−α)

• γ

n +δ α/(1−α)

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Extensions

Human capital.

◮ Production function

Y = AK α (hL)1−α ⇐ ⇒ y = Akαh1−α

◮ Capital accumulation equation as before ˙

k = γf (k)−(δ +n)k.

◮ Hence steady state is

γAkαh1−α = (δ +n)k k1−α = h1−α γA δ +n kSS = h γA δ +n 1/(1−α) .

Growth in productivity A.

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Development accounting

Production function (intensive form, with human capital) y = Akαh1−α If we know y, k and h, then we can back out productivity A: A = y kαh1−α If α is the same across countries, then we can decompose differences in output per capita into

1

Productivity differences

2

Differences in factors of production.

Appears that (1) is (slightly) more important than (2).

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Growth accounting

Production function (intensive form, with human capital) y = Akαh1−α Growth rates: ˆ y = ˆ A+α ˆ k +(1−α)ˆ h ⇐ ⇒ ˆ A = ˆ y −α ˆ k −(1−α)ˆ h Productivity growth = output growth - growth in inputs. Appears that ˆ A is more important than growth in inputs in explaining growth.

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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.

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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 Tt,j = Tt,i ×(1+g)G Tt,i Tt,j = (1+g)−G And relative productivity Ai Aj = (1+g)−G × Ei Ej Recall: Differences in A’s way too big to be explained by T − → differences in efficiency must be dominant souce of productivity differences.

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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

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The production possibility frontier

130 mill farmers in Nigeria and 390 mill in America, LN = 130, LA = 390.

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Autarky: RS/RD curve in Nigeria

PR/PC = 3 because otherwise only one good would be produced. A farmer can produce 1 ton of rice - his income is pR. A farmer can produce 3 tons of cocoa - his income is 3PC.

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Trade: RS/RD curves

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Gains from trade : Nigeria

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Specific Factors

Allows us to analyze the short-run impact of trade on different groups in the economy.

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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.

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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

LU ↑ − → Unskilled labor constraint shifts out − → QA up, QP down.

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Stolper Samuelseon

PP/PA ↑ − → Plastics curve shifts out − → real skilled wages ↑. Intuition: PP/PA ↑ generates profits in the Plastics industry − → Wages wSmust go up. But that generates negative profits in Apparel − → wU ↓ .

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Heckscher-Ohlin theorem

High rel. supply QA/QP in China (bc LU/LS high). Low rel. supply QA/QP in US (bc LU/LS low). Countries export the good that is intensive in the factor in which it is abundant.

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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.

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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).

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