13–1 copyright 2005 mcgraw-hill australia pty ltd powerpoint® slides t/a principles of...

Copyright 2005 McGraw-Hill Australia Pty Ltd PowerPoint® Slides t/a Principles of Macroeconomics by Bernanke, Olekalns and Frank

13–1

Chapter 13Savings, Capital Formation and Comparative Economic Growth


13–2

Chapter 13: Savings, Capital Formation and Comparative Economic Growth

• Savings, investment and economic growth• The Solow–Swan model of economic growth• Recent developments in the study of economic

growth


13–3

Saving, Investment and Capital

• Saving frees resources for investment, both public and private

• Investment adds to the capital stock• A greater capital stock raises labour productivity

and GDP per capita

13–4

Investment and GDP per capita


13–5

The Solow–Swan Growth Model

• Also referred to as ‘Neo-classical Growth Model’• Gives primary role to saving and capital formation• Minor role to total factor productivity• ‘Growth’ refers to growth in output per worker,

which by implication extends to growth in GDP per capita


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The Production Function Again

• Y = Af (K, L)• Rewrite this function in ‘per worker’ terms by

dividing both sides by L• Y/L = y = Af (k) where k = K/L• GDP per worker rises with the stock of capital per

worker


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Diminishing Returns to k

• Diminishing returns to capital accumulation apply• The higher is the existing capital–labour ratio (k),

the smaller is the increase in GDP per worker (y) when there is an increase in k

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Capital–Labour Ratio and Output


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Are There Limits to Growth?

• Yes, because at some point the capital stock becomes so large that all of the economy’s saving is devoted to equipping new workers at the existing capital–labour ratio, and to replacing that part of the capital stock which wears out, rather than to increasing the stock of capital per worker


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Three Types of Investment

• Physical capital wears out through depreciation and needs to be replaced by ‘replacement investment’

• This form of investment needs to be distinguished from ‘new or net investment’ which refers to the investment over and above replacement which increases the size of the capital stock

• Gross Investment = Net Investment + Replacement Investment (Depreciation)

• Net Investment = Gross Investment – Depreciation


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‘Investment’ in Growth Models

• In growth models, the terminology is slightly different

• ‘Replacement investment’ also includes the amount of new investment which is required to equip new workers with the same capital as existing workers

• ‘New investment’ refers to investment which increases the capital–labour ratio, k

• ‘Gross investment’ is said to be zero when the capital–labour ratio is constant, even though the stock of capital has increased


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Two Claims on Saving

• Before there can be net investment – an increase in capital per worker – and further growth, saving must be sufficient to meet two claims on it– First, new workers have to be equipped with enough

capital that the capital–worker ratio does not fall– Second, a fraction of the capital stock which wears

out (depreciates) each year and must be replaced


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Requirements for Growth

• When these two claims are just met by saving, the stock of capital per worker, k, remains constant: net investment is said to be zero and output per worker, y, remains constant

• When saving exceeds these two claims, k can increase: net investment is is said to be positive and y rises


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First Requirement for Constant k

• Suppose the existing capital–labour ratio is k• To maintain a constant k in the face of growth in

the labour force, the capital stock must grow at the same rate as the labour force, say n.

• This requires an increase in the capital stock of nK• This is because, if Δ/K = n, Δ = nK, where Δ

means the change in the capital stock


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Second Requirement

• Let the fraction of the capital stock which wears out be d

• So the required replacement investment is dK


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Total Requirements

• In the face of an increase in the labour force and depreciation, the gross investment which is required to maintain a constant capital–labour ratio is (n + d)K– nK to equip the entrants to the labour force– dK to offset depreciation


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Saving Puts a Ceiling on k and y

• Saving S finances replacement and net investment• S = sY, where s is the average propensity to save• Growth continues whenever the capital–labour

ratio increases: when sY > (d + n)K• Growth ceases whenever the capital–labour ratio

remains constant: when sY = (d + n)K• At this point there is zero net investment, and the

capital–labour ratio and labour productivity are both constant

• The economy is in a ‘steady state’


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Meaning of the ‘Steady State’

• Capital per worker, k, is constant so that output per worker, y, is also constant

• Below the ‘steady state’ k is rising so that y is also rising

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The Path to the ‘Steady State’


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Going Backwards

• An economy could lie beyond its steady state if the rate of growth of the labour force had accelerated, so that saving was now inadequate to equip new workers with the same capital as existing workers

• The capital labour ratio and income per capita would fall back to the steady state

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Going Backwards


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Implications of the Steady State

• An end to growth in living standards• Convergence of living standards between rich and

poor countries – but only if they have the same production functions and the same rates of saving and long-run labour force growth

• Poor countries will grow faster than those richer countries which have reached their steady state


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When is there Convergence?

• We need to compare countries with similar labour force growth rates and with similar production functions and degrees of ‘open-ness’ to the rest of the world

• Convergence is ‘conditional’


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Evidence of Convergence

• For high-income countries, there is an inverse relationship between the level of income and the growth rate

• This means that, among these countries, the relatively poorer ones are ‘catching up’ to the richer ones

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The Rich Converge


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Convergence and Openness

• Open economies tend to converge• This is because their openness allows them to

influence each others’ economies

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Convergence and Openness

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The World Is Not Converging


13–29

Solow–Swan Model Just a Start

• Steady state not yet observed for rich countries• Growth accounting tells us that investment and a

rising capital–labour ratio are not the main ingredients in growth of living standards


13–30

Endogenous Growth Models

• Key role for raising total factor productivity (TFP)• Role of education and human capital in TFP• Role of research and development (R&D) in TFP• Role of patent protection in R&D• Protection of property rights in general• Role of political structure in protecting property

rights and punishing policy failures• All these factors are inter-related

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