University:
University of Edinburgh
Course:
ECNM10069 | Topics in Macroeconomics
Academic year:

2023
Views:

242

Pages:

42
Author:

disruptorn0m1

Macroeconomics Lecture 5 Recap: The natural levels of production and interest rate Y n = C (Y,Y e, r, A) + I ( r,Y e , K ) where Y n = F(K, E(1- un )L) Capital stock was taken as exogenous 2 Recap: The natural rate of interest for given K r ( S Y n ,Y e , r , A ) rn I  r, Y e , K  S,I 3 Introduction Presentation Outline: • Capital accumulation and growth • Wage determination and unemployment • Money and inflation in the long run 4 Growth (Chapter 5) Question: • What factors determine the capital stock, production and the real interest rate in the very long run? Analysis of two cases: • Constant population and technology • Constant population growth and technical development We also examine income differences between countries 5 Growth: Given population & technology Optimal capital stock: MPK -d = r 1+ m … but what determines the real interest rate? u'(Ct ) =1+ rt u'(Ct+1 ) / (1+ r ) In a closed economy, long-run equilibrium, without growth in population or technology, consumption must be constant, so we must have r = r 6 Growth: Given population & technology Thus we have, in long-run equilibrium without growth in population or technology: MPK -d = r 1+ m Þ K* We call long-run equilibrium ‘steady state’ (this term will be explained later) 7 Growth: Given population & technology 8 Growth: Given population & technology What happens if we start with KK* the opposite occurs 9 Growth: Given population & technology We can also illustrate the adjustment in the diagram with savings and investment. In the long-run equilibrium (steady state) : S(Y * ,Y * ,r, A) = I(r,Y * , K) where Y * = F(K * , EN n ) If we start out with a lower capital K’ then investments are higher and income and savings are lower for a given real interest rate, so the real interest has to be higher 10 Growth: Given population & technology 11 Growth: Given population & technology What happens if the consumer starts to care more about the future (lower  )? 12 Growth: Given population & technology What happens if the consumer starts to care more about the future (lower  )? 13 Growth: Given population & technology Convergence Using CRS we can express the model in terms of capital and income per effective worker • CRS means that F ( zK, zEN ) = zY for any z 1 EN • We can choose z= • Production function: æ K ö Y = Fç ,1÷ è EN ø EN 14 Growth: Given population & technology • Let Y K yº , kº EN EN and æ K ö æ K ö f (k) = f ç º F ,1÷ ÷ ç è EN ø è EN ø • Production function: y = f ( k ) • Production per effective worker depends only upon capital per effective worker, regardless of the size of the population. This is a consequence of CRS. • Marginal product of capital: MPK = FK ( k,1) = f ' ( k ) • Condition for long-run equilibrium: f '(k * ) -d = r 1+ m 15 Growth: Given population & technology K* = k * EN Y* = f ( k *) EN 16 Growth: Given population & technology For given population and technology: • The capital stock and production reach their long-run equilibrium levels over time • In long-run equilibrium we have no growth • If different countries have the same technology and same subjective discount rate, they will in the long run have the same real GDP per capita – convergence! 17 Growth: Population growth and technical development • With given population and technology there is growth only during the adjustment period if you start out from low capital stock. • To explain growth in the very long run we have to have population growth and technical development. Assume that the population is growing and technology is improving at constant rates: r DE =g E 18 Growth: Population growth and technical development Let us guess that real interest is constant on the long-term growth path: r = r . The optimal capital stock per effective worker is determined by the same condition as before: f '(k * ) -d = r 1+ m 19 Growth: Population growth and technical development But what factors determine the real interest rate? To see this we assume a logarithmic utility function: ( ) ( ) u Ct = ln Ct ( ) Þ u' Ct = 1/ Ct u'(Ct ) =1+ rt u'(Ct+1 ) / (1+ r ) r » r+g Ct+1 Þ 1+ rt = 1+ r = 1+ r 1+ g Ct ( ) ( )( ) Real interest is determined by the subjective discount rate ( r) and the pace of technological development (g). Consumers must be ‘bribed’ not to consume more today. 20 Growth: Population growth and technical development In steady state: K =k* EN Þ K = k * EN Y = f k* EN Þ Y = f k * EN Þ ( ) ( ) Þ DK DE DN = + = g +n K E N DY DE DN = + = g +n Y E N • K/EN and Y/EN are constant • K and Y grow at the rate g+n • K/N and Y/N grow at the rate g 21 Growth: ‘The golden rule’ • Does a larger capital stock always mean more consumption? • Which capital stock maximises consumption in steady state? 22 Growth: ‘The golden rule’ (golden rule capital stock) • Investments in steady state where I = DK + d K = DY DK = = n+ g : Y K DK K +dK = n + g K +dK = n + g +d K K ( ) ( ) • Consumption per effective worker: Y I = f k - n + g +d k EN EN () ( ) • To get the capital stock that maximises consumption, take the derivative with respect to k: () f ' k = n + g +d 23 Growth: ‘The golden rule’ (golden rule capital stock) f '(k ) = n + g + d Assume K=2Y and, for the sake of simplicity, m = 0 () a -1 f ' k = MPK = a K N 1-a K a N 1-a Y 1 1 =a = a » × » 0.17 K K 3 2 n  g    0  0.03  0.07  0.10 Marginal return on capital is higher than n + g + d Conclusion: the capital stock is lower than the consumption-maximising capital stock Increased saving would increase consumption in the long run. The problem is that we are impatient ... 24 Growth: The Solow model Central assumptions: • Constant savings rate (s) (no optimising) • Closed economy: Investments = savings: I = sF(K, EN ) 25 Growth: The Solow model • Change in capital stock: DK = sF(K, EN) - d K sF(K * ) = d K * steady-state sF(K) > d K Þ K grows sF(K) < d K Þ K falls 26 Why are some countries richer than others? GDP per capita in 2010 (PPP, 2005 constant prices, USD) • • • • • USA Sweden China India Zimbabwe 41 365 36 132 7 130 3 477 319 27 Why are some countries richer than others? 28 Why are some countries richer than others? Our theory: convergence • Two countries with the same E,a , m ,u n and d should converge to the same income per capita in the long run • If one of the countries is poorer, growth should be higher and over time the country should catch up with the richer country • Obviously, this is not happening – at least not very quickly. Income differentials are large and persistent 29 Why are some countries richer than others? Capital stocks What does ‘capital’ do in the model? • Contributes to the production of goods and services • Is produced and increases through savings/investments • Decreases through capital consumption Different kinds of capital are complements in production: • Private capital: machinery, buildings • Public capital: infrastructure such as roads, airports, telecommunication, schools, courts, admin, buildings • Human capital: education, experience Differences in policies, taxes, corruption can lead to different capital stocks per worker 30 Why are some countries richer than others? Can differences in physical capital explain income differences? a 1-a Y K E N = N N 1-a = K a E 1-a N -a = a K 1-a E a N a æ K ö 1-a =ç ÷ E èNø Compare two counties: YIndia / N India YUS / NUS 0.08 1.00 a æK / N India ö India = çç ÷÷ è KUS / NUS ø 1/3 æ 0.07 ö = ç ÷ è 1.8 ø 1-a æE ö India çç ÷÷ è EUS ø 2/3 2/3 æE ö æE ö India çç ÷÷ = 0.34 × çç India ÷÷ è EUS ø è EUS ø Differences in physical capital explain only part of the differences in income 31 Why are some countries richer than others? 32 Why are some countries richer than others? Can differences in human capital explain income differences? • Hard to measure • One measure is the average number of years the adult population went to school • To see how much it can explain we need to measure the effect on productivity of one more year of schooling • Empirical estimates: Between 10 and 30% of the differences in income can be explained by differences in human capital 33 Why are some countries richer than others? 34 Why are some countries richer than others? 35 Why are some countries richer than others? Conclusion: • At most 50 % of the income differences can be explained by differences in physical capital and schooling • At least 50% of the differences in income must be explained by other factors than the differences in physical capital and schooling 36 Why are some countries richer than others? What other factors can explain differences in income? • Inadequate access to technology – different E • Overpopulation, lack of natural resources? No! • Inadequate institutions (‘social infrastructure’) – – – – – Corruption and lawlessness Lack of competition Poor public infrastructure Taxes and regulations Poorly functioning labour markets 37 Why are some countries richer than others? 38 Why are some countries richer than others? 39 Why are some countries richer than others? Does income per capita converge? • Some convergence in Europe but no general convergence between rich and poor countries • The growth funnel: – in rich countries, GDP per capita grows by about 2 per cent per year – some poorer countries catch up, others fall behind • Geographical differences: many Asian countries have had rapid growth while many African countries have fallen behind 40 What determines technical development? • In the long run it is technology that drives growth in GDP per capita • We have treated E as exogenous – our theory did not explain what determines technical development • Endogenous growth theory tries to explain what drives technical development • These models often contain an explicit sector for research and development 41 What determines technical development? Production function for knowledge DE = aN Rn Eq where N R is the number of staff in R&D Assume NR = lN Þ g = DE = a(l N )n Eq -1 E – Growth depends on how many people work in R&D – Growth depends on the amount of existing knowledge that influences the development of new knowledge: growth eventually slows down q <1: DE q =1: g= = a( l N )n growth goes on forever E ‘We stand on the shoulders of giants’ 42