WEEK IX Economic Growth Model

W EEK IX Economic growth Improvement of standard of living of society due to increase in income therefore the society is able to consume more goods & services (measurement: output per person or GDP per capita). refers to growth of potential aggregate output/economic capacity i.e. natural rate of output (Y n ). Thus economic growth is concerned with the long-run trend in aggregate output due to structural causes. In the contrary, a short-run and medium-run variation in economic growth (Y t ) is called the business cycle. Economic growth is a dynamic analysis: 1.Change over time: A trend in the long-run (in which the business cycle moves up and down, creating fluctuations around the trend)

W EEK IX

2.Compare across countries: at PPP (purchasing power parity) prices in which GDP is measured on how much consumers must pay for the same "basket of goods" in each country.

W EEK IX Dynamic analysis of economic growth: force of compounding 1.A large increase in GDP per capita over time 2.A convergence of GDP per capita across Models of economic growth to explain the conclusions including: 1. Adam Smith (“Wealth of Nations”, 1776); factors affect economic growth: (i) specialization and technology advancement and (ii) market expansion 2. Joseph Schumpeter (“the Theory of Development”, 1908); Economic growth depends on innovation of entrepreunership in producing goods & services. 3.(Roy) Harrod (“An Essay in Dynamic Theory“, 1939) - (Evsey) Domar (“Capital Expansion, Rate of Growth, and Employment”, 1946); Economic growth is determined by aggregate demand side particularly investment. 4.(Robert) Solow (“Contribution of the Theory of Economic Growth”, 1956). The Solow’s model demonstrates how capital stock/saving, population, technology progress affects level of output and growth.

W EEK IX Building blocks of the Solow’s growth model: 1.Aggregate production function Production function: a specification of the relation between aggregate output and inputs in production Assumptions: 1.Output (Y) is a function of 2 inputs i.e. capital stock (K) and labor (N). 2. State of technology of the production function is constant return to scale in which the increase all the inputs (K & N) by the same percentage will increase output (Y) by exactly the same percentage.

W EEK IX 3.Decreasing returns to factors (recall: Law of diminishing marginal product) in which increases in a certain input (e.g. K), given other inputs (e.g. L), lead to smaller and smaller increases in output (= ∆Y/∆K). 4.The production function can also be written in relative term to labor. If x = 1/N: Output per worker (Y/N) is the function of capital per worker (K/N). This relation: The use of labor as a denominator in the above equation implies that labor does not affect the relationship between economic growth and capital stock. Can be drawn in a 2-dimensional graph Upward-sloping curve Decreasing returns to capital

W EEK IX Aggregate production curve: capital accumulation

W EEK IX Sources of increase in GDP per capita: Increase in K/N: capital accumulation (i.e. a movement along the aggregate production curve) Improvement in the state of technology: technological progress (i.e. a shift of aggregate production curve) Capital accumulation by itself can sustain a higher level of output (Y/N) but cannot sustain a high growth rate of output [∆(Y/N)] due to the decreasing returns to capital. Thus economy requires larger and larger increases in the level of capital per worker (i.e. investment and saving) to sustain steady increase in output. Sustained growth requires technological progress.

W EEK IX Effects of improvement in state of technology

W EEK IX Output and capital: 2 relations Capital stock (K)  output (Y): Production function Output (Y)  saving (S)  investment (I) = capital accumulation (∆K): Saving/investment function

W EEK IX Model I: Economic growth due to capital accumulation Thus assumption: (i) size of population and labor is constant (growth of population = 0) and (ii) no technological progress 1 st relation: K  Y Time index (t) for Y and K ONLY: higher K/N leads to higher Y/N 2 nd relation: Y  S  I Assumption: closed economy thus Y = C + I + G I = (Y – C – T) + (T – G) I = S + (T – G) Assumption: (T – G) = 0 thus I = S Investment = private saving

W EEK IX Private saving is proportional to income: S = s*Y Where s: saving rate (0 < s < 1) I t = sY t Saving rate, s, has no relations with level of income, Y. Time index, t, for I and Y thus the higher output (Y), the higher saving (S) and the higher investment (I). 2 nd relation: I = ∆K Capital: stock concept at a point in time, while investment: flow concept during a given period Capital depreciates per year at rate: δ K t+1 = K t – δ*K t + I t

W EEK IX K t+1 = (1 – δ)*K t + I t Substitute I by sY and dividing both sides by N

W EEK IX Implications of changes in saving rate Production function = saving/investment function K/N  Y/N therefore ∆(K/N)  ∆(Y/N) ∆(K/N) = I/N – δK/N Interpretation: Increases in investment (I/N) will increase capital stock (K/N) which (1) produce higher output (Y/N) as well as (2) generates higher depreciation ( δ K/N): I/N > δ K/N  K/N  I/N < δ K/N  K/N 

W EEK IX Steady state capital & output: capital accumulation

W EEK IX Investment curve has the same shape as the production function but it is lower (= sY) Depreciation curve has a straight line that proportional to capital If an economy’s initial K/N δ K/N so that K/N increases over time until K/N = K*/N; If an economy’s initial K/N > K*/N, then I/N < δ K/N so that K/N falls over time until K/N = K*/N; Y/N also moves around its Y*/N as K/N moves toward K*/N Point K*/N that indicates I/N = δ K/N whereby investment and depreciation reaches its equilibrium (or ∆K/N = 0) therefore the level of output (Y/N) and capital stock (K/N) is constant over time.

W EEK IX K*/N is called a steady-state capital (and Y*/N is a steady-state output). The steady-state reflects an economic equilibrium in the long-run. The steady-state suggests that economies converge in the long run: Countries with low initial levels of capital and output per worker will grow rapidly as K/N and Y/N will rise until they reach their steady state values. Countries with high initial levels of capital and output per worker will grow slowly as K/N and Y/N will fall until they reach their steady state values.

W EEK IX Implication of change in saving rate on economic growth 1.Saving rate has no effect on the long-run growth rate of output per worker which is equal to 0; 2.The saving rate determines the level of output per worker in the long run

W EEK IX 3.An increase in the saving rate will lead to higher growth of output per worker for some time but not forever

W EEK IX Golden rule of level of capital Does a maximum saving (i.e. s = 100%) will always be good for economy? Economic policies can be used to determine saving rate thus it can reach the steady-state: (i) positive public saving; (ii) tax incentives to affect private saving What matters for society is not how much is produced (Y) but how much they consume (C). Society is willing to maximize level of consumption of goods & services at certain saving rate (0 < s < 1). Golden rule of level of capital is a level of capital stock associated with the certain saving rate that maximizes level of consumption.

W EEK IX Golden rule of level of capital

W EEK IX Model II: Economic growth due to technological progress Technological progress and production function Technological progress results in: (i) larger quantities of output for given inputs, (ii) better products, (iv) new products, (iv) larger variety of products and (iv) more service. State of technology: how much output can be produced from given inputs; A. Y = F(K, N, A) Where AN is effective labor indicates: Technological progress reduces labor needs to produce given output Technological progress increases output that can be produced with a given labor

W EEK IX Assumption of constant returns to scale: xY = F(xK, xAN) By substitute X = 1/AN to get in relative term of labor Output per effective worker is a function of capital per effective worker

W EEK IX Aggregate production curve: technological progress

W EEK IX 1 st relation: K  Y 2 nd relation: I = ∆K I = S = sY

W EEK IX 3 rd relation: δ K/I  ∆K Growth rate of effective labor = g A + g N in which g A is growth rate of technological progress, g N is growth rate of labor

W EEK IX Steady-state capital and output: technological progress

W EEK IX Steady state (= balance growth) K/AN and Y/AN are constant Growth of K/N and Y/N = growth of technological progress (g A ) Or growth of K and Y = sum of population growth and rate of technological progress (g N + g A ). Implications of increase in saving rate Changes in saving rate; s, do not affect steady-state growth rate ∆(K/AN) but increase the steady-state level of output per effective worker (K/AN)

W EEK IX Implications of an increase in saving rate

W EEK IX