Macroeconomics Chapter 5 Conditional Convergence and Long-Run Economic Growth Macroeconomics Chapter 5

Conditional Convergence in Practice Growth rate of capital per worker, ∆k/k: ∆k/k= ϕ[ k(0) , k*] (−) (+) y= A· f(k) Growth rate of real GDP per worker is a function of initial and steady-state real GDP per worker ∆ y/y= ϕ[ y(0) , y*] (−) (+) Macroeconomics Chapter 5

Conditional Convergence in Practice Macroeconomics Chapter 5

Conditional Convergence in Practice Variables that influence y* that are held constant. A measure of the saving rate The fertility rate Subjective measures of maintenance of the rule of law and democracy The size of government The extent of international openness, measured by the volume of exports and imports Changes in the terms of trade Measures of investment in education and health The average rate of inflation Macroeconomics Chapter 5

Conditional Convergence in Practice Japan and Germany after 2nd world war. East Asia countries African Countries Macroeconomics Chapter 5

Long-Run Economic Growth Solow model, the growth rate of capital per worker, k, is given by ∆k/k= s· (y/k) − sδ − n Macroeconomics Chapter 5

Long-Run Economic Growth A case in which capital broadly defined to include human and infrastructure capital is the only factor input to production. AK model y= Ak Macroeconomics Chapter 5

Long-Run Economic Growth k – capital per worker y/k= A ∆k/k= sA− sδ − n Macroeconomics Chapter 5

Long-Run Economic Growth Macroeconomics Chapter 5

Long-Run Economic Growth Conclusions The long-run growth rate of capital per worker, ∆k/k, is greater than zero and equal to sA− sδ − n Growth rates of capital and real GDP per worker, ∆k/k and ∆y/y, do not change as capital and real GDP per worker, k and y, rise. poor economies with low k and y do not tend to grow faster than rich economies Macroeconomics Chapter 5

Long-Run Economic Growth The regular process of improvement in technology is called technological progress. exogenous technological progress - the improvements in technology were not explained within the model. ∆A/A= g Macroeconomics Chapter 5

Long-Run Economic Growth Exogenous Technological Progress ∆Y/Y= ∆A/A+α·(∆K/K)+(1−α)·(∆L/ L) Using ∆A/A= g and and ∆L/L = n ∆Y/Y= g+ α·(∆K/ K) + (1−α) · n ∆y/y= ∆Y/Y− ∆L/L = ∆Y/Y− n Macroeconomics Chapter 5

Long-Run Economic Growth Exogenous Technological Progress ∆y/y= g+α·(∆K/K)+(1−α)·n − n = g+α·(∆K/K − n) ∆ k/k= ∆ K/K − ∆L/L = ∆K/K − n ∆y/y= g+α·(∆k/k) Macroeconomics Chapter 5

Long-Run Economic Growth Exogenous Technological Progress ∆k/k - in the Solow model ∆k/k= sA·f(k)/k− sδ − n Growth rate of real GDP per worker with technical progress ∆y/y= g+α·[ sA· f(k)/k− sδ−n] Macroeconomics Chapter 5

Long-Run Economic Growth Steady state: all variables grow at constant rates. ∆k/k is constant ∆k/k= s(y/k)− sδ − n y/k is constant Macroeconomics Chapter 5

Long-Run Economic Growth Exogenous Technological Progress (∆y/y)* = (∆k/k)* (∆y/y)* = g+ α·(∆k/k)* (∆y/y)* = g+ α·(∆y/y)* (∆y/y)* − α·(∆y/y)* = g (1−α)·(∆y/y)* = g Macroeconomics Chapter 5

Long-Run Economic Growth Exogenous Technological Progress Steady-state growth rate with technological progress (∆y/y) * = g/(1 − α) Since 0 < α < 1 the steady-state growth rate of real GDP per worker, (∆y/y)∗, is greater than the rate of technological progress, g. Macroeconomics Chapter 5

Long-Run Economic Growth Exogenous Technological Progress (∆k/k)* = (∆y/y)* (∆k/k)* = g/(1−α) Exogenous technological progress at the rate ∆A/A= g leads to long-term growth in real GDP and capital per worker, k and y, at the rate g/(1−α) Macroeconomics Chapter 5

Long-Run Economic Growth Exogenous Technological Progress ∆k/k= s·(y/k) − sδ − n (∆k/k)* = g/(1 − α) g/(1−α) = s·(y/ k)* − sδ − n s·[(y/k)*−δ] = n+g/(1−α) (y/k)*= δ+(1/s)·[n+g/(1−α)] For Cobb-Douglas function Macroeconomics Chapter 5

Long-Run Economic Growth Macroeconomics Chapter 5

Long-Run Economic Growth Macroeconomics Chapter 5

Long-Run Economic Growth Macroeconomics Chapter 5

Endogenous Growth Theory Extend the model to explain why technological progress occurs. Most endogenous growth models focus on investments in research and development (R&D) Macroeconomics Chapter 5

Endogenous Growth Theory The essential feature of knowledge or technology: non-rival good not diminishing with the rise of A. Macroeconomics Chapter 5

Macroeconomics Chapter 5 The basic R&D model Assumptions The labor force is the single production factor Generalized Cobb-Douglas function without capital 3. The fraction of the labor force is exogenous Macroeconomics Chapter 5

Macroeconomics Chapter 5 The basic R&D model The evolution function of labor where The evolution function of knowledge Macroeconomics Chapter 5

Macroeconomics Chapter 5 The basic R&D model The dynamic of knowledge accumulation Macroeconomics Chapter 5

Macroeconomics Chapter 5 The basic R&D model Interpretation: endogenous long run growth rate positive link with population growth Macroeconomics Chapter 5

Diffusion of Technology The Diffusion of Technology The imitation and adaptation of one country’s technology by another country. The rate of technological diffusion to a developing country is high when the country trades a lot with rich countries, has high education levels, and has well functioning legal and political systems. Macroeconomics Chapter 5