Macroeconomics Chapter 51 Conditional Convergence and Long- Run Economic Growth C h a p t e r 5

Macroeconomics Chapter 52 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 53 Conditional Convergence in Practice

Macroeconomics Chapter 54 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 55 Conditional Convergence in Practice  Japan and Germany after 2nd world war.  East Asia countries  African Countries

Macroeconomics Chapter 56 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 57 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 58 Long-Run Economic Growth  k – capital per worker  y/k= A  ∆k/k= sA− sδ − n

Macroeconomics Chapter 59 Long-Run Economic Growth

Macroeconomics Chapter 510 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 511 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 512 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 513 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 514 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 515 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 516 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 517 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 518 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 519 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 520 Long-Run Economic Growth

Macroeconomics Chapter 521 Long-Run Economic Growth

Macroeconomics Chapter 522 Long-Run Economic Growth

Macroeconomics Chapter 523 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 524 Endogenous Growth Theory The essential feature of knowledge or technology: non-rival good  MC is zero Production function of A: ∆A =f(A,K,L) Is the marginal product of A decreasing, increasing, or constant? Human capital

Macroeconomics Chapter 525 Endogenous Growth Theory The determinants of the allocation of resources to R&D Support for basic scientific research Private incentives for R&D and innovation Alternative opportunities for talented individuals: rent-seeking Learning-by-doing:

Macroeconomics Chapter 526 Endogenous Growth Theory  Optimal intellectual property rights  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 527 Endogenous Growth Theory

Macroeconomics Chapter 528 The basic R&D model Assumptions 1. The labor force is the single production factor 2. Generalized Cobb-Douglas function without capital 3. The fraction of the labor force is exogenous

Macroeconomics Chapter 529 The basic R&D model The evolution function of labor where The evolution function of knowledge

Macroeconomics Chapter 530 The basic R&D model The dynamic of knowledge accumulation

Macroeconomics Chapter 531 The basic R&D model Case 1:

Macroeconomics Chapter 532 The basic R&D model Case 1: has a level effect but not a growth effect Interpretation: endogenous long run growth rate 1.positive link with population growth 2.

Macroeconomics Chapter 533 The basic R&D model Case 2: ever-increasing growth has a growth effect

Macroeconomics Chapter 534 The basic R&D model Case 3: linear growth model has a growth effect