# Agenda. Long-Run Economic Growth, Part 2. The Solow Model. The Solow Model. Fundamental Determinants of Living Standards. Endogenous Growth Theory.

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1 Agenda Fundamental Determinants of Living Standards. Long-Run Economic Growth, Part 2 Endogenous Growth Theory. Policies to Raise Long-Run Living Standards The saving rate. Increasing the saving rate: Population growth. Productivity growth

2 Effect of an increase in the saving rate Y/N (Y/N) A Y/N = A*f(K/N) The adjustment mechanism: (S/N) A = (I b /N) A A I b /N = (n + d)k/n S/N = s*a*f(k/n) A higher saving rate shifts the saving function up. At the original K/N, at (K/N) A, S/N is now greater than I b /N. (K/N) A K/N Consequently, K/N will increase, causing: Y/N to increase along the production function, S/N to increase along the new saving function, and I b /N to increase along the balanced investment function The adjustment mechanism (continued): Because of diminishing marginal product of capital, the increase in S/N is smaller than the increase in I b /N for every increase in K/N. Eventually S/N will equal I b /N at a new, higher steady state at B. The adjustment mechanism (continued): At B, Y/N has increased, K/N has increased, S/N has increased, and I b /N has increased. At steady state B, ΔY/Y = ΔN/N = ΔK/K. During the transition period from steady state A to steady state B: ΔY/Y > ΔN/N because Y/N was increasing, and ΔY/Y > ΔK/K because K/N was increasing

3 Increasing the saving rate means: A higher capital-labor ratio, K/N, A higher output per worker, Y/N, and A higher consumption per worker, C/N. Increasing the saving rate: Should raising the saving rate be a policy goal? Not necessarily.» There is a trade-off between present and future consumption.» The cost is lower consumption in the short run Effect of a faster population growth rate Slowing the population growth rate: Y/N (Y/N) A Y/N = A*f(K/N) I b /N = (n + d)k/n (S/N) A = (I b /N) A A S/N = s*a*f(k/n) (K/N) A K/N

4 The adjustment mechanism: A slower population growth rate rotates the balanced investment function down. At the original K/N, at (K/N) A, S/N is now greater than I b /N. Consequently, K/N will increase, causing: Y/N to increase along the production function, S/N to increase along the saving function, and I b /N to increase along the new I b /N function. The adjustment mechanism (continued): Because of diminishing marginal product of capital, the increase in S/N is smaller than the increase in I b /N for every increase in K/N. Eventually S/N will equal I b /N at a new, higher steady state at B The adjustment mechanism (continued): At B, Y/N has increased, K/N has increased, S/N has increased, and I b /N has increased. At steady state B, ΔY/Y = ΔN/N = ΔK/K. During the transition period from steady state A to steady state B: ΔY/Y > ΔN/N because Y/N was increasing, and ΔY/Y > ΔK/K because K/N was increasing. Slowing the population growth rate means: A higher capital-labor ratio, K/N, A higher output per worker, Y/N, and A higher consumption per worker, C/N

5 Slowing the population growth rate : Increasing the productivity growth rate: Should reducing population growth be a policy goal? Doing so will raise consumption per worker but it will reduce total output and consumption. We have also assumed that the proportion of the population of working age is fixed which may not be true Effect of a productivity improvement Y/N (Y/N) A Y/N = A*f(K/N) The adjustment mechanism: I b /N = (n + d)k/n An improvement in productivity shifts both the production and saving functions up. (S/N) A = (I b /N) A A S/N = s*a*f(k/n) At the original K/N, at (K/N) A, Y/N is now higher. Also at the original K/N, at (K/N) A, S/N is now greater than I b /N. (K/N) A K/N

6 The adjustment mechanism: Consequently, K/N will increase, causing: Y/N to increase along the new production function, S/N to increase along the new saving function, and I b /N to increase along the balanced investment function. The adjustment mechanism (continued): Because of diminishing marginal product of capital, the increase in S/N is smaller than the increase in I b /N for every increase in K/N. Eventually S/N will equal I b /N at a new, higher steady state at B The adjustment mechanism (continued): At B, Y/N has increased, K/N has increased, S/N has increased, and I b /N has increased. At steady state B, ΔY/Y = ΔN/N = ΔK/K. During the transition period from steady state A to steady state B: ΔY/Y > ΔN/N because Y/N was increasing, and ΔY/Y > ΔK/K because K/N was increasing. An improvement in productivity means: A higher capital-labor ratio, K/N, Higher output per worker, Y/N, and Higher consumption per worker, C/N

7 An improvement in productivity means: Productivity improvement directly improves the amount that can be produced at any capital-labor ratio. The increase in output per worker also increases the supply of saving, and indirectly causes the long-run capital-labor ratio to rise. Can consumption per worker grow indefinitely? The saving rate cannot rise forever. The population growth rate cannot fall forever. Productivity and innovation can always occur So living standards can rise continuously. The rate of productivity improvement is the dominant factor determining how quickly living standards rise. Application: The growth of China Population of 1.3 billion people. A huge labor force with a comparative advantage in labor-intensive industries where wages are low. A low, but rapidly growing, level of GDP. About 1/9 of US GDP per capita in About 1/7 of US GDP per capita in

8 Real GDP growth in China and the US Application: The growth of China Rapid output growth attributable to: Saving is very high. Current consumption is very low. Huge increases in capital investment. Productivity growth is very rapid. Due in part from changing to a market economy. Due to adopting foreign technologies through FDI, etc. Population growth has slowed Application: The growth of China Application: The growth of China Y/N (Y/N) A Y/N = A*f(K/N) Will China ever catch up to the U.S.? I b /N = (n + d)k/n Problems China faces: Weak banking system. (S/N) A = (I b /N) A A S/N = s*a*f(k/n) Rapidly aging population. Increasing income inequality. (K/N) A K/N Much unemployment in rural areas

9 Endogenous Growth Theory Endogenous growth theory attempts to explain the sources of productivity growth. Assume the aggregate production function is: Y = AK which implies constant MPK. Endogenous Growth Theory How can the MPK be constant?: The existence of human capital: Human capital is the knowledge, skills, and training of the labor force. Human capital tends to increase in the same proportion as physical capital Endogenous Growth Theory How can the MPK be constant?: The presence of research and development. Increases in capital and output generate increased technical knowledge, which offsets decline in MPK from having more capital. Endogenous Growth Theory Implications of a constant MPK: Assume saving is a constant fraction of output: S = sy = sak Investment = net investment + depreciation, I = K + dk

10 Endogenous Growth Theory Implications of a constant MPK: In equilibrium, saving equals investment so: sak = K + dk or K/K = sa d Endogenous Growth Theory Implications of a constant MPK: If Y is proportional to K, then Y/Y = K/K, so K/K = sa d => Y/Y = sa d And the saving rate does affect long-run growth. Which is not true in Solow model Endogenous Growth Theory Summary: Endogenous growth theory attempts to explain, rather than assume, changes in productivity. The growth rate depends on many things which can be affected by government policies, including the saving rate. Policies to Raise Long-Run Living Standards Policies to increase the saving rate: If private markets are efficient, the government should not try to change the saving rate. The private markets saving rate represents its optimal trade-off of present for future consumption. However, if tax laws or myopia cause an inefficiently low level of saving, government policy to raise the saving rate may be justified

11 Policies to Raise Long-Run Living Standards Policies to increase the saving rate: Increase private saving. Raise the real interest rate to encourage saving. The response of saving to changes in the real interest rate seems to be small. Provide tax incentives to encourage saving. The response of saving to changes in tax incentives also seems to be small. Policies to Raise Long-Run Living Standards Policies to increase the saving rate: Increase government saving. Reduce the government deficit or run a surplus. Through reduced government purchases or higher taxes.» But under Ricardian equivalence, tax increases to reduce the deficit won t affect national saving Policies to Raise Long-Run Living Standards Policies to raise the productivity growth rate: Improve the infrastructure: Infrastructure is the highways, bridges, utilities, dams, airports, etc. Research suggests a link between the amount and quality of infrastructure and productivity growth. Policies to Raise Long-Run Living Standards Policies to raise the productivity growth rate: Build human capital: Research shows a strong connection between productivity and human capital. Government can encourage human capital formation through educational policies, worker training and relocation programs, and health programs. Another form of human capital is entrepreneurial skill. Government could help by removing barriers like red tape

12 Policies to Raise Long-Run Living Standards Policies to raise the productivity growth rate: Encourage research and development: Encourage R & D through direct and/or indirect means: Government funding of R & D efforts. Government tax incentives for R & D activities. Enforcement of patents, trademarks, etc. Summary The saving rate, The population growth rate, and Productivity growth. The productivity growth rate is the dominant factor in determining how quickly living standards increase Summary Endogenous growth theory is an explicit attempt to explain changes in productivity. If improvements in human capital and research and development programs can keep the MPK constant (as K increases), then saving will also be an important factor in determining living standards. Summary Government can influence living standards with policies designed to: Increase the saving rate, Slow the population growth rate, and/or Raise the productivity growth rate

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