Lecture 3. Exogenous Economic Growth Theory
Recommended reading : 【Macroeconomics】 Macroeconomics Table of Contents
1. The Harrod–Domar Model
2. The Solow Model
1. The Harrod–Domar Model
⑴ Leontief production function : No substitution at all between labor and capital
⑵ Equilibrium condition
⑶ Problems : Unstable equilibrium
① Because the saving rate (s), capital coefficient (v), and population growth rate (n) in the equilibrium condition are all determined exogenously, achieving equilibrium is unstable.
② If the economy deviates from equilibrium, there is no automatic mechanism that brings it back.
2. The Solow Model
⑴ Assumption 1. Population growth
① n : average annual population growth rate ＞ -1
② In a long-run growth model, population represents the labor force.
③ In a short-run growth model, unemployment is an important issue.
⑵ Assumption 2. Balance between injections and leakages
① Yt : total income in period t (total production income)
② s : saving rate, or marginal propensity to save (MPS, marginal propensity to save)
③ 1-s : consumption rate, or marginal propensity to consume (MPC, marginal propensity to consume). Generally given as 0.6.
④ Note: This is a closed economy and considers only the private sector, so government spending and net exports are not considered.
⑶ Assumption 3. Cobb–Douglas production function : Substitution between labor and capital is possible
① Total output
② Output per person
③ Feature 1. Passes through the origin
④ Feature 2. Constant returns to scale : If each factor of production is doubled, output also doubles.○ yt : Yt / Lt, output per person
○ kt : Kt / Lt, capital per person
○ zt : total factor productivity (TFP), also called the Solow residual⑤ Feature 3. Diminishing marginal product : If the other inputs are held fixed and one input increases, its marginal product decreases.
⑷ Assumption 4. The process of aggregate capital accumulation
① Kt : total capital stock in period t
② It : total investment in period t
③ d : depreciation rate per unit of capital
④ Depreciation : as fixed assets such as factories or machinery are used, they wear out.
⑸ Intertemporal accumulation process of the steady-state capital stock
⑹ Per-capita steady-state capital accumulation process
Figure 1. Per-capita steady-state capital accumulation process]
① Steady state (steady state)
Figure 2. Steady state]
○ Full employment of labor and capital is achieved : the economic growth rate = the capital growth rate = the population growth rate + the depreciation rate
○ Right-hand side : the amount of capital accumulation required to keep per-capita capital at a constant level
○ Left-hand side : equilibrium saving = the amount of capital that is actually invested
② When including the rate of technological progress g
○ Reason : effective labor increases by the sum of the population growth rate and the rate of technological progress.
③ Since zt has continued to rise after the Industrial Revolution, the economy has not reached a converged steady state.
⑺ Golden-rule capital stock and golden-rule saving propensity
Figure 3. Golden-rule capital stock and golden-rule saving propensity]
① Consumption per person in the steady state
② Golden-rule capital stock : the level of capital per person that maximizes steady-state consumption c*○ (Note) Since consumers are more satisfied when consumption is maximized, the rate that maximizes it is called the “golden rule.”
③ Golden-rule saving propensity : the steady-state saving propensity at the golden-rule capital stock
○ If the per-capita production function is f(k) = k^α, the golden-rule saving rate is independent of total factor productivity (z), the population growth rate (n), and the depreciation rate (d).
○ If the production function is Cobb–Douglas, the golden-rule saving propensity coincides with the capital income share.
○ The Solow model has no mechanism to adjust the discrepancy when the actual saving rate does not match the golden-rule saving rate.
○ Therefore, the government can intervene to adjust the actual saving rate toward the golden-rule saving level.④ Conditions at the golden rule
○ Capital income = investment = saving
○ Labor income = consumption
○ Saving rate = capital income share
○ Economic growth rate (n) = net marginal product of capital (MPk − d)
⑻ Problem 1. The law of diminishing returns holds : it cannot explain the driving force behind long-run economic growth
① Determinants of growth : increases in factor inputs, technological progress
② Factor 1. Increase in factor inputs○ Negative correlation between per-capita income and population growth : reducing population growth does not generate sustained economic growth.
○ Positive correlation between per-capita income and the saving rate : increasing the saving rate does not generate sustained economic growth.○ Example : Korea’s saving rate reached 20% in the 1960s.
○ It raises the overall level of production, but there is a limit to increases in output per person : only a level effect exists.
③ Factor 2. Technological progress
○ Although technological progress is said to be a source of sustained economic growth, the model cannot explain the determinants of technological progress within the model.
④ (Note) “Long-run growth” (for Korea) refers to growth from the 1950s to the present.
⑼ Problem 2. The convergence hypothesis : it cannot explain persistent income gaps across countries
① Closed-economy assumption
○ With the Solow model’s diminishing marginal product of capital assumption, capital accumulation is faster in poorer countries → incomes across countries converge.
② Open-economy assumption : convergence is accelerated even further.
○ Rich countries have a low marginal product of capital (MPk).
○ Poor countries have a high marginal product of capital (MPk).
○ Conclusion : physical capital moves from rich countries to poor countries.③ In reality, per-capita incomes across the world do not converge, but they do converge among rich countries.
Figure 4. Relationship between per-capita income level and growth rate]
④ Cause 1. In endogenous growth models such as the AK model, the marginal product of capital does not diminish.
⑤ Cause 2. If countries differ in the economy’s technology level (total factor productivity), production function, saving rate, population growth rate, depreciation rate, etc.○ (Note) Absolute convergence : if only initial capital differs, two countries converge to the same income level.
○ (Note) Conditional convergence : two countries converge only if other conditions are the same.
○ Empirical analyses find that cross-country differences in technology levels are the most important factor behind conditional convergence.
⑽ Balanced growth path
① Long-run growth equilibrium (or steady state) is a situation in which output per person, capital per person, consumption per person, etc. grow at a constant rate.
② Long-run growth equilibrium (or steady state) is a special case of a balanced growth path where the constant growth rate equals 0.
Entered: 2020.09.21 11:19