ECON 450 Development Economics Classic Theories of Economic Growth and Development The Solow Growth Model University of Illinois at Urbana-Champaign Summer 2017
Introduction In this lecture we start the discussion on why some countries are richer than others. The first step is to introduce the Neoclassical Theory of Development, aka the Solow-Swan growth model. As we ll see, the model predicts that differences in technology is the main factor responsible for income disparities across the globe.
Outline 1 The Solow Neoclassical Growth Model
The Solow Neoclassical Growth Model The Solow neoclassical growth model, for which Robert Solow of the Massachusetts Institute of Technology received the Nobel Prize, is probably the best-known model of economic growth. The Solow model is the basic framework for the study of convergence across countries.
Contextualization Economic Growth is a recent phenomenon in mankind history. Moreover, worldwide growth is far from constant. Growth has been rising over most of modern history. Evidences suggest that average real income today in the United States and Western Europe are between 50 and 300 times larger than two centuries ago.
Contextualization There are also great differences in standards of living across parts of the world. Average income in such countries as the United States, Germany and Japan appear to exceed those in such countries as Bangladesh and Kenya by a factor of about 20. Cross-country income differences are not an immutable process, though. Growth "miracles": South Korea, Taiwan, Singapore, and Hong Kong; Growth "disasters"": Argentina, and many of the countries in Sub-Saharan africa.
Contextualization Although economic growth does not guarantee economic development, the implications of the vast differences in standards of living over time and across countries for human welfare are enormous. In general terms, differences in economic levels are associated with large differences in Nutrition Literacy Infant Mortality Life Expectancy
Contextualization In his paper, published in 1956, Robert Solow presented the most important economic growth model, explaining the "recent phenomenon" of growth and why countries differ in income levels. In the same year, an Australian economist named Trevor Swan also published a paper on the same grounds. Therefore, the model is also known as the Solow-Swan Economic Growth Model.
Robert Solow - Nobel Prize Winner (1987)
Trevor Swan - Reserve Bank Board (1975-85)
The Model Model Assumptions Countries consume and produce one single homogeneous good (output); The economy is closed: no international trade; Technology is exogenous.
The Model Production Function The general formulation for the aggregate production function is given by F (K (t), L(t)). Aggregate production function exhibits constant returns to scale. F(αK (t), αl(t)) = αf(k (t), L(t)) Cobb-Douglas production function Y (t) = F (K, L) = K (t) α (A(t)L(t)) 1 α
The Model Production Function The technology variable A is said to be "labor-augmenting" or "Harrod-neutral". The interpretation of this formulation is that an unit of labor is more productive when the level of technology is higher. Thus, A represents the productivity of labor, which grows at an exogenous rate ("Solow residual").
The Model Production Function L and A are assumed to grow exogenously at rates n and g: L(t) = L(0)e nt A(t) = A(0)e gt.
The Model The Growth "Trick" To obtain rates of growth for any variable, we take the logs and differentiate with respect to time. L(t) = L(0)e nt log L(t) = log L(0) + nt Differentiating the above expression with respect to time: L L = n Apply this trick to see that Ȧ/A = g!
The Model Production Function Since we are seeking to understand differences in productivity levels, we can rewrite the production function in per capita (or per "effective worker") terms. That is, define k = K /AL and y = Y /AL. What is the growth rate of the number of effective units of labor A(t)L(t)?
The Model Production Function Given the constant returns assumption Y (t) = f (K (t)/a(t)l(t), 1) or y = f (k) A(t)L(t) y = k α The above equation states that output per worker is a function that depends on the amount of capital per worker.
The Solow Equation The Solow equation gives the growth of the capital-labor ratio (k) Assuming A is constant, it shows that the growth of k depends on savings sf (k), after allowing for the amount of capital required to service depreciation, δk, and after providing the existing amount of capital per effective worker to net new effective workers joining the labor force, (n + g)k. k = sf (k) (n + g + δ)k k = sk α (n + g + δ)k
The Solow Equation Steady State In the steady state, output and capital per worker are no longer changing. That is, k = 0. sf (k ) = (n + g + δ)k
The Solow Equation Using the Cobb-Douglas production function: sk α = (n + g + δ)k Solving for the steady state capital per worker k, we have: ( k s = n + g + δ ) 1/1 α
Equilibrium in the Solow Growth Model
Changing the Saving Rate It is instructive to consider what happens in the Solow neoclassical growth model if we increase the rate of savings, s. A temporary increase in the rate of output growth is realized as we increase k by raising the rate of savings. We return to the original steady-state growth rate later, though at a higher level of output per worker in each later year. The key implication is that an increase in s will not increase growth in the long run; it will only increase the equilibrium k.
The Long-Run Effect of Changing the Saving Rate in the Solow Model
Your turn! Shocks to an economy, such as wars, famines, or the unification of two economies, often generate large one-time flows of workers across borders. One recent example is the increasing number of Syrian refugees in western European countries, such as Germany. What are the short-run and long-run effects on an economy of a one-time permanent increase in the stock of labor? Use a diagram to guide your arguments.