Development Economics and Growth Models

Demographic transition and population structure

Population structure is described by three broad age groups: children aged 0 to 14, the working-age population aged 15 to 64, and the elderly aged 65 and above. The dependency ratio is the number of people outside the working-age group divided by the number of people inside it, so it measures how many dependants each worker must support. Children and the elderly are both dependants, so a ratio that counts only children against adults understates the burden and is not the standard definition. The old-age dependency ratio applies the same logic to the elderly alone, as the population aged 65 and above divided by the population aged 15 to 64, multiplied by 100. A change in this ratio over time is a percentage change, computed as (new ratio − old ratio) / old ratio × 100, not as the simple difference in percentage points. For example, a rise from 20 to 22 is a 2-point increase in the ratio but a 10 percent increase in relative terms. The demographic transition describes how a population moves from high birth and death rates to low ones in four stages. Stage I has high fertility and high mortality, so population growth is slow. Stage II has falling mortality while fertility stays high, so population grows rapidly. Stage III has declining fertility, so growth slows. Stage IV has low fertility and low mortality, so the population becomes roughly stationary. The key point is that mortality falls first and fertility falls later.

Solow steady-state capital accumulation

In the Solow model, capital per worker changes by saving per worker minus the break-even investment needed to keep capital per worker constant. With output per worker y = f(k), the law of motion is \dot{k} = s f(k) - (n+\delta)k, where s is the saving rate, n is the population growth rate and \delta is the depreciation rate. The steady state occurs where s f(k) = (n+\delta)k. When the population does not grow, n = 0 and the condition becomes s y = \delta k. For example, if y = k^{1/3}, s = 0.24 and \delta = 0.06, then 0.24k^{1/3} = 0.06k, so k^{2/3} = 4 and k = 8. This type of question is solved by writing the steady-state condition and substituting the production function carefully, since the output per worker must be expressed in terms of k. At steady state, capital per worker and output per worker are constant. With no technological progress, aggregate output Y = yN therefore grows at the population growth rate n. The saving rate changes the level of steady-state output but not its long-run growth rate.

Convergence and catch-up growth

The convergence hypothesis holds that poor economies tend to grow faster than rich ones because of diminishing returns to capital. Countries with similar saving rates, technologies and institutions therefore tend to catch up over time. A poor country may fail to catch up when factors lower its capital per worker or its productivity relative to the rich country. Rapid population growth dilutes capital per worker, and a rich country with more human capital or deeper integration into world trade enjoys higher productivity and knowledge spillovers that widen the gap. A higher saving ratio, by contrast, raises investment and the steady-state capital stock, and so promotes rather than prevents catch-up.

Kuznets curve

Simon Kuznets hypothesised that income inequality follows an inverted U-shaped path as income per capita rises. Inequality first increases in the early stages of development, when labour moves from low-productivity agriculture to higher-productivity industry and the gap between sectors widens. Inequality then falls at later stages, as the modern sector absorbs most workers and institutions such as education and social security develop. Plotted against income, this pattern forms an inverted U. A convex curve, which implies inequality rising without a turning point, or a V-shaped path, which reverses the order, does not match the hypothesis. The Kuznets curve is an empirical hypothesis, and the position of the turning point differs across countries.

Endogenous growth and non-rival ideas

Endogenous growth theory, developed by Paul Romer and others, explains long-run growth as the outcome of deliberate investment in knowledge rather than of an exogenous technology trend. The key distinction is between rival and non-rival goods. A good is rival when one user's consumption reduces its availability to others, as with a machine or a plot of land. An idea is non-rival: a blueprint or a formula can be used by many firms at the same time without being depleted. Because ideas are non-rival, they can yield increasing returns at the economy level. Ideas are only partially excludable, since patents and secrecy give innovators some protection, and this partial protection provides the rents that finance research and development.

Human Development Index

The Human Development Index combines three dimensions: a long and healthy life, knowledge, and a decent standard of living. The longevity dimension is measured by life expectancy at birth, expressed in years. Other health indicators such as child survival rates, healthy life expectancy and disability-adjusted life years are used in different studies of health and disease burden, but they are not the longevity variable of the standard HDI. Students should therefore memorise the three components of the index together with their specific indicators.

Solow growth accounting

Growth accounting decomposes the growth rate of output into the contributions of capital, labour and technology. For a Cobb-Douglas production function with labour-augmenting technology, Y = K^{\alpha}(AL)^{1-\alpha}, where \alpha is the output elasticity of capital. The growth rate of output is g_Y = \alpha g_K + (1-\alpha)(g_A + g_L), so effective labour grows at the sum of labour growth and technology growth. For example, if \alpha = 0.4, g_K = 2, g_L = 1 and g_A = 1, then g_Y = 0.4(2) + 0.6(1+1) = 2.0 percent per annum. The weights in the formula are the capital and labour shares of output, so a common error is to apply the labour weight to the capital growth rate or to omit the technology term. Rounding should follow the instruction given in the question.