(a) What do you mean by the warranted rate of growth ? Explain the knife edge instability problem in Harrod's growth model. (15…

Harrod’s warranted rate and knife-edge instability. In Harrod’s model, the warranted rate, Gw, is the growth rate at which planned investment exactly matches the capital stock implied by the desired capital-output ratio: Gw = s/Cr, where s is the saving-investment ratio and Cr the desired capital-output ratio. Actual G is realised growth, while natural Gn is the maximum growth allowed by labour-force growth and technology. The knife-edge problem is causal: if G > Gw, the capital-output ratio falls below Cr, firms perceive excess demand for capital, raise investment, and G rises further; if G < Gw, the ratio is above Cr, firms cut investment, and G falls further. Deviations are cumulative, not self-correcting. A diagram would show Gw and Gn as horizontal lines; within the corridor between them, paths above Gw have upward arrows and paths below have downward arrows, so only G = Gw is stable. Since Gw and Gn usually differ, full employment also needs G = Gn, making stability a knife-edge coincidence.

Lewis’s dual economy and unlimited labour supply. Lewis explains development in a less developed country as a shift from a subsistence sector to a capitalist sector. Unlimited labour supply comes from the subsistence sector, where marginal productivity of labour is zero or below the subsistence wage, so workers can be withdrawn without reducing output. Population growth, seasonal underemployment, and institutional factors such as landlessness and weak rural mobility reinforce the surplus. The capitalist sector pays an institutional wage, typically about 30 per cent above subsistence, not the marginal product, to attract labour. In the labour-supply diagram, the curve is horizontal at this wage and kinks upward at the turning point, when surplus labour is exhausted and marginal productivity rises. The mechanism is cumulative: the capitalist sector hires surplus labour at a constant wage, earns profits, reinvests them, expands capital and output, and creates further labour demand. As labour moves out, the industrial sector’s growing share changes terms of trade and raises national income. At the turning point, wages must rise with marginal productivity, the horizontal supply curve ends, and the dual economy becomes modern. India’s rural-urban migration illustrates this transition.

GDI and GEM: components and construction. The Gender Development Index measures the gender gap in HDI-based human development. Its components are life expectancy, education, and income; the income component compares female and male estimated earned income in PPP US$, not shares of income. For each dimension, the female-to-male achievement ratio is calculated; if female achievement exceeds male, the ratio is capped at 1.05, imposing a 5 per cent penalty. The GDI averages the three ratios, recording welfare outcomes. The Gender Empowerment Measure measures inequality in power and agency. Its components are political participation (share of parliamentary seats), economic participation (share of professional and technical positions), and power over economic resources, using female and male estimated earned income in PPP US$ to compute the relevant share. Its construction is different: for each dimension, female and male shares are converted into an equally distributed equivalent percentage, calculated as 100 times one minus the Gini coefficient of the two-group distribution; the three equally distributed equivalent percentages are then averaged to obtain GEM. Thus GDI measures gaps in development achievements, while GEM measures gaps in control over political and economic resources.

Conclusion. Harrod and Lewis show that growth requires structural balance: Harrod’s knife-edge shows instability without coordinated investment, labour and technology; Lewis shows surplus labour and reinvestment transform a dual economy until the turning point. Gender indices extend this to distribution: GDI records welfare gaps, GEM records empowerment gaps, so inclusive growth requires raising women’s achievements and agency.