Explain the convergence hypotheses and judge how well they hold

Convergence asks whether poorer economies catch up in output per person. Absolute convergence says they do regardless of their characteristics, because returns to capital are higher where capital is scarce. Conditional convergence says catch-up happens only among countries with the same saving rate, population growth and production function, since each approaches its own steady state. Club convergence says countries converge only if they join a club with the right institutions and policies; those outside may fall into a non-convergence trap. The neoclassical model predicts convergence through diminishing returns, while endogenous models need not, and openness speeds catch-up. The trap is expecting every poor economy to converge; the evidence favours conditional and club versions.