Contrast technological progress with capital deepening and explain how each drives growth and labour productivity

Output per worker can rise in two ways. Capital deepening means more capital per worker; it raises labour productivity, but diminishing marginal returns mean each extra unit adds less, so it lifts the level of output per worker without sustaining its growth. It is a move along the per-worker production function. Technological progress, measured by total factor productivity, shifts the function upward so the same inputs produce more, and in the neoclassical model it is the only source of permanent growth in output per worker. With Cobb–Douglas, labour productivity growth equals TFP growth + α × growth in capital per worker. The trap is expecting more investment to raise the long-run growth rate.