Questions: Technological Progress and Total Factor Productivity

Question 1

An economy doubles its capital stock over 20 years while labor and TFP (A) remain constant. According to Y = A·F(K, L) with standard diminishing returns, what happens to output?

• A. Output doubles, because capital doubled
• B. Output more than doubles, because capital and its returns compound over time
• C. Output increases by less than double, because capital is subject to diminishing returns
• D. Output is unchanged — only TFP growth can increase output in the long run

Answer: (C)

With standard diminishing returns to capital, doubling K raises output by less than double. The capital share of income (typically about one-third in empirical estimates) tells us roughly how much: if capital's share is 1/3, doubling K raises output by about 2^(1/3) ≈ 1.26, or 26%. Option A is the common mistake of treating capital like a constant-returns input. Option D confuses the long-run growth result (only TFP sustains indefinite growth) with the short-run effect of capital accumulation, which is real but diminishing.

Question 2

Why do economists consider TFP the most important driver of long-run increases in living standards, more so than capital accumulation?

• A. Because physical capital depreciates over time, canceling out any gains from investment
• B. Because capital accumulation faces diminishing returns and requires sacrificing current consumption, while TFP growth shifts the entire production frontier outward without those constraints
• C. Because labor is more abundant than capital in developing countries, making TFP relatively more valuable there
• D. Because TFP is defined to include all government spending on infrastructure, which dominates private investment

Answer: (B)

Capital accumulation hits diminishing returns: each additional unit of capital contributes less to output, and investment requires foregone consumption. An economy relying only on capital accumulation converges to a steady state where growth stops. TFP growth (innovation, organizational improvement, knowledge spillovers) shifts the entire production function outward — more output from the same inputs — without diminishing returns, and can continue indefinitely. The industrial revolution, electrification, and computing were primarily TFP events, not capital accumulation stories.

Question 3

In the production function Y = A·F(K, L), a doubling of TFP (A) has the same effect on output as doubling the capital stock K.

• T. True
• F. False

Answer: False

A doubling of A multiplies the entire output by 2, regardless of how much K and L there are — it's a proportional shift of the whole frontier. Doubling K, by contrast, is subject to diminishing returns: its contribution to output is weighted by capital's income share (roughly 1/3 empirically), so doubling K raises output by about 26%, not 100%. TFP growth is more powerful precisely because it acts as a multiplier on all inputs rather than adding to just one.

Question 4

The 'Solow residual' is called the measure of our ignorance because TFP is computed as whatever output growth remains after accounting for capital and labor growth.

• T. True
• F. False

Answer: True

TFP cannot be directly observed — there is no meter measuring 'amount of technology.' Instead, economists compute it as a residual: take total output growth, subtract the weighted contributions of capital and labor, and attribute the remainder to A. Because this residual captures everything we cannot directly measure — managerial efficiency, knowledge spillovers, organizational improvements, genuine innovation — Solow called it the 'measure of our ignorance.' This residual empirically accounts for the majority of long-run growth in developed economies.

Question 5

What does it mean to say TFP acts as a 'multiplier' on the production function, and why does this make TFP growth more powerful than capital accumulation for long-run prosperity?

Model answer: TFP (A) multiplies the output of all inputs combined rather than being one input among many. In Y = A·F(K,L), a 10% rise in A raises output 10% no matter how much K and L are present — there are no diminishing returns to A itself. Capital accumulation, by contrast, faces diminishing returns (each additional machine adds less than the previous one) and requires sacrificing consumption today. An economy that only accumulates capital eventually reaches a steady state where investment just replaces depreciation and growth stops. TFP growth can continue indefinitely through innovation and learning, so it is the only sustainable engine of long-run growth in living standards.

This is the central insight of growth theory stemming from Solow's model: sustained growth in per-capita income requires sustained growth in TFP. Countries that grow primarily through capital investment see growth slow as diminishing returns bite; countries that achieve ongoing improvements in technology and organization continue growing. This explains why innovation policy, education, and R&D investment matter for long-run prosperity — they are investments in A, not just in K or L.