Over the last several decades the observed relationship between capital per worker and real-GDP per worker for the United States was linear. What is the most plausible explanation for this observation?

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Question restatement: Over the last several decades the observed relationship between capital per worker and real-GDP per worker for the United States was linear. What is the most plausible explanation for this observation?

Option 1: 'There have been no diminishing returns to capital per worker.' This would imply a constant or increasing marginal product of capital, which is inconsistent with the typical linear long-run relationship observed alongside other factors. In growth models, diminishing returns to capital are standard, so claiming no diminishing returns does not align with standard theory.

Option 2: 'There have been constant returns to capital per worker.' Constant returns to scale with respect to capital per worker would suggest a proportional change in output for proportional changes in inputs, but the usual depiction in the data is not of constant returns to capital alone; instead, output per worker responds with diminishing marginal effects of additional capital, holding other factors, like technology, constant.

Option 3: 'There have been diminishing returns to capital per worker but advances in technology had caused shifts in the production function.' This combination captures two key ideas: each additional unit of capital yields smaller increases in output per worker (diminishing returns), and technology improvements shift the production function upward or outward, maintaining a relatively linear look when capital deepening and technological progress interact over time.

Option 4: 'There have been diminishing returns to capital per worker, but labor migration had caused shifts in the production function.' Labor migration can affect the capital-labor mix and potentially the effective productivity of labor, but the phrasing about shifts in the production function due to labor migration is less standard as a primary explanation for the observed long-run linear relationship between capital per worker and GDP per worker. The dominant, widely cited explanation centers on technology and the production function shifts rather than migration effects.

Option 5: 'There have been diminishing returns to capital per worker, but series of expansionary fiscal policies had caused shifts in the production function.' Expansionary fiscal policy can influence overall demand and short-run output and may affect certain components of production, but attributing the long-run linear relationship primarily to shifts in the production function from fiscal policy is less conventional. The more robust explanation centers on technological progress shifting the production function rather than policy-induced shifts alone.

Summary of reasoning across options: Across macroeconomic theory, diminishing returns to capital per worker are standard in production functions such as Cobb-Douglas. However, advances in technology shift the production function outward, which can preserve or create a near-linear relationship when examined over decades, as capital deepening interacts with continual technological progress. Other options either deny diminishing marginal returns without accommodating the observed context, or attribute the observed pattern to factors (like migration or fiscal policy shifts) that are not the primary drivers of the long-run relationship described in standard growth theory.

ECN 001B B01-B04 FQ 2025 Final Examination

Over the last several decades the observed relationship between capital per worker and real-GDP per worker for the United States was linear. What is the most plausible explanation for this observation?

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