In the production per worker function, what does the slope represent?

In the production per worker function, the slope represents the Marginal Product of Capital (MPK), which refers to the additional output produced when one more unit of capital is added while keeping the amount of labor constant. This concept is central to understanding how capital contributes to production.

As one moves along the production function, the steepness of the slope indicates how productive additional capital is in generating extra output, capturing the increasing or diminishing returns to capital. In essence, when you add more capital, such as machinery or tools, the additional output gained per worker will vary, and this is reflected in the slope of the production per worker function.

The other concepts—Rate of Return on Investment (ROI), Average Total Cost (ATC), and Marginal Cost (MC)—are related but do not specifically describe what the slope of the production function represents. ROI pertains to the profitability of an investment, ATC relates to the average cost of production per unit, and MC measures the cost of producing one more unit of output. Thus, these options do not accurately capture the idea of the slope in the production per worker function, which specifically pertains to the change in output attributable to additional capital, hence reinforcing the correctness of identifying the slope as the Marginal Product