8.2 short run production function

• In the short run, at least one input (usually capital) is fixed, while others (like labor) can be varied.
• Diminishing marginal returns occur when increasing the variable input (e.g., adding more workers) leads to smaller and smaller increases in output because the fixed input (e.g., machines) cannot be expanded.
• Total Product: The total quantity of output produced by a given number of workers (labor input).
• Average Product (AP): The output per worker, calculated by dividing the total output by the number of workers.
• Marginal Product (MP): The extra output produced by one additional unit of labor, calculated by subtracting the total output of the previous labor input from the current one.
• average product = total product / labour input
• marginal product = ∆ total product / ∆ labor input
• Law of Diminishing Marginal Returns:

  • In the short run, increasing the quantity of a variable input (e.g., labor) while keeping at least one input fixed (e.g., capital) will eventually lead to a point where additional units of the variable input result in smaller increases in output.
• Why Diminishing Returns Occur:

  • As more workers are added to a fixed amount of capital, each worker has less capital to work with. This leads to overcrowding or inefficient use of resources, so each additional worker contributes less to output than the previous one.
• Marginal Product and Efficiency:

  • Initially, adding more workers increases efficiency (e.g., through specialization), but after a certain point, the fixed capital becomes a constraint, and efficiency declines.
• • Rising Marginal Product: Initially, the marginal product increases (up to the 3rd worker in this example), as each additional worker adds more to output.
  • Diminishing Marginal Returns: After a certain point, adding more workers results in diminishing marginal returns. The marginal product begins to decline after the 4th worker, as the fixed input (capital) becomes a constraint.
• • Relationship between Average and Marginal Product:
  • When the marginal product is above the average product, the average product is increasing.
  • When the marginal product is below the average product, the average product begins to decline.
  • This relationship helps determine when diminishing returns set in.
• Top Graph (Total Output Curve):

  • The x-axis shows the number of workers (labor input).
  • The y-axis shows the total output (goods produced per week).
  • Point A: As more workers are added, output increases at a rising rate due to specialization. Workers can focus on specific tasks, increasing efficiency.
• total output curve:

  Point B: After point A, output still increases but at a diminishing rate (this is the point of diminishing marginal returns). Here, each additional worker contributes less to total output because the fixed capital (e.g., machines) is already fully utilized.
• total output curve:

  Beyond Point B: Adding even more workers leads to no increase in output and may even cause output to decline (if workers get in each other's way or the workplace becomes overcrowded).
• • Rising Marginal Product: Initially, the marginal product increases (up to the 3rd worker in this example), as each additional worker adds more to output.
  • Diminishing Marginal Returns: After a certain point, adding more workers results in diminishing marginal returns. The marginal product begins to decline after the 4th worker, as the fixed input (capital) becomes a constraint.
• • Relationship between Average and Marginal Product:
  • When the marginal product is above the average product, the average product is increasing.
  • When the marginal product is below the average product, the average product begins to decline.
  • This relationship helps determine when diminishing returns set in.
• Law of Diminishing Marginal Returns:

  • In the short run, increasing the quantity of a variable input (e.g., labor) while keeping at least one input fixed (e.g., capital) will eventually lead to a point where additional units of the variable input result in smaller increases in output.
• Why Diminishing Returns Occur:

  • As more workers are added to a fixed amount of capital, each worker has less capital to work with. This leads to overcrowding or inefficient use of resources, so each additional worker contributes less to output than the previous one.
• 1. Marginal Product and Efficiency:

  • Initially, adding more workers increases efficiency (e.g., through specialization), but after a certain point, the fixed capital becomes a constraint, and efficiency declines.
• Application in Production Decisions:

  • Firms must consider the point at which adding more labor leads to diminishing returns. In the short run, there’s a limit to how much output can be increased by simply adding more workers, especially if capital cannot be expanded.
  • This is important for determining the optimal number of workers and the level of production that maximizes profit without incurring excessive labor costs that do not result in proportional increases in output.