The Production Function and Diminishing Returns: Videos & Practice Problems

The production function is a crucial concept in economics that illustrates the relationship between inputs, such as labor, and the output produced. Specifically, it helps us understand how the addition of workers affects the total quantity of goods produced, which in this case is represented by the number of pizzas made in a pizza shop.

One key term in this discussion is the marginal product of labor (MPL), which refers to the additional output generated by adding one more worker. This concept can be thought of as the "fruits of our labor," indicating how much extra production results from hiring an additional employee. For example, if a pizza shop starts with no workers and then hires one, resulting in the production of 30 pizzas, the MPL for that first worker is 30 pizzas. As more workers are added, the MPL can change significantly.

To illustrate this, consider a scenario where a pizza shop has two ovens and hires workers at a wage of $80 per day. Initially, with no workers, no pizzas are produced. When the first worker is hired, production increases to 30 pizzas. Hiring a second worker raises output to 80 pizzas, yielding an MPL of 50 pizzas (80 - 30). The third worker increases production to 150 pizzas, resulting in an MPL of 70 pizzas (150 - 80). However, as more workers are added, the additional output per worker begins to decline. The fourth worker only adds 30 pizzas (180 - 150), and the fifth worker adds just 10 pizzas (190 - 180).

This phenomenon leads to the law of diminishing returns, which states that as more variable inputs (like labor) are added to fixed inputs (like ovens), the additional output produced by each new worker will eventually decrease. In our example, with only two ovens available, the workers may start to interfere with each other's productivity, leading to less efficient operations.

Graphically, the production function can be represented with the number of workers on the x-axis and total pizzas produced on the y-axis. The slope of this graph at any point represents the MPL. Initially, as more workers are added, the slope is steep, indicating increasing returns. However, as diminishing returns set in, the slope becomes less steep, reflecting the reduced productivity of additional workers.

In summary, understanding the production function and the marginal product of labor is essential for analyzing how labor inputs affect output. The law of diminishing returns highlights the limitations of adding more workers when fixed resources are constrained, emphasizing the importance of balancing labor and capital for optimal production efficiency.

In analyzing costs associated with production, it's essential to differentiate between fixed and variable costs. Fixed costs remain constant regardless of output levels; for instance, the cost of ovens in a pizza business is a fixed cost of $100 per day. This means that no matter how many pizzas are produced, the cost of the ovens does not change.

On the other hand, variable costs fluctuate with production levels. In this scenario, the variable cost is determined by the number of workers hired, each earning a wage of $80 per day. Therefore, if no workers are hired, the variable cost is $0. As workers are added, the variable cost increases proportionally: one worker incurs a cost of $80, two workers cost $160, three workers cost $240, and so forth, following the formula:

Variable Cost = Number of Workers × Wage per Worker

To find the total cost of production, one must sum the fixed and variable costs:

Total Cost = Fixed Cost + Variable Cost

For example, with one worker, the total cost would be $100 (fixed) + $80 (variable) = $180. This pattern continues as more workers are added, leading to total costs of $260, $340, $420, and $500 for two, three, four, and five workers, respectively.

Next, to determine the average cost per pizza, the total cost is divided by the quantity of pizzas produced. This average total cost can be calculated as follows:

Average Total Cost = Total Cost / Quantity of Pizzas

For instance, with a total cost of $180 for 30 pizzas, the average cost per pizza is $6. As production increases, the average cost per pizza can decrease, reflecting economies of scale. However, as diminishing returns set in—where adding more workers yields less output—the average cost per pizza may begin to rise again. This relationship highlights the importance of understanding marginal product, which refers to the additional output generated by adding one more unit of input (in this case, a worker).

In summary, as the marginal product increases, the average cost tends to decrease, but once diminishing returns occur, the average cost starts to rise. This dynamic illustrates the balance between input and output in production economics.