Final answer:
To graph a short-run production function with one variable resource, plot the increases in total product due to additional labor input, showing initial increasing marginal returns, followed by diminishing marginal productivity as more input is added.
Step-by-step explanation:
To graph a short-run production function with one variable resource and show the correct relationships between total product, average product, and marginal product, we must consider the input of the variable resource and the resulting output. For instance, in the production of trees, if we start increasing labor from zero, initially, the total product will increase at an increasing rate because of increasing marginal returns due to specialization.
Next, as more workers are added, the total product continues to rise but at a decreasing rate. This is visible on a graph as a curve that first steepens and then gradually flattens out as the quantity of the input (e.g., number of barbers) increases. This change in the slope represents the diminishing marginal productivity which occurs because each additional unit of the variable input contributes less to the overall production. When plotted, the marginal product curve starts high and gradually decreases, eventually becoming negative.
The average product is calculated by dividing the total product by the number of units of the variable input. On a graph, the average product curve starts at zero, rises to its peak, and eventually falls as the total product curve begins to increase at a decreasing rate.
If we consider costs, we see that total costs and variable costs rise with production. Initially, as output increases due to increasing marginal returns, variable costs increase at a decreasing rate. But as diminishing marginal returns set in, variable costs increase at an increasing rate. Understanding these relationships and analyzing patterns of costs is crucial to determining potential profit in the short run.
Graph Interpretation
- The point where the average product and marginal product curves cross represents the highest point of the average product curve.
- The region where the marginal product is above the average product indicates increasing average product.
- When marginal product falls below average product, it indicates decreasing average product and inefficiencies in production.