Final answer:
In the short run, the production function is represented by the equation Q = f[L]. We can determine the production function by examining the relationship between the quantity of output (Q) and the quantity of labor (L) used. For example, using a table with different quantities of workers (L) and the corresponding quantities of widgets produced (Q), we can derive the production function.
Step-by-step explanation:
In the short run, the production function is represented by the equation Q = f[L]. Since capital is fixed, the production function only depends on the quantity of labor input (L). To solve for the production function, we need to look at the relationship between the quantity of output (Q) and the quantity of labor (L) used.
For example, if we have a table with different quantities of workers (L) and the corresponding quantities of widgets produced (Q), we can determine the production function. Let's say the table shows:
- Widgets (Q): 0.2, 0.4, 0.8, 1
- Workers (L): 1, 2, 3, 3.25, 4.4, 5.2, 6, 7, 8, 9
Based on this data, we can see that as the quantity of labor increases, the quantity of widgets produced also increases. This relationship can be represented by a production function such as Q = 0.2L.