Question

Theresa's Trees is a tree-planting company that charges local governments $1 per tree planted. The number of trees they can plant per day is given by Q=15K^(1/3)L^(1/3). Discuss the factors influencing their daily tree planting capacity.

Answer 1

The daily tree planting capacity of Theresa's Trees is affected by the amount of labor and capital, with labor being a significant variable. As more laborers are employed, productivity increases to a point before diminishing returns are experienced.

Step-by-step explanation:

The daily tree planting capacity of Theresa's Trees is influenced by factors including labor and capital, as represented by the production function Q=15K(1/3)L(1/3). The number of trees planted per day, or Total Product (TP), is a function of the quantity of labor (L) and capital (K). Here, since capital is fixed, the output chiefly depends on labor. For instance, the equation illustrates that if one lumberjack using a two-person saw can cut down four trees in an hour, two lumberjacks with the same equipment can cut down ten trees in an hour, showing increasing productivity with more labor up to a certain point.

As such, labor is a significant factor, and productivity can be expressed numerically—for example, with one lumberjack (as labor), the total number of trees (TP) that can be cut down is specified. However, there are diminishing returns; as more labor is added, the productivity per additional laborer might decrease after reaching an optimum level. This concept demonstrates the relationship between labor, capital, and output in production.