A Gardening Story

Suppose it is early spring and it is time to prepare the family backyard garden for the first planting of the year. The father in the household sets aside one Sunday afternoon to do the job but hopes to complete the job as quickly as possible. Preparation of the garden requires the following tasks. First, the soil must be turned over and broken up using the roto-tiller, then the soil must be raked and smoothed. Finally, seeds must be planted or sowed.

This year the father's seven-year-old son is anxious to help. The question at hand is whether the son should be allowed to help if one's only objective is to complete the task in the shortest amount of time possible.

At first thought, the father is reluctant to accept help. Clearly each task would take the father less time to complete than the time it would take the son. In other words, the father can perform each task more efficiently than the seven-year-old son. The father estimates that it will take him three hours to prepare the garden if he works alone, as shown in the following table.

Task -----------Completion Time (hours)
Roto-Tilling ----------1.0
Raking ----------1.0
Planting ---------1.0
Total -------------3.0



On second thought, the father decides to let his son help according to the following procedure. First the father begins the roto-tilling. Once he has completed half of the garden, the son begins raking the roto-tilled section while the father finishes roto-tilling the rest of the garden plot. After the father finishes roto-tilling he begins planting seeds in the section the son has already raked. Suppose the son rakes slower than the father plants, and that the father completes the sowing process just as the son finishes raking. Note this implies that raking takes the son almost 2 hours compared to one hour for the father. However, because the son's work is done simultaneously with the father's work, it does not add to the total time for the project. Under this plan the time needed to complete the tasks in shown in the following table.

Task --------Completion Time (hours)
Roto-Tilling ----------1.0
Raking & Planting ----1.0
Total-------- 2.0



Notice that the total time needed to prepare the garden has fallen from 3 hours to 2 hours. The garden is prepared in less time with the son's help than it could have been done independently by the father. In other words, it makes sense to employ the son in (garden) production even though the son is less efficient than the dad in every one of the three required tasks. Overall efficiency is enhanced when both resources (the father and son) are fully employed.

This arrangement also clearly benefits both the father and son. The father completes the task in less time and thus winds up with some additional leisure time which the father and son can enjoy together. The son also benefits because he has contributed his skills to a productive activity and will enjoy a sense of accomplishment. Thus both parties benefit from the arrangement.

However, it is important to allocate the tasks correctly between the father and the son. Suppose the father allowed his son to do the roto-tilling instead. In this case the time needed for each task might look as follows.

Task ---------Completion Time (hours)
Roto-Tilling------------ 4.0
Raking ---------1.0
Planting ---------1.0
Total -----------6.0



The time needed for roto-tilling has now jumped to 4 hours because we have included the time spent traveling to and from the hospital and the time spent in the emergency room! Once the father and son return, the father must complete the remaining tasks on his own. Overall efficiency declines in this case compared to the father acting alone.

This highlights the importance of specializing in production of the task in which you have a comparative advantage. Even though the father can complete all three tasks quicker than his son, his relative advantage in roto-tilling greatly exceeds his advantage in raking and planting. One might say that the father is most-best at roto-tilling while he is least-best at raking and planting. On the other hand, the son is least-worse at raking and planting but most-worse at roto-tilling. Finally, because of the sequential nature of the tasks, the son can remain fully employed only if he works on the middle task, namely raking.

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