Final answer:
The choice between the proportional and incremental methods for allocation depends on the specific situation. The former looks at costs in relation to each other, while the latter considers the additional gains or costs of one option over another. A cost-benefit analysis of production methods shows Method 1 as the most cost-effective initially, which may change with fluctuating labor costs.
Step-by-step explanation:
The decision to use the proportional method versus the incremental method for allocation often depends on the context of the allocation problem. In budgeting and resource allocation within a company, for instance, these methods would guide how incremental resources affect the potential gains or losses in the productivity or efficiency of the company's operations.
When we consider the scenario with different methods of production involving units of labor and capital: Method 1 (50 units of labor, 10 units of capital), Method 2 (20 units of labor, 40 units of capital), and Method 3 (10 units of labor, 70 units of capital), we must evaluate costs to decide the best production method. Initially, if hiring labor for the winter costs $100/unit and a unit of capital costs $400, we would calculate the total costs for each method like so:
- Method 1: (50 * $100) + (10 * $400) = $5000 + $4000 = $9000
- Method 2: (20 * $100) + (40 * $400) = $2000 + $16000 = $18000
- Method 3: (10 * $100) + (70 * $400) = $1000 + $28000 = $29000
From this analysis, Method 1 is the most cost-effective. However, if the cost of labor rises to $200/unit, the calculations and consequently the most cost-effective method may change.
It's important to note that while the proportional method considers costs relative to each other, the incremental method would look at the additional cost or benefit gained from choosing one option over another. Given relatively large gains could be expected initially, but if resources are already largely committed, further commitments may bring relatively smaller gains.