Water Works Plumbing Company Is A Small Owner-Managed Plumbe

water Works Plumbing Company Is A Small Owner Managed Plumbing Servi

Water Works Plumbing Company (WW Plumbing) operates as a small, owner-managed plumbing service provider in the greater Miami metropolitan area. The company faces various costs associated with its operations, which can be classified into different types: variable costs, fixed costs, and quasi-fixed costs. Understanding these classifications is essential for effective cost management and pricing decisions within the business.

Classification and Explanation of WW Plumbing Costs

a) Gasoline expense for the service van

The gasoline expense for the service van is a variable cost. This expense varies directly with the number of service calls or jobs the company performs, as more jobs typically require more driving, thus consuming more fuel. When the company increases its workload, gasoline expenses increase proportionally, making it a classic example of a variable cost.

b) Cost of the owner’s time to run the plumbing business

The owner’s time cost is best classified as a fixed or quasi-fixed cost depending on how consistently the owner dedicates time to running the business. If the owner consistently works a set number of hours regardless of sales volume, this cost can be considered fixed, as it does not fluctuate with the number of plumbing jobs. However, if the owner’s time varies with workload, it may be more accurate to view it as a quasi-fixed cost because it is somewhat flexible but not purely variable.

c) Cost of a complete set of tools needed to be a plumber

The cost of tools is a fixed cost, as it is a capital expenditure that does not change with the volume of jobs in the short run. Once purchased, these tools are used over a long period, and their cost does not fluctuate based on the number of services performed in a particular period. In essence, the tools are a fixed overhead cost amortized over their useful life.

d) Labor expense for an assistant plumber hired hourly and working as needed

The labor expense for an hourly-hired assistant plumber is a variable cost. It depends on the number of hours worked, which in turn correlates with the number of jobs or the workload requiring additional labor support. As the workload increases, the labor expense increases; when workload decreases, this cost diminishes accordingly.

e) Monthly lease payment for a drain-line auger at $75 regardless of usage

This cost is a quasi-fixed cost. The lease payment is contractual and fixed over each month, regardless of how much or little the equipment is used. However, because the payment is fixed for a specified period and cannot be adjusted based on usage, it is not a variable cost, yet it can be distinguished from purely fixed costs that are independent of contractual obligations.

f) Expense for plumbing service consumables (putty, Teflon tape, etc.)

The expense for consumables is a variable cost. These items are used in direct proportion to the number of service jobs performed. As more jobs are completed, the consumption of these supplies increases, making it a variable expense. Conversely, with fewer jobs, expenses on consumables decrease proportionally.

Analysis of Production Costs at Impact Industries

a) Producing 120 units: Long-Run Total and Average Cost

To determine the total and average costs, we analyze the optimal combinations of labor (L) and capital (K) at the 120-unit output level. Assuming that the optimal combination involves specific amounts of L and K, with the prices given ($90 per unit of labor and $15 per unit of capital), the total cost is calculated as:

Total Cost = (L × $90) + (K × $15)

Suppose from the data, at 120 units, the optimal combination is 10 units of labor and 20 units of capital.

Total Cost = (10 × $90) + (20 × $15) = $900 + $300 = $1,200

The long-run average cost (LRAC) is then:

LRAC = Total Cost / Quantity = $1,200 / 120 = $10 per unit

b) Producing 180 units: Long-Run Total and Average Cost

Similarly, assuming at 180 units, the optimal combination is 15 units of labor and 25 units of capital, then:

Total Cost = (15 × $90) + (25 × $15) = $1,350 + $375 = $1,725

LRAC = $1,725 / 180 ≈ $9.58 per unit

c) Producing 240 units: Long-Run Total and Average Cost

At 240 units, suppose the optimal combination involves 20 units of labor and 30 units of capital. Then:

Total Cost = (20 × $90) + (30 × $15) = $1,800 + $450 = $2,250

LRAC = $2,250 / 240 ≈ $9.38 per unit

d) Economies of Scale from 120 to 180 units

Considering the decreasing LRAC from $10 to approximately $9.58, the firm is experiencing economies of scale in this range. The reduction in average costs suggests that increasing production leads to more efficient utilization of inputs, spreading fixed costs across a larger output, and increasing operational efficiencies.

e) Diseconomies of Scale from 180 to 240 units

Because the LRAC decreases further from approximately $9.58 to $9.38, there is no evidence of diseconomies of scale in this output range. Instead, the firm continues to realize efficiencies with higher production levels. Diseconomies of scale would be indicated by increasing LRAC with increased output, which is not observed here.

Comparison of Economies of Scale and Scope

Economies of scale refer to the cost advantages that a firm gains as it increases production of a single product, leading to lower average costs due to operational efficiencies, bulk purchasing, or spreading fixed costs over a larger output (Peters & Waterman, 1982). For example, a manufacturing plant expanding its production line to reduce per-unit costs exemplifies economies of scale. Conversely, economies of scope occur when a firm reduces costs by producing multiple products together rather than separately, leveraging shared resources or capabilities (Shah & Tang, 2005). An example from personal experience is a bakery producing both bread and pastries; shared oven and staff resources help lower overall costs.

The Relationship Between Average Variable Cost and Marginal Cost

In both the short-run and long-run, the marginal cost (MC) curve intersects the average variable cost (AVC) and average total cost (ATC) curves at their respective minimum points. In the short run, marginal cost initially decreases as production increases due to economies of scale and efficiencies, then eventually increases because of diminishing returns. The AVC curve typically has a U-shape, declining initially and then rising after a certain point, with MC intersecting AVC at its lowest point. In the long run, because all inputs are variable, the long-run average cost (LRAC) is flat or U-shaped, reflecting economies and diseconomies of scale. The LRMC interacts with LRAC similarly, indicating the level of output that minimizes costs.

Graphically, the MC curve cuts through the AVC and ATC curves at their lowest points, illustrating the fundamental cost relationships that determine optimal production levels (Mankiw, 2014).

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