Econ 310

Unforeseen inflation
Unpredictable changes in technology
Unpredictable changes in input and output market prices and conditions
Difference between accounting and economic cost measures
- Economic worth is measured by profit-generating capability
- Economic cost includes opportunity cost, which requires that we not only understand actions taken, but also understand actions not taken
Historical cost indicates market conditions at time of purchase, and is used in tax analysis, while current cost, which reflects current market conditions, is more relevant in valuation and cost analysis at the managerial level. Current costs can be represented by replacement cost, which is the cost of replacing the productive capability of the capital item at current market prices.

The opportunity cost of an asset (or, more generally, of a choice) is the highest valued opportunity that must be passed up to allow current use. Thus the monthly opportunity cost of a latte cart owned by Isabel may be, for example, the monthly income the cart could have generated if Isabel had rented the cart for someone else to use.

Explicit costs are expenses for which one must pay with cash or equivalent. Because a cash transaction is involved, they are relatively easily accounted for in analysis.

Implicit costs do not involve a cash transaction, and so we use the opportunity cost concept to measure them. This analysis requires detailed knowledge of alternatives that were not selected at various decision points. Relevant here are the opportunity cost of the firm's assets and cash, and of the owner's time invested in the firm.

Incremental and Sunk Costs in Decision Analysis

Incremental cost is the change in cost caused by a particular managerial decision. Thus the increment is at the decision level, and may involve multiple units of change in output or input. Incremental costs may be involved when considering a product or service modification or a change in production process.

Sunk costs are those parts of the purchase cost that cannot later be salvaged or modified through resale or other changes in operations. Image advertising for a new product is a classic example of a sunk cost, as is an option or investment in assets whose value is specific to a particular situation. Sunk costs reflect commitment, or irreversibility, and so are not a part of incremental analysis.

Short-Run and Long-Run Costs

In microeconomics and managerial economics, the short run is the decision-making period during which at least one input is considered fixed. The fixed input is commonly considered to be some aspect of capital, such the production facility, but may also be a normally variable input that is fixed because of production technology requirements, or a contractual commitment (e.g., a facility lease) related to production. So when one refers to short-run analysis, the analysis is focused on a planning period in which some input is fixed and others are variable, and the manager is selecting levels of variable input and production output to optimize given the constraint of the fixed input.

The actual time period that makes up the economic short run depends on how long the fixed input remains fixed. A pizza shop whose primary fixed input in the short run is their lease on their facility has a short-run planning horizon equal to the period of time remaining in their lease, which may be 6 months or 2 years. A utility with a new coal-fired electric generating plant faces an economic short run planning period for that plant that may span 20 years or more. At Arcata's Foodworks business incubator, which offers leased commercial kitchen spaces for startups, entrepreneurs typically install use-specific modifications to the space for their particular needs, and so the lease commitment (and so the short-run planning horizon) may be 1-3 years or more.

In contrast, the economic long run is a planning horizon that looks beyond current commitments to a future period in which all inputs can be varied. A typical long-run analytical problem is the decision of whether to adjust capacity, seek a larger (or smaller) facility, to change product lines, or to adopt a new technology.

At any given time managers must be concerned with both short-run and long-run analysis. Firms must be concerned with both the problem of optimizing in the current (short-run) situation as well positioning the firm for optimizing in the future (long-run).

By definition, fixed costs do not vary with the volume of goods or services produced as output. Fixed costs are the costs associated with the fixed inputs that define the economic short run. Thus fixed costs are only relevant in the economic short run. Even if the firm temporarily shuts down, it still continues to incur the fixed cost expense. This is typical of capital loans or facility lease agreements.

Variable costs, in contrast, vary (usually directly) with the volume of good or services produced as output, and thus can be avoided by a temporary shutdown.

Short-Run Cost Curves

We can see the relationships between these various costs a bit more clearly if we plot them:

In the diagram above, we can see that the vertical difference between TC and TVC is equal to TFC, which is constant (thus TC and TVC are parallel). Lets have a look at a plot of the average and marginal cost relations:

Note here that the vertical difference between AC and AVC is equal to AFC, similar to the situation with the total cost relations, but the key difference is that AFC declines (monotonically) as Q rises -- there is more output over which to 'spread' the TFC, and thus AFC declines. This was the argument given for why the cost/jet for fancy new military jets declines as more are ordered -- the fixed R&D and setup costs are spread across more jets.

Another relation that is important to notice is that marginal cost crosses the average costs at their minimum point. The story here is that marginal pulls average down when marginal is less than average, and pulls average up when marginal is above average. Thus if marginal drops below average, but then rises faster than average, it must cross the average curves at their minimum points. Consider the analogy between cumulative average grade point average (GPA) and semester (marginal) GPA. If semester GPA is less than the cumulative average, it pulls the average down, while if semester GPA is greater than the cumulative average, it pulls the cumulative average up. Note too that the larger is 'Q', the less impact the marginal has on the average. The metaphor for 'Q' would be semesters in the GPA analogy.

Long-Run Cost Curves

Here we will discuss issues relating returns to scale (production) to economies of scale (costs). We will also discuss the long-run average cost curve (LRAC) as the lower envelope of the set of all possible short-run average cost (SRAC) curves. These points will then lead us to the concept of minimum efficient scale. A key long-run issue addressed here is planning associated with changes in scale of operation.

Recall that returns to scale relates to productivity of inputs. Thus increasing returns to scale occurs when the output elasticity is greater than 1 -- when, for example, a 10% increase in input usage results in more than a 10% increase in output. Increasing returns to scale occur when the economies of specialization outweigh the diseconomies of congestion in a given production facility. Decreasing returns to scale occur, on the other hand, when a 10% increase in input usage results in less than a 10% increase in output. Decreasing returns to scale occur when the diseconomies of congestion outweigh the economies of specialization.

Increasing returns to scale means that the total product (TP) curve is rising at an increasing rate, and that marginal product (MP) is rising. Decreasing returns to scale occur when TP is rising at a decreasing rate (or is actually declining), and MP is declining.

It ends up that there is a linkage between returns to scale on the production side, and economies of scale on the cost side. Economies of scale occur when average cost (AC) is declining as Q rises, while diseconomies of scale occur when AC is rising as Q rises.

Take a moment and try to figure out the story for why increasing returns to scale imply economies of scale, and why decreasing returns to scale imply diseconomies of scale. Hint: its easiest to see when marginal factor cost (e.g., hourly labor cost) is fixed, and so marginal cost is inversely related to marginal product.

To see this duality between production and cost, lets expand the example given above to include a variable factor X used in relatively large amounts to produce a given unit of output Q:

Compare the two diagrams below. We can then see that marginal cost (MC) rises when marginal product (MP) falls, and MC falls when MP rises:

Thus when there are economies of scale there is an incentive for firms to grow larger because increasing Q results in lower unit cost (AC), and thus allows the firm to be more price competitive with its rivals. That's why we rarely see firms operating when there are returns to scale in production -- there is an incentive to exploit them and grow larger.

Next, lets discuss the notion of the long-run average cost curve (LRAC). The LRAC is the lower envelope of the efficient short-run average cost curves for all different scales of operation for a firm. The term 'lower envelope' simply means that at any given production level, in the long run the firm can select the technology appropriate for that production level, and thus placing it on the minimum point on the most efficient short-run average cost curve. Thus the LRAC is made up of the minimum points on all the short-run average cost curves that would be efficient for various possible output levels.

Minimum Efficient Scale

Firm Size and Plant Size

In most consumer products markets there is multiplant production by a particular firm. For example, a brewer facing relatively high transportation costs may find it advantageous to have regional breweries. This in fact is the case with the major national breweries in the US. This is an example of a situation featuring multiplant economies of scale, meaning that it is more economical to increase output by increasing the number of production plants than to increase the scale of existing facilities. In addition to transportation costs, most production facilities will eventually experience diseconomies of scale -- they just get too big to be efficiently managed. Either way, what happens is that the average cost curve for a single production plant grows steeply, creating an incentive to shift output growth to a new facility.

You can see that average unit cost of production (including distribution costs) is actually lower at 8000 units (per day) when two smaller plants are used than when one big plant is used.

Another problem confronting a multiplant operation producing the same good or service is to correctly set output across the multiple plants. The solution to this problem calls for the application of a microeconomic concept called the equimarginal principle. This principle calls for each plant to produce at the same marginal cost level, which, if the plants have different cost structures, will generally call for them to produce at different output levels.

If this firm is producing a good for sale in a highly competitive market where price is currently $12, for example, then each plant should be operated at an output level at which MR = MC. Since MR = P in a competitive market, the equimarginal principle would call for each plant to operate where P = MC = $12. To prove this to yourself, suppose (for simplicity) that each plant has a fixed cost of 100. Add up the marginal costs to get TVC, add that to TFC = 100 to get TC. Calculate profit (PxQ) at the indicated output level when price = $12, and determine whether it is possible to re-allocate production and raise profit.

Learning Curves

Average costs may decline with cumulative production because of managerial and other learning effects. Simply speaking, experience with a particular set of suppliers, production process, facility, workforce, distribution network, and manageral team can result in improvements in technical efficiency.

Economies of Scope

Economies of scope refer to a situation in which average costs (unit costs) are lower when two complementary products are produced by a single enterprise (either the same facility, the same management team, the same firm or trademark owner, or the same proximate location) than when they are produced separately. This economy to joint production is fairly common. Universities are conglomerations of different colleges, each of which produce different forms of educational experience. In this case the economy to joint production has to do with the concept of a liberal education, in which students are advantaged by having contact with classes from outside their major area. Moreover, each college benefits from the umbrella brand of the university name. Othe examples of economies of scope include mutual fund firms that include a range of investment vehicles (e.g., from stock funds to checkable money market funds) that investors can switch to and from over time. The economy to joint production here is the ease with which one can transfer funds across investment vehicles within a given family of funds. Another example of umbrella branding is in ready-to-eat (RTE) breakfast cereal, where firms have an array of goods in product type space that lessen outside competition -- its easier to collude with yourself than with others. An athletic shoe store may also offer athletic socks and apparel because the complementary nature of the goods lowers shopping costs for consumers.

Cost-Volume Profit Analysis

This is simply a fancy name for breakeven analysis, which is a common and useful analytical tool for determining the viability of new products. Simply put, breakeven analysis is about determining profit at various projected sales volume levels, identifying the breakeven point, and making a managerial decision regarding the relationship between likely sales and the breakeven point.

We can relatively easily derive the breakeven quantity. Recall that AVC = TVC/Q. Then the breakeven quantity, Qb, occurs where:

This is relatively easily computable by firms because TFC and AVC are more readily available than MC.

3 Oct 2000

Cost Analysis

Lecture Outline

Lecture Notes

Difficulties in Cost Analysis

Opportunity Costs