6.1 Why Firms? Entrepreneur, Owner, Manager
Business firms are artificial creations, organized to produce goods and services for the market. But individuals and groups can produce for the market without creating a firm. Why are they formed?
- Take advantage of team production while minimizing costs of contracting. Instead of multilateral contracting, only bilateral (two firms) needs to happen.
- Management acts in the name of the firm, but the owners are the "residual claimants," meaning the ones entitled to the firm's income/assets after all contractual payments are made. Hence, entrepreneurship is an essential feature of firms because managers manage themselves.
- Firms are a specific type of contract among multiple owners that consists of two keys: limited liability (contractual obligations are not personal obligations) and transferable shares (ease of entry and exit). This corresponds to two necessary measures: the need for monitoring and distribution of risk.
Economic vs. Accounting Profit
Economic profit is the difference between total revenue and total cost, though here, the cost includes the opportunity cost (value of best foregone alternative). Economic profit is a signal as to whether a firm should stay in business or shut down-- negative means the resources are better used elsewhere.
Accounting profit is a measure used for controlling fraud and computing tax liabilities. There is no calculation of opportunity cost from the owners' self-supplied services. Another difference is that accounting takes into account depreciation, while economic calculation measures market price.
Separation of Ownership and Control
Managers seem to have very little skin in the game when it comes to profit maximization, since they are hired by the shareholders. However, there is still competition when we realize that shareholders can exercise privileges by voting, competition by other managers who could make more money for the firm, and certain legal restrictions and/or compensation packages that attempt to align incentives.
6.2 The Optimum of the Firm in Pure Competition
Economic profit is mathematically represented by:
\(\Pi \equiv R - C\) where
\(R \equiv P \cdot q\) and
\(C \equiv F + V\)
For a price-taking firm, revenue is market price multiplied by the quantity they can produce, and costs will be the sum of fixed and variable costs. The graphs below exhibit certain features:
- At low output, cost rises with quantity at a decreasing rate (advantages of large-scale production).
- At high output, costs rises with quantity at an increasing rate due to the Law of Diminishing Return.
As for the Revenue side, the Marginal Revenue is the slope of the Total Revenue Curve, and since the firm is a price-taker, this is equal to market price. Since price is constant, we can see that Average Revenue will then be equal to market price as well:
\(MR \equiv \frac{\Delta R}{\Delta q}\)
\(AR \equiv \frac{R}{q}\)
Turning to the cost side, Marginal Cost is the slope along the Total Cost curve. Average Cost is falling when the Marginal Cost lies below it; when the Average Cost is rising, the Marginal Cost lies above it:
\(MC \equiv \frac{\Delta C}{\Delta q}\)
\(AC \equiv \frac{C}{q}\)
Thus, the maximum profit occurs where the Total Revenue and Total Cost curve are parallel:
\(MC = MR = P\)
However, this only works if the MC curve cuts the MR curve from below. Profit then covers the area:
\(\Pi \equiv (AR - AC) \cdot q\)
To complete the curve analysis, we can say that variable cost and average variable costs are defined:
\(VC \equiv C - F\)
\(AVC \equiv \frac{VC}{q} \equiv \frac{C - F}{q}\)
The cost functions below have these properties:
- When \(q = 0\), the marginal cost equals average variable cost.
- Marginal cost is related to average variable cost in the same way as to average cost. When average cost is constant, marginal cost equals average variable cost.
- The minimum of average variable cost is to the left of average cost.
The Shutdown Decision
Even when a firm satisfied the condition \(MC = MR = P\) and the marginal cost curve cuts the horizontal price line from below, Total Revenue could still be less than Total Cost. Should the firm go out of business?
The crucial values are the minimum values of average cost and average variable cost. Whether the firm should shut down depends on whether the decision involves the short (when inputs cannot be changed) or long run (all inputs could be varied). In the short run, a firm should continue if Total Revenue exceeded Total Variable Cost:
\(R \geq VC \), or equivalently \(P \geq AVC\)
In the long run, a firm should continue to operate only if all costs are covered, so the conditions are:
\(R \geq C \), or equivalently \(P \geq AC\)
*Sometimes fixed costs are confused with sunk costs. A sunk cost does not enter calculation of opportunity cost since it would not have alternative uses (i.e. special machinery), whereas fixed costs do enter the analysis, but only at the long-run level since they cannot be changed quickly.
An Application: Division of Output among Plants
Suppose a firm can divide output between factories in Albany and Buffalo,
\(q \equiv q_a + q_b\)
Thus the optimizing rule would be:
\(MC_a = MC_b = MR \equiv P\)
In words, the firm should make the Marginal Costs in the plants equal, when set equal to the price. Then, the output must be chosen to satisfy the condition. This can be shown below in the graphs:
6.3 Cost Functions
Short Run vs. Long Run
The range of inputs taken as fixed costs is actually a matter of degree; in a sense, all costs are variable in the long run. The graph below shows three different cost functions. In the Long-Run Total Cost function, only the lowest cost of producing any given level of output is displayed, because when all costs are variable, the firm can choose the most economical mix of resources:
Some inefficiencies arise when we consider that the fixed inputs are usually not smooth, but rather come in lump-sum payments. Why are there some costs that are fixed? Transaction costs and the specialization of the resources of a firm are the biggest reasons. Thus, even in the face of a temporary demand fluctuation, inputs may be held fixed.
Rising Costs and Diminishing Return
Can falling Average Costs, due to increasing returns to scale, create a "natural monopoly"? No, since both the AC and MC curve must eventually rise according to the Law of Diminishing Returns. This principle explains how holding one input constant means additional production would require increasing amounts of the other inputs. In the short run this is evident, however, in the long run this is the case because not all inputs are readily expandable (i.e. entrepreneurial ability, natural resources).
6.4 An Application: Peak vs. Off-Peak Operation
A firm facing peak and off-peak demands (i.e. restaurant during times of the day or seasons) must decide how to divide its efforts between the two. To do this, we must distinguish between common costs, which are present in both peak and off-peak times, and separable costs that are incurred during specific periods. Both of these types can be fixed or variable costs.
It turns out that there are two different types of solutions: stable-peak and shifting-peak cases:
In the stable-peak solution of the first graph, Marginal Common Cost is counted as already having occurred, thus the off-peak period is simply a by product of the total function. Thus, only separable costs are relevant for the off-period output decision. The optimal off-peak output is determined by \(MC = MSC = P\). During the on-peak period, both common and separable variable costs are incurred, thus the marginal cost is higher, the vertical sum: \(MC_P = MCC + MSC\).
In the shifting-peak solution of the second graph, if the Marginal Common Costs exceeds the price difference between the periods \(MCC > P_P - P_0\), the profit-maximizing peak and off-peak outputs are equal. This is determined by setting the joint Marginal Cost equal to the price difference: \(MC_j = MCC + 2MSC = P_P + P_0\).