Profit maximizing decisions depend on accurate estimates and projections of costs. Examples: What would be the cost of increasing production by X%, what is the impact on production costs if input costs increase by X%, what production changes will reduce costs, etc.
These examples illustrate the important role that cost analysis plays in managerial decisions, and how costs affect profits, etc. We consider several issues related to COSTS:
RELEVANT COSTS
The only factors to consider are always the relevant costs and the relevant benefits, which are the differential (marginal) costs and benefits of alternative courses of action.
Opportunity Cost (OC)
OC is always one of the relevant costs for decision making. OC is defined as the benefits foregone in the next highest valued alternative. For example, if you are making an exclusive choice between A and B (movies, jobs, vacations, majors, etc.), the OC of choosing A (B) is B (A). Examples:
1. What is the OC of getting an MBA degree?
a. Explicit, Monetary cost:
b. Implicit OC (foregone benefit):
2. What is the OC of using excess factory capacity to supply specialty orders?
What is the foregone benefit of using the factory to supply specialty orders?
3. What is the OC of city-owned land that will be used as the site for a downtown parking garage?
Foregone benefit:
Application of using OC for optimal decision making: Pursue activities ONLY when the incremental (marginal) benefits exceed the incremental (marginal) costs. Applies to individuals, households, organizations, governmental units, etc. Pursue an MBA ONLY if the MB > MC (including OC).
Economic Profit vs. Accounting Profit
Accounting profit = TR - TC (explicit, accounting costs) = NIAT (after-tax profits, earnings). Most of the time, when the word "profit" is used, we are referring to accounting profits (NIAT). Accounting profits are important to managers, shareholders, govt. (for taxes), etc. However, managerial decisions should not be based only on accounting profits, but should always include the more comprehensive concept of "economic profits."
Economic Profits = TR - TC (explicit accounting costs + implicit costs, including OC). Managerial decisions should always be based on Economic Profits, not accounting profits.
Example, p. 255, "Starting a Business."
Accounting Profit from new business = $74,000 (explicit costs only)
Opportunity costs:
a) Foregone interest on $80,000 personal funds tied up in business @ 8% = $6400 per year.
b) Foregone income at current job = $56,000
Economic Profit from new business = $11,600
Other considerations:
Benefits: Being your own boss
Costs: Uncertainty of starting a new business, especially during the first few years.
Long Run Condition: ZERO ECONOMIC PROFIT.
Remember that Accounting Profit can only go two places:
a.
b.
Firm can get investment capital from two sources: Debt or Equity, and must pay its bondholders and stockholders a normal, risk-adjusted rate-of-return for those funds, otherwise it won't attract any investment capital. When the firm pays interest to its bondholders, it gets to deduct the interest payment as a tax-deductible business expense. However, due to IRS code, a firm cannot deduct dividend payments to shareholders. Dividends get paid out of after-tax profits (NIAT), leading to the double-taxation of corporate earnings (taxable at both the corporate and individual levels). Assume that all NIAT gets paid out as Dividends, and that 10% is the normal, risk-adjusted rate-of-return that investors expect from equity in all industries. Three possibilities:
a. Stocks in Industry A pay a higher-than-normal 15% rate of return to shareholders, i.e. profits are above normal. What will happen in Industry A to the number of firms, amount of competition, level of output, prices, etc.?
b. Stocks in Industry B pay a lower-than-normal 5% rate of return, i.e. profits are below normal. What will happen in Industry A to number of firms, output, prices, etc.?
c. Stocks in Industry C pay a normal 10% rate of return, based on normal profits. What will happen in Industry C?
POINT: ZERO ECON PROFITS IN LONG RUN.
Fixed and Sunk Costs
General Rule: Ignore FC and Sunk Costs. Reasons:
For costs that are fixed, costs will NOT vary with respect to different courses of action, and so the differential (marginal) cost = 0 for FC. Only differential costs are relevant for managerial decisions.
Example: Should a company retain its current production method OR switch to a new method that will save on labor costs with a modification to existing equipment. Ignore all FC (cost of original equipment, costs of raw material, selling expenses, advertising, etc.), and consider only differential costs and benefits: the cost to modify the equipment (cost) and the reduction in labor costs (benefit).
Sunk Costs are similar to FC, in that they represent costs that do NOT play a relevant role in managerial decisions. Sunk cost = an expense that: a) has already been incurred, and b) cannot be recovered.
Example: You paid $120,000 for your house, and now the most you can get is $100,000.
It is often difficult to ignore sunk costs, they can often incorrectly sneak into decision making.
Example: A firm spends $20m on R&D for a new product over many years. Now an additional $10m is needed to complete a prototype. Should the firm consider the original $20m investment? No, because it is a sunk cost and cannot be recovered whether the firm markets the new product or not. The firm should look only at the product's current expected future revenue compared to the current marginal (incremental) additional costs of bringing the product to the market.
For example, if the current expected revenue is $15m compared to the $10m cost, then the firm should continue with the project, even though the expected loss will be $15m - $30m = -$15m. If they consider the sunk cost of $20m and abandon the project, the loss be even greater, -$20m.
Application of OC for bookstore. Two scenarios: a) Excess Capacity vs. b) Limited Capacity. A new, best seller book has demand equation: P = 24 - Q, where P is the price in dollars and Q is hundreds of books sold per month. The cost per book is $12.
Scenario 1: There is excess shelf space to stock the new book. Set MR = MC:
24 - 2Q = $12 and Q* = 6 hundred and P* = $18. Profit = $3,600 per month, Table 7.1, p. 260, part (a).
Scenario 2: There is limited shelf space, so that stocking the new best seller will take valuable shelf space, sales, and profits away from other books. The opportunity cost of each copy of the best seller is $4 in foregone profits from selling one of the other books. Therefore, the total cost of selling each new book is $12 + $4 (OC) = $16. Set MR = MC:
24 - 2Q = $16 and Q* = 4 hundred and P* = $20. Profit = $1600 per month (part b). The store should order fewer books and charge a higher price, after taking into account the OC of lost sales of other books. Notice that if they do NOT take into account OC, and continue to order 600 books and charge $18 as in Scenario 1, the profit will be less ($1200 instead of $1600, see part b in brackets).
Scenario 3: After receiving the order of 400 books in Scenario 2, actual sales of the "best" seller are disappointing, and actual demand is determined to be: P = 18 - 2Q. Books can be returned to the publisher for a $6 refund. New decision is: How many books (if any) should be returned and how many should be sold and at what price?
The original $12 price per book is a sunk cost and should be ignored, and ONLY the OC of keeping and selling the new book should be considered: $4 foregone profit + $6 foregone refund = $10. Set MR = MC:
18 - 4Q = $10 and Q* = 2 hundred and P* = $14. The other 200 books should be returned for a $1200 refund, resulting in an optimal loss of -$1600 (part c). Notice that selling ALL of the books or returning ALL of the books would result in a loss of -$2400, part (c).
COST OF PRODUCTION
A firm's cost function [C = f (Q)] summarizes the firm's TC of producing a given level of output (Q), assuming the least-cost production. Cost information is a distillation of production information, and combines information in the production function [TP = f (Q)], with information about input prices.
Short-run (SR) Costs
In SR, remember that one or more inputs are fixed, not flexible.
Consider a firm that provides electronic repair services TC = FC + VC.
Fixed Costs. FC = costs incurred even when Q = 0, such as: overhead expenses, lease payments for factory space, lease payments for equipment, some energy costs, property taxes, licenses, fees, memberships, administrative costs for support staff, etc. FC = $270,000 per year for this firm.
Variable Costs. VC = f (Q), and include labor as the main VC for this firm. We assume that:
a) there is a flexible, and readily available supply of workers in the local labor market,
b) adding additional works puts upward pressure on wages, so the firm faces increasing costs of getting workers: $31.5 per repair for Q = 5 ($157.5 / 5); $39 for Q = 30 ($1170 / 30); and $48 for Q = 60 ($2880 / 60). AVC rises.
Average Total Costs. ATC = TC / Q (ATC = SAC), usually a U-shaped curve, see p. 264, Figure 7.2. At both low and high levels of output, ATC is high. Also, as Q increases, ATC first falls, reaches a minimum (Q=30,000 in this case) and then increases.
Average Variable Costs. VC / Q (rises from $31.50 to $48, see above).
Marginal Cost. MC = dTC / dQ. See Figure 7.2, for a graph and table of MC. Why is MC upward sloping? Because labor is the only variable input, so therefore MC = f (L) only, (K is constant so that dTC / dK = 0) and we have:
SMC = PL / MPL, where PL = wage per hour, and MPL = marginal product of labor. SMC will go DOWN if either MPL goes UP, or PL goes DOWN. SMC will go UP if either MPL goes DOWN, or PL goes UP.
SMC goes up in this case because of the Law of Diminishing Returns, which makes the MPL go down, and SMC go up. Also, there is upward pressure on wages as more workers are hired and PL rises.
The pattern of MC helps explains the shape of the SAC curve (ATC):
When Q is low, MC is low, but FC is spread over very few units, so the ATC is high. Plant is "underutilized." When Q is high, MC is very high, and ATC is very high, due to "overutilization" of the plant. Also, we know mathematically that:
1. When SMC = SAC (MC = ATC), ATC is at a MINIMUM. MC curves intersects the ATC curve at the ATC's minimum point.
2. a. When MC < ATC, ATC is falling.
b. When MC > ATC, ATC is rising.
Think of your overall GPA as your overall "average", and your semester GPA as your "marginal" GPA. If your overall GPA is 3.0 and your semester GPA is 4.0, your overall GPA must rise. If your overall GPA is 3.0 and your semester GPA is 2.0, your overall GPA must fall.
Firm's SR Cost Function, C = f (Q):
C = $270 + (30 Q + .3 Q2)
FC VC
where Q is thousands of units and C are thousands of dollars.
Dividing all terms by Q, we have ATC:
ATC = (270 / Q ) + (30 + .3Q)
AFC AVC
As Q increases, AFC steadily decreases and AVC rises. At low levels of Q, AFC dominates; at high levels of Q, AVC dominates, and the combination of the two effects explains the U-shaped ATC.
SMC = d TC / d Q = 30 + .6Q
and we can see that MC rises as Q increases.
Note: We can take the derivative of ATC and set = 0 to find minimum ATC:
ATC = 270 Q-1 + 30 + .3Q
dATC / dQ = -270 Q-2 + .30 = 0
270 = .30
Q2
Q2 = 900
Q*min = 30
We can also verify that SMC = ATC = 30 when ATC is at a minimum:
30 + .6Q = 270 Q-1 + 30 + .3Q
Simplify, and solve for Q = 30
Long-Run (LR) Costs
In the LR, ALL costs are variable. In other words, FC are only fixed in the SR, in the long-run everything is flexible. Two points:
1. Being able to vary ALL inputs allows the firm to produce at lower costs in the LR than in SR. The firm still has to find the least-cost combination of inputs, but LR flexibility to vary all inputs is valuable. Any size firm and any amount of Q is possible in LR.
2. Shape of LR costs depends on returns to scale.
Examples:
a) With constant returns to scale, LAC is constant.
b) With increasing returns to scale, LAC falls.
c) With decreasing returns to scale, LAC rises.
SR vs. LR Cost
Assume: a) constant returns to scale, and b) two inputs (K and L), see graph page 267, Figure 7.3. As firm expands output, SAC remains constant, and LAC remains constant at $4 per unit. In this case, SAC = SMC = LAC = LMC = $4 per unit. The firm can produce at a constant cost of $4 per unit, whether the plant size is 9,000 sq. ft. (Q = 72,000), 18,000 sq. ft. (Q = 144,000) or 27,000 sq. ft. (Q=216,000). Firm should use the optimal K/L ratio at any level of output, e.g. double inputs to double Q.
Actually, under most circumstances, the firm would probably have more options than just 3 plant sizes, it has the flexibility in the LR to build any plant size represented on the graph and LAC = $4. However, once a plant is built, K is now fixed in SR, and the firm would face rising SMC and SAC if it produces at level where ATC is NOT at a minimum.
For example, given a 9,000 or an 18,000 sq. ft. plant, producing 108,000 units would result in C > $4. See Figure 7.3. For the smaller plant, the facility is over utilized and the firm faces diminishing marginal returns. For the larger plant size, the facility is underutilized. In either case, C > $4.
RETURNS TO SCALE (ECONOMIES OF SCALE):
a) determine the shape of the LRAC curve.
b) help answer questions such as: i) are large firms or small firms more efficient in an industry?, ii) can small firms successfully compete with large firms in an industry?, iii) how would a 50% increase (decrease) in output affect AC per unit?
See page 272, Figure 7.4, for LRAC and SRAC curves for a typical firm in an industry. The LRAC is U-shaped indicating:
a) falling LRAC at levels of output below Qmin because of increasing returns to scale and
b) rising LRAC when Q > Qmin because of decreasing returns to scale.
LRMC is also shown, and intersects the LRAC curve at the MIN LRAC. Three different possible SRAC curves are also indicated in Figure 7.4. If the firm can produce at any possible plant size, then the LRAC would summarize all possible SRAC curves.
Remember that cost curves summarize information about: a) the firm's productivity and production function (engineering information) and b) prices of all inputs.
THREE POSSIBILITIES:
1. Constant returns to scale = constant AC, like in the example on page 267. The firm can expand (or contract) output at a constant cost, due to constant returns to scale, in the case where a firm can simply double output by replicating the existing operation at a new location, e.g. opening another fast-food restaurant, factory, grocery store, etc. Firm faces neither increasing nor decreasing costs when it expands (or contracts) and LRAC = $4.
2. Increasing returns to scale = declining AC. A firm can operate more efficiently at larger levels of output due to increased specialization of labor, more efficient manufacturing methods, more automation, spreading fixed costs (like advertising) over more units of output - 30 second TV commercial costs the same for a huge chain (like McDonald's) as for a very small chain), general economies of scale, etc. Example: Doubling the size of a cruise ship allows the firm to more than double the number of passengers per ship and only requires a small increase in crew size, resulting in increasing returns to scale and declining LRAC per passenger.
3. Decreasing returns to scale = increasing AC. Large firms eventually face diseconomies of scale, and increasing LRAC due to the inefficiencies of large, bureaucratic organizations. As the firm gets larger and larger, it becomes more and more costly to coordinate, organize and monitor the firm's various activities. The inefficiencies of large operations eventually result in rising LRAC as Q increases.
Empirical Evidence of LRAC
Economists have conducted extensive research on SRAC and LRAC using OLS and either: a) time-series or b) cross-section accounting and production data. General findings: for most goods and most industries the LRAC looks like Panel (b) on page 274, Figure 7.5, where there are significant economies of scale and decreasing AC at low levels of output, followed by a wide region of constant returns to scale and constant LRAC.
Implications of the empirical evidence:
a. Minimum firm size. To be competitive, a firm must produce at minimum level of output, where Q > Qmin (Figure 7.5, panels a and b), called the Minimum Efficient Scale (MES).
b. Range of firm size. Once a firm produces the minimum level of output where Q = Qmin, there may be a wide range of firm sizes with the same LRAC, i.e. there could be many small, medium and large firms all competing (panel b). Examples: banking, retail, book publishing, newspapers, accounting, advertising, universities, medical, farming, etc.
c. Number of firms. MES determines the maximum number of firms that an industry can support. For example, assume that annual market demand is 10m units. If MES = 100,000, then the maximum number of equal-sized firms will be 100 firms (10m / 100,000). If MES = 5m, then the maximum number of firms = 2, each supplying half of the annual demand. If LRAC declines for all levels of Q up to 10m, the market may only support one firm.
ECONOMIES OF SCOPE
Most firms produce a variety of goods and services, e.g. banks, Proctor and Gamble, General Mills, Walt Disney, etc. In the production of various products, there may likely be Economies of Scope, which are the potential efficiencies and cost advantages of producing closely related goods or services. For example, Coca-Cola has economies of scope in the production of various beverages: different soft drinks, juices, sports drinks, iced tea, spring water, etc. Chase Bank has economies of scope providing various financial services and products such as mutual funds, checking and savings accounts, loans, insurance, etc.
Economies of Scope (SC) exist when joint production of multiple goods is less than the aggregate cost of producing each item separately, measured as:
SC = C (Q1) + C (Q2) - C (Q1, Q2)
C (Q1) + C (Q2)
where:
C (Q1) = cost of producing Q1 alone
C (Q2) = cost of producing Q2 alone
C (Q1, Q2) = cost of jointly producing Q1 and Q2
For example: Suppose that joint production of Q1 and Q2 is $17m. Producing each good separately would be $12m for Q1 and $8m for Q2, for a total of $20m. In other words, the firm saves $3m with joint production. Or:
SC = $20m - $17m = .15 or 15%.
$20m
This means that the firm saves 15% with joint production ($20m to $17m = -15% cost savings).
Sources of Economies of Scope:
1. Shared activities between Q1 and Q2. Coca-Cola can use the same bottling equipment and machinery to produce many different beverage lines.
2. Transfer of skills between Q1 and Q2. Coca-Cola can use its expertise in soft drink production for other beverages, like orange juice, bottled iced tea, bottled water, etc.
3. Consolidated sales, ordering, and delivery. Coca-Cola can use the same sales force for all of its beverage lines, and can consolidate shipments of beverages.
4. Consolidated advertising. Proctor and Gamble can advertise all products simultaneously.
5. Multiple outputs from a single input. Cattle producers selling both beef and hides. Lumber company producing lumber and sawdust. Airline providing both passenger and freight services.
6. Micromarketing. General Mills can produce 20 different breakfast cereals, all aimed at different niche markets. Proctor and Gamble can produce 20 different kinds of shampoo. Anheuser-Busch can produce 20 different types of beer. Coke can produce 20 different types of soft drinks, etc.
LEARNING CURVE
Learning curve concept summarizes the inverse relationship between cumulative production and ATC. As cumulative production increases, ATC declines because of increased productivity gains, increased efficiency gains from learning and experience.
Sources of learning:
1. Worker skills increase over time, as they learn the production process and become more efficient over time.
2. Trial-and-error and experimentation with different methods of production result in increased efficiency/productivity over time. Equipment can be redesigned and improved with experience, as engineers learn how to produce more efficiently. Research and development result in continual improvements in production efficiency.
Examples of the Learning Curve:
1. When VCRs first came out in early 1980s, they sold for $2000. Over time, learning resulted in prices less than $100, with significant improvements in quality, durability, features, reliability, etc.
2. Ball point pens were originally $12.50 in 1945, or about $125 in today's dollars!
3. Hand held calculators, introduced in early 1970s, fell from $1000 to $10 over the decade.
4. Model T prices fell from $950 in 1908 to $260 in 1924, sales went from 15,000 to 577,000.
See p. 281, Figure 7.6 Panel a, for a typical learning curve. ATC = f (Cumulative Q). Notice that the greatest cost reductions occur in the early part of the new product's life, and once cumulative output is large, further reductions in ATC are minor after the gains from learning are exhausted.
Using the Learning Curve.
The firm's goal is to maximize LR profits, and can use the learning curve concept to guide decision making. For example, the firm may initially lose money with a new product because P < ATC. However, recognizing that ATC may decline significantly over time, the firm is making an investment with the new product for LR profits. Eventually, ATC will fall and P > ATC, firm will make profits. SR losses, LR profits. May be sensible to initially price the product < ATC, assuming ATC is initially high, but will decline. "Predatory pricing" (P < ATC) may be a sensible LR strategy for the firm.
By aggressively cutting price initially, the firm gains on two dimensions:
a) gains market share with the new product, establishes "first mover advantage," e.g. AOL.
b) lower prices mean more sales, which allows the firm to work down the learning curve faster.
IMPORTANT REMINDER: Firm's goal is to MAXIMIZE LR PROFITS, and NOT MAX TR, or MAX Market Share, or MIN ATC!
COST ANALYSIS AND OPTIMAL DECISIONS
Single Product
Profit Maximization Rule: Produce output as long as MR > MC, produce Q* where MR = MC. See Figure 7.7 on p. 283.
MR > MC until Q*, where MR = MC. Q* is the profit maximizing level of output. Knowing Q*, we find P* from the demand curve. (Remember: Given a demand curve, you give me a P and I can tell you Q, or you give me a Q and I can tell you P.) Also, given Q* (or any Q), we can determine ATC at that level of output. In this case, given Q*, ATC = AC. The green shaded area is ECONOMIC PROFITS, which is positive in this case, meaning that the firm is generating a greater-than-normal rate of return.
Logic: TR - TC = PROFITS
TR = P x Q = Large rectangle with P* and Q* at opposite corners.
TC = ATC x Q = Smaller rectangle with AC and Q* in opposite corners.
TR - TC = Green shaded rectangle = PROFITS
NOTICE: The profit-maximizing level of output is less than the MES (Qmin where ATC is at a MIN). In fact, if the firm produced Qmin, P < ATC, and the firm would suffer economic losses. The firm's optimal level of output depends on market demand as well as cost. The current market demand is insufficient to justify exploiting all economies of scale. Alternatively, the market Demand' and MR' and Q' could occur at level of output beyond the MES. Point: Profit maximization always takes precedence over MES. Rule: Max Profits, Don't MIN ATC.
The Shut-Down Rule
Under adverse economic conditions (which could be temporary or permanent), managers face a shut-down decision (temporary or permanent shut down). For example, during the 6-week UAW strike in 1998, restaurants near GM plants that depended heavily on UAW lunch and dinner business saw business fall to almost zero. Firms had to decide: Should we shut down temporarily during the strike or continue to operate?
Shut Down Rules:
1. P < ATC and this is PERMANENT, the firm should shut down. P < ATC = Economic Losses, and if this is a LR permanent situation, the firm will never make money, so it should: a) go out of business completely, or b) eliminate the unprofitable product, unit, division, store, etc. Examples: GM eliminates Oldsmobile line, Wal-Mart closes an unprofitable store, Montgomery Wards goes out of retail business (re-emerges with online store), Coca-Cola eliminates the New Coke, etc.
If P < ATC, but this is TEMPORARY (P > ATC eventually), then the firm has to decide whether to a) shut down in SR or b) continue to operate as follows to MIN ECON LOSSES according to these rules:
2. If P > AVC, the firm should continue to operate in SR, since TR > TVC and the firm is more than covering its VC, making a contribution towards FC, to MIN LOSS.
3. If P < AVC, the firm should shut down in the SR, since TR < TVC and the firm is not even covering its VC, MIN LOSS.
Example: Before the strike, a restaurant operating near GM plant has FC = $400 per week + VC = $600 per week, and TR = $1000 per week, so TR = TC and ECON PROFITS = 0. After the strike there are two scenarios:
a. Firm can now generate only $700/week in TR. Shut down or operate? Firm should operate, since TR > TVC, $700 > $600, so the firm generates $100 of operating profit to pay FC.
Operate: TR = $700
TC = $1000
-$300 LOSS
vs.
Shut Down: -$400 LOSS (FC)
Firm should operate to MIN LOSS.
b. Firm can now only generate $500 per week in TR. Shut down or operate? Firm should shut down since TR < TVC, $500 < $600, and the firm cannot even generate enough sales to cover TVC.
Operate: TR = $500
TC = $1000
-$500 LOSS
Shut Down: -$400 LOSS (FC)
Firm should shut down to MIN LOSS.
Average Total Costs. ATC = TC / Q (ATC = SAC), usually a U-shaped curve, see p. 264, Figure 7.2. At both low and high levels of output, ATC is high. Also, as Q increases, ATC first falls, reaches a minimum (Q=30,000 in this case) and then increases.
Average Variable Costs. VC / Q (rises from $31.50 to $48, see above).
Marginal Cost. MC = dTC / dQ. See Figure 7.2, for a graph and table of MC. Why is MC upward sloping? Because labor is the only variable input, so therefore MC = f (L) only, (K is constant so that dTC / dK = 0) and we have:
SMC = PL / MPL, where PL = wage per hour, and MPL = marginal product of labor. SMC will go DOWN if either MPL goes UP, or PL goes DOWN. SMC will go UP if either MPL goes DOWN, or PL goes UP.
SMC goes up in this case because of the Law of Diminishing Returns, which makes the MPL go down, and SMC go up. Also, there is upward pressure on wages as more workers are hired and PL rises.
The pattern of MC helps explains the shape of the SAC curve (ATC):
When Q is low, MC is low, but FC is spread over very few units, so the ATC is high. Plant is "underutilized." When Q is high, MC is very high, and ATC is very high, due to "overutilization" of the plant. Also, we know mathematically that:
1. When SMC = SAC (MC = ATC), ATC is at a MINIMUM. MC curves intersects the ATC curve at the ATC's minimum point.
2. a. When MC < ATC, ATC is falling.
b. When MC > ATC, ATC is rising.
Think of your overall GPA as your overall "average", and your semester GPA as your "marginal" GPA. If your overall GPA is 3.0 and your semester GPA is 4.0, your overall GPA must rise. If your overall GPA is 3.0 and your semester GPA is 2.0, your overall GPA must fall.
Firm's SR Cost Function, C = f (Q):
C = $270 + (30 Q + .3 Q2)
FC VC
where Q is thousands of units and C are thousands of dollars.
Dividing all terms by Q, we have ATC:
ATC = (270 / Q ) + (30 + .3Q)
AFC AVC
As Q increases, AFC steadily decreases and AVC rises. At low levels of Q, AFC dominates; at high levels of Q, AVC dominates, and the combination of the two effects explains the U-shaped ATC.
SMC = d TC / d Q = 30 + .6Q
and we can see that MC rises as Q increases.
Note: We can take the derivative of ATC and set = 0 to find minimum ATC:
ATC = 270 Q-1 + 30 + .3Q
dATC / dQ = -270 Q-2 + .30 = 0
270 = .30
Q2
Q2 = 900
Q*min = 30
We can also verify that SMC = ATC = 30 when ATC is at a minimum:
30 + .6Q = 270 Q-1 + 30 + .3Q
Simplify, and solve for Q = 30
Long-Run (LR) Costs
In the LR, ALL costs are variable. In other words, FC are only fixed in the SR, in the long-run everything is flexible. Two points:
1. Being able to vary ALL inputs allows the firm to produce at lower costs in the LR than in SR. The firm still has to find the least-cost combination of inputs, but LR flexibility to vary all inputs is valuable. Any size firm and any amount of Q is possible in LR.
2. Shape of LR costs depends on returns to scale.
Examples:
a) With constant returns to scale, LAC is constant.
b) With increasing returns to scale, LAC falls.
c) With decreasing returns to scale, LAC rises.
SR vs. LR Cost
Assume: a) constant returns to scale, and b) two inputs (K and L), see graph page 267, Figure 7.3. As firm expands output, SAC remains constant, and LAC remains constant at $4 per unit. In this case, SAC = SMC = LAC = LMC = $4 per unit. The firm can produce at a constant cost of $4 per unit, whether the plant size is 9,000 sq. ft. (Q = 72,000), 18,000 sq. ft. (Q = 144,000) or 27,000 sq. ft. (Q=216,000). Firm should use the optimal K/L ratio at any level of output, e.g. double inputs to double Q.
Actually, under most circumstances, the firm would probably have more options than just 3 plant sizes, it has the flexibility in the LR to build any plant size represented on the graph and LAC = $4. However, once a plant is built, K is now fixed in SR, and the firm would face rising SMC and SAC if it produces at level where ATC is NOT at a minimum.
For example, given a 9,000 or an 18,000 sq. ft. plant, producing 108,000 units would result in C > $4. See Figure 7.3. For the smaller plant, the facility is over utilized and the firm faces diminishing marginal returns. For the larger plant size, the facility is underutilized. In either case, C > $4.
RETURNS TO SCALE (ECONOMIES OF SCALE):
a) determine the shape of the LRAC curve.
b) help answer questions such as: i) are large firms or small firms more efficient in an industry?, ii) can small firms successfully compete with large firms in an industry?, iii) how would a 50% increase (decrease) in output affect AC per unit?
See page 272, Figure 7.4, for LRAC and SRAC curves for a typical firm in an industry. The LRAC is U-shaped indicating:
a) falling LRAC at levels of output below Qmin because of increasing returns to scale and
b) rising LRAC when Q > Qmin because of decreasing returns to scale.
LRMC is also shown, and intersects the LRAC curve at the MIN LRAC. Three different possible SRAC curves are also indicated in Figure 7.4. If the firm can produce at any possible plant size, then the LRAC would summarize all possible SRAC curves.
Remember that cost curves summarize information about: a) the firm's productivity and production function (engineering information) and b) prices of all inputs.
THREE POSSIBILITIES:
1. Constant returns to scale = constant AC, like in the example on page 267. The firm can expand (or contract) output at a constant cost, due to constant returns to scale, in the case where a firm can simply double output by replicating the existing operation at a new location, e.g. opening another fast-food restaurant, factory, grocery store, etc. Firm faces neither increasing nor decreasing costs when it expands (or contracts) and LRAC = $4.
2. Increasing returns to scale = declining AC. A firm can operate more efficiently at larger levels of output due to increased specialization of labor, more efficient manufacturing methods, more automation, spreading fixed costs (like advertising) over more units of output - 30 second TV commercial costs the same for a huge chain (like McDonald's) as for a very small chain), general economies of scale, etc. Example: Doubling the size of a cruise ship allows the firm to more than double the number of passengers per ship and only requires a small increase in crew size, resulting in increasing returns to scale and declining LRAC per passenger.
3. Decreasing returns to scale = increasing AC. Large firms eventually face diseconomies of scale, and increasing LRAC due to the inefficiencies of large, bureaucratic organizations. As the firm gets larger and larger, it becomes more and more costly to coordinate, organize and monitor the firm's various activities. The inefficiencies of large operations eventually result in rising LRAC as Q increases.
Empirical Evidence of LRAC
Economists have conducted extensive research on SRAC and LRAC using OLS and either: a) time-series or b) cross-section accounting and production data. General findings: for most goods and most industries the LRAC looks like Panel (b) on page 274, Figure 7.5, where there are significant economies of scale and decreasing AC at low levels of output, followed by a wide region of constant returns to scale and constant LRAC.
Implications of the empirical evidence:
a. Minimum firm size. To be competitive, a firm must produce at minimum level of output, where Q > Qmin (Figure 7.5, panels a and b), called the Minimum Efficient Scale (MES).
b. Range of firm size. Once a firm produces the minimum level of output where Q = Qmin, there may be a wide range of firm sizes with the same LRAC, i.e. there could be many small, medium and large firms all competing (panel b). Examples: banking, retail, book publishing, newspapers, accounting, advertising, universities, medical, farming, etc.
c. Number of firms. MES determines the maximum number of firms that an industry can support. For example, assume that annual market demand is 10m units. If MES = 100,000, then the maximum number of equal-sized firms will be 100 firms (10m / 100,000). If MES = 5m, then the maximum number of firms = 2, each supplying half of the annual demand. If LRAC declines for all levels of Q up to 10m, the market may only support one firm.
ECONOMIES OF SCOPE
Most firms produce a variety of goods and services, e.g. banks, Proctor and Gamble, General Mills, Walt Disney, etc. In the production of various products, there may likely be Economies of Scope, which are the potential efficiencies and cost advantages of producing closely related goods or services. For example, Coca-Cola has economies of scope in the production of various beverages: different soft drinks, juices, sports drinks, iced tea, spring water, etc. Chase Bank has economies of scope providing various financial services and products such as mutual funds, checking and savings accounts, loans, insurance, etc.
Economies of Scope (SC) exist when joint production of multiple goods is less than the aggregate cost of producing each item separately, measured as:
SC = C (Q1) + C (Q2) - C (Q1, Q2)
C (Q1) + C (Q2)
where:
C (Q1) = cost of producing Q1 alone
C (Q2) = cost of producing Q2 alone
C (Q1, Q2) = cost of jointly producing Q1 and Q2
For example: Suppose that joint production of Q1 and Q2 is $17m. Producing each good separately would be $12m for Q1 and $8m for Q2, for a total of $20m. In other words, the firm saves $3m with joint production. Or:
SC = $20m - $17m = .15 or 15%.
$20m
This means that the firm saves 15% with joint production ($20m to $17m = -15% cost savings).
Sources of Economies of Scope:
1. Shared activities between Q1 and Q2. Coca-Cola can use the same bottling equipment and machinery to produce many different beverage lines.
2. Transfer of skills between Q1 and Q2. Coca-Cola can use its expertise in soft drink production for other beverages, like orange juice, bottled iced tea, bottled water, etc.
3. Consolidated sales, ordering, and delivery. Coca-Cola can use the same sales force for all of its beverage lines, and can consolidate shipments of beverages.
4. Consolidated advertising. Proctor and Gamble can advertise all products simultaneously.
5. Multiple outputs from a single input. Cattle producers selling both beef and hides. Lumber company producing lumber and sawdust. Airline providing both passenger and freight services.
6. Micromarketing. General Mills can produce 20 different breakfast cereals, all aimed at different niche markets. Proctor and Gamble can produce 20 different kinds of shampoo. Anheuser-Busch can produce 20 different types of beer. Coke can produce 20 different types of soft drinks, etc.
LEARNING CURVE
Learning curve concept summarizes the inverse relationship between cumulative production and ATC. As cumulative production increases, ATC declines because of increased productivity gains, increased efficiency gains from learning and experience.
Sources of learning:
1. Worker skills increase over time, as they learn the production process and become more efficient over time.
2. Trial-and-error and experimentation with different methods of production result in increased efficiency/productivity over time. Equipment can be redesigned and improved with experience, as engineers learn how to produce more efficiently. Research and development result in continual improvements in production efficiency.
Examples of the Learning Curve:
1. When VCRs first came out in early 1980s, they sold for $2000. Over time, learning resulted in prices less than $100, with significant improvements in quality, durability, features, reliability, etc.
2. Ball point pens were originally $12.50 in 1945, or about $125 in today's dollars!
3. Hand held calculators, introduced in early 1970s, fell from $1000 to $10 over the decade.
4. Model T prices fell from $950 in 1908 to $260 in 1924, sales went from 15,000 to 577,000.
See p. 281, Figure 7.6 Panel a, for a typical learning curve. ATC = f (Cumulative Q). Notice that the greatest cost reductions occur in the early part of the new product's life, and once cumulative output is large, further reductions in ATC are minor after the gains from learning are exhausted.
Using the Learning Curve.
The firm's goal is to maximize LR profits, and can use the learning curve concept to guide decision making. For example, the firm may initially lose money with a new product because P < ATC. However, recognizing that ATC may decline significantly over time, the firm is making an investment with the new product for LR profits. Eventually, ATC will fall and P > ATC, firm will make profits. SR losses, LR profits. May be sensible to initially price the product < ATC, assuming ATC is initially high, but will decline. "Predatory pricing" (P < ATC) may be a sensible LR strategy for the firm.
By aggressively cutting price initially, the firm gains on two dimensions:
a) gains market share with the new product, establishes "first mover advantage," e.g. AOL.
b) lower prices mean more sales, which allows the firm to work down the learning curve faster.
IMPORTANT REMINDER: Firm's goal is to MAXIMIZE LR PROFITS, and NOT MAX TR, or MAX Market Share, or MIN ATC!
COST ANALYSIS AND OPTIMAL DECISIONS
Single Product
Profit Maximization Rule: Produce output as long as MR > MC, produce Q* where MR = MC. See Figure 7.7 on p. 283.
MR > MC until Q*, where MR = MC. Q* is the profit maximizing level of output. Knowing Q*, we find P* from the demand curve. (Remember: Given a demand curve, you give me a P and I can tell you Q, or you give me a Q and I can tell you P.) Also, given Q* (or any Q), we can determine ATC at that level of output. In this case, given Q*, ATC = AC. The green shaded area is ECONOMIC PROFITS, which is positive in this case, meaning that the firm is generating a greater-than-normal rate of return.
Logic: TR - TC = PROFITS
TR = P x Q = Large rectangle with P* and Q* at opposite corners.
TC = ATC x Q = Smaller rectangle with AC and Q* in opposite corners.
TR - TC = Green shaded rectangle = PROFITS
NOTICE: The profit-maximizing level of output is less than the MES (Qmin where ATC is at a MIN). In fact, if the firm produced Qmin, P < ATC, and the firm would suffer economic losses. The firm's optimal level of output depends on market demand as well as cost. The current market demand is insufficient to justify exploiting all economies of scale. Alternatively, the market Demand' and MR' and Q' could occur at level of output beyond the MES. Point: Profit maximization always takes precedence over MES. Rule: Max Profits, Don't MIN ATC.
The Shut-Down Rule
Under adverse economic conditions (which could be temporary or permanent), managers face a shut-down decision (temporary or permanent shut down). For example, during the 6-week UAW strike in 1998, restaurants near GM plants that depended heavily on UAW lunch and dinner business saw business fall to almost zero. Firms had to decide: Should we shut down temporarily during the strike or continue to operate?
Shut Down Rules:
1. P < ATC and this is PERMANENT, the firm should shut down. P < ATC = Economic Losses, and if this is a LR permanent situation, the firm will never make money, so it should: a) go out of business completely, or b) eliminate the unprofitable product, unit, division, store, etc. Examples: GM eliminates Oldsmobile line, Wal-Mart closes an unprofitable store, Montgomery Wards goes out of retail business (re-emerges with online store), Coca-Cola eliminates the New Coke, etc.
If P < ATC, but this is TEMPORARY (P > ATC eventually), then the firm has to decide whether to a) shut down in SR or b) continue to operate as follows to MIN ECON LOSSES according to these rules:
2. If P > AVC, the firm should continue to operate in SR, since TR > TVC and the firm is more than covering its VC, making a contribution towards FC, to MIN LOSS.
3. If P < AVC, the firm should shut down in the SR, since TR < TVC and the firm is not even covering its VC, MIN LOSS.
Example: Before the strike, a restaurant operating near GM plant has FC = $400 per week + VC = $600 per week, and TR = $1000 per week, so TR = TC and ECON PROFITS = 0. After the strike there are two scenarios:
a. Firm can now generate only $700/week in TR. Shut down or operate? Firm should operate, since TR > TVC, $700 > $600, so the firm generates $100 of operating profit to pay FC.
Operate: TR = $700
TC = $1000
-$300 LOSS
vs.
Shut Down: -$400 LOSS (FC)
Firm should operate to MIN LOSS.
b. Firm can now only generate $500 per week in TR. Shut down or operate? Firm should shut down since TR < TVC, $500 < $600, and the firm cannot even generate enough sales to cover TVC.
Operate: TR = $500
TC = $1000
-$500 LOSS
Shut Down: -$400 LOSS (FC)
Firm should shut down to MIN LOSS.
