We illustrate competitive manufacturing with an original theoretical model of manufacturers and buyers of cars over a business cycle that have peak and off-peak demand periods. There are two types of plants manufacturing cars, plantK and plantL, each having linear total costs with absolute capacity limits. PlantK operates with low VC and high FC by being capital intensive. PlantK is output-rates rigid since it produces throughout the business cycle and always at capacity. PlantL operates with low FC and high VC by relying on outsourcing major components and parts. PlantL is output-rates flexible since it produces only in the peak-demand periods. We show results under SRMC pricing. Then we examine an alternate arrangement which increases demand irregularity. We show, under conditions of the model, that the added cost to supply irregular demand should be small because of the low FC of plantL. We show, under the conditions of the model, that the added gain in consumer surplus to have irregular demand supplied should be large because consumers will have more available for the peak periods. The main policy implication of this theoretical model—for regularly recurring cycles—is to urge focus, even in the off-peak periods, on adequate capacity for the peak periods.
John M. Clark (1884-1963) wrote of the desirability of manufacturing plants to operate at their normal capacity with production costs per unit output the lowest. John M. Clark attributed the main problems of the business cycle to the dominant role of fixed costs that are incurred irrespective of output rates:
“It is needless to point out that overhead costs play a fundamental part in the behavior of business at every stage of that many-sided phenomenon, the business cycle. The part they play is most paradoxical. For they make regular operation peculiarly desirable and peculiarly profitable, so that business feels a definite loss whenever output falls below normal capacity, yet it is largely due to this very fact of large fixed capital that business breads these calamities for itself, out of the laws of its own being. And the largest businesses, which have the highest percent of constant costs due to invested capital, are, as we have seen, precisely the ones which fluctuate the most, so far as employment is an index. There is something about the commercial-industrial system which bewitches business so that it does just the thing it is trying to avoid, and is held back from doing just the thing it yearns to do—maintain steady operation and avoid idle overhead. And while the contributing causes of this strange auto-hypnosis are many and of varied character, technical, financial, commercial, and psychological; the underlying fact of large capital plays a central part, and the inelasticity of cost, sunk cost, and the shifting and conversion of overhead cost are all facts of major importance.”1
The US manufacturing industries are now some 6 or 7 years in a recession, as the figures in
In his 1923 book John M. Clark illustrated the calculations for expected average cost,
In traditional manufacturing the focus is on the production phase of a product. In high-value manufacturing the recommendation is for manufacturers to concern themselves with the entire manufacturing value chain:
“A New Definition of High-Value Manufacturing... A successful manufacturing industry goes beyond production, it means thriving research and development (R&D), design, supply management, sales and marketing as well as after sales services... Highly successful manufacturers do not need to rely on production alone and they can accommodate effective outsourcing.”4
Outsourcing means buying components and parts instead of making them. In high-value manufacturing firms
. % capacity utilization manufacturing USA.
1972-73 Avg | 1988-89 High | 1990-91 Low | 1994-95 High | 2009 Low | 2013 April | 2014 April |
---|---|---|---|---|---|---|
78.7 | 85.6 | 77.3 | 84.6 | 63.9 | 75.8 | 76.4 |
. Annual budgets at various operating rates.
. Annual budgets at various operating rates. | . Annual budgets at various operating rates. | . Annual budgets at various operating rates. | . Annual budgets at various operating rates. |
---|---|---|---|
0.111 | 0 | $41,700 | undefined |
0.222 | 60 | $92,820 | $1,547 |
0.222 | 80 | $103,000 | $1,288 |
0.222 | 100 | $113,400 | $1,134 |
0.222 | 120 | $138,340 | $1,153 |
Weighted Average | 80 | $104,091 | $1,301 |
are increasing product flexibility, meaning which products they make. In traditional manufacturing, as here and in John M. Clark’s writings, the industry is composed of manufacturers that produce a particular product, such as a car. In high-value manufacturing firms are part of other industries depending on what products they sell. In traditional manufacturing, outsourcing increases a firm’s output-rate flexibility of production of a particular product.
We illustrate an original model of manufacturing and buying cars over the business cycle. The product is homogeneous in that all cars are assumed identical in looks, driveability and value in the market. We assume fluctuating demand over a business cycle of a number of years, with peak periods, part of the cycle, and off-peak periods, the balance of the cycle. We assume car manufacturers set two prices, one at the peak and one for the off-peak times of the business cycle. We assume no price collusion among car manufacturers. We assume car manufacturers know the consumer-demand schedules for their cars produced. We assume zero expected profits for all car manufacturers in long-run equilibrium. Initially we assume SRMC pricing.
We assume a single homogeneous product, Q, cars. We assume ease of entry of new car manufacturers. We assume a business cycle of two states of demand,
We envision investors and managers walking into a car manufacturing plant store that has two shelves: each with a model plant
SR total-cost curves of plantK and plantL
The key assumptions of the model are:
A1:
A2: Demand fluctuates with frequencies,
A3: We assume SRMC (short-run marginal-cost) pricing behavior. With linear TC functions and SRMC pricing, plants will operate at either 0% or 100%.
A4: We assume market prices in off-peak times
A5: Long-run equilibrium requires zero expected profits for both plant types.
We prove in the following proposition the conditions of indifference for investors to choose between plantK and plantL in LR equilibrium.
Proposition 1 Under Assumptions A1 through A5 with both plants used in long-run equilibrium, then it must be true:
If
Proof: Investors in plantK have zero expected economic profits per Assumption A5:
This gives us:
PlantL added cost of supplying irregular demand:
Investors in plantL have zero expected economic profits per Assumption A5:
This gives us:
Equations (3) and (5) can be combined:
For plantsL to shut-down in the off-peak period per Assumption A4 must be
Since
which is the asserted left-side inequality condition:
By Assumption A4,
By Assumption A4,
Thus
yields the right-side inequality condition assertion.
The left-side condition in (1) is that
The right-side condition in (1) is that
The right-hand condition is that where production is used only in high-demand times, plantL is superior. The right-hand condition requires that SACL be flatter shaped than SACK. We define output flexibility as the relative flatness of the SAC curve. We suggest calling this condition that plantlL be more output-rates flexible efficient6.
If demand for cars were static with no irregularities, then firms would choose only plantK and
Thus, a measure of added cost of supplying irregular demand in the model would be the expected manufactured cars to meet peak demand × the difference in SRAC between the two plants, or:
There are two groups in our hypothetical society: Suppliers (manufacturers of cars) and consumers (households who buy cars). Consumers buy cars in a free market on a daily basis from various manufacturers where each manufacturer posts its prices. Consumers pay the lowest price per-car in the local market. The intersection of this price with the consumer-demand schedules (off-peak and peak) determine the quantity of cars the consumers order.
Consumers have a fixed budget for car purchase expenditures. They are price sensitive in buying cars, in the sense that consumers will buy more cars at a lower market price and less cars at a higher market price. Consumers pay market price times quantities purchased,
The demand curve shows the maximum quantities consumers would be willing to purchase at various prices. The assumption is that the demand curve is downward sloping, meaning that consumers would be willing to buy more cars if prices were lower, all else being the same. The area under the demand curve up to the point of quantities of market purchases shows the value to the consumer.
Using hypothetical numbers to make the economic concepts clearer, point K could be that, at a market price of $36 per car consumers are willing to buy 35 cars. Point H might be that at a market price of $33 per car consumers are willing to buy 37 cars.
Let
The demand curve
We define consumer surplus as the area under the demand curve and above the price line. We define expected values, E, as the sum of each outcome times its expected value. Using the illustrated numbers for points H and D, the market equilibrium points for pricing rule A, varying prices, we can calculate
Using the illustrated numbers for points K and J, the market equilibrium points for pricing rule B, fixed prices, we can calculate
the same amount and buy the same number of cars over the year. We show graphically this increase in consumer surplus. This becomes a maximum willingness for consumers to pay suppliers for that arrangement.
We assume that suppliers are willing to offer cars according to two alternative pricing schemes: a fixed price,
Proposition 2 A comparison of alternative pricing schemes, A: varying prices, versus B: fixed prices, under conditions of shifting downward-sloping demand curves shows
and
Pricing Rule | Equilibrium Points | Frequencies |
---|---|---|
.png" width="162.124996185303" height="42.7500009536743" /> (12) | .png" width="162.124996185303" height="42.7500009536743" /> (12) | .png" width="162.124996185303" height="42.7500009536743" /> (12) |
.png" width="162.124996185303" height="42.7500009536743" /> (12) | .png" width="162.124996185303" height="42.7500009536743" /> (12) | .png" width="162.124996185303" height="42.7500009536743" /> (12) |
Proof: By definition of
and
By definition of
and
By definition of
and
By Assumption (11) We can state:
By Assumption (12) We can state:
Combining Assumptions (11) and (12):
Rearranging:
Using the letters of the
This is important because it shows consumer-surplus comparisons for perfectly inelastic, zero price elasticity,
We can state:
Rearranging:
We can state:
Using the results of Equation (23), We can state:
Thus,
We present here an original theoretical model of manufacturers and buyers of cars over a business cycle that have peak and off-peak demand periods to illustrate competitive manufacturing. We permit two types of car manufacturing plants, plantK operated year around and plantL opens only in peak-demand times. PlantK is static efficient but output-rates rigid while plantL is output-rates flexible but static inefficient. These are the two conditions for co-existence of diverse plant types.
To make policy recommendations, we need research on how realistic and critical are the assumptions of the model. Areas of future research include relaxing the assumption of linear total costs with absolute capacity limits. The more firms can produce beyond their normal capacity such as by paying over-time reduces the need for plantL.
The model here assumes easy entry which should eliminate super-normal profits over time. The ease of entry of the model for car manufacturing may be realistic today with the vast increase in outsourcing and in world trade. With internet, computers and smart-phones, firms could rely on suppliers to make parts and components and deliver them “just-in-time”. This is plantL of the model—a factory that is largely assembly only. The model assumes parts and factor-input prices remain constant. If they rise with shifts to plantL this would lessen the advantages of plantL.
What may be surprising is that in the model of the paper consumers have a huge willingness to pay to get suppliers to switch from SRMC pricing to a fixed-year around price (triangles
Consumers have a huge willingness to pay, in the model of the paper, for the car manufacturers to switch from SRMC pricing, because the consumers will be buying more cars in the peak of the business cycle, when their demand is high. Making the peak of the business cycle better, adds considerably to consumer welfare even though the peak is infrequent. The gains to consumers increase with more price elasticity of demand curves. Making the cost of a car higher in the off-peak is less importance, though the off-peak is far more frequent. Likely that consumer demand curves are elastic in high-demand times more so than in low-demand times, especially for cars. This would further increase the importance of focusing on sufficiency of supply for the high- demand periods.
The policy implication of this theoretical model is that though capacity utilization rates today are low as we’re in the off-peak period of the business cycle, we advise investors to think of the peak period and to plan for it. Investors should invest in plantL today. They will be amply rewarded during the peak of the business cycle with only a modest investment today7.
This is an important lesson—for regularly recurring cycles—because it urges focus, even in the off-peak periods, on making the peak periods better. This agrees with business cycle theories that urge social focus on increasing and prolonging cyclical peaks. This supports John M. Clark’s workable competition thesis [
8See, “Monopoly” by John M. Clark, Encyclopedia of the Social Sciences, 1933, volume 10 623-629.