Costs - space travel-oriented, examination etc.

In this thread I will describe

1. which way costs are examined in Political Economics and
2. which way they are calculated and examined regarding projects.

The second point has to do with Enterprise Economics, Management and studies on projects.

Currently I am preparing the beginning of point 1.

May be I will refer to concrete space vehicles sometimes but this will be for illustration only.

The contents can be applied to other threads of this section but is meant to inform about the Thinking in Economics.



Dipl.-Volkswirt (bdvb) Augustin (Political Economist)

1. Costs in Political Economics

I. Fixed Costs and Variable Costs
II. Costs of the Passenger
III. Costs of Operation
IV. Degression of Costs
V. Vehicles of different scale
going to be continued in my next post)



I. Fixed Costs and Variable Costs

Fixed Costs are the costs of operation (or production) that occur also if there is no operation (or no production).

Variable Costs are the costs that are caused by the service (or product) operated (or
produced).

To carry a passenger to space - for example - is operating of service (or production of a product) - so Variable Costs are those costs that increase with number of passengers directly. Directly doesn't mean linear, proportional or something like that but only direct impact. In production of space vehicles the material, components and elements of the space vehicle make up the Variable Costs of production - the amount of material, components and elements required to produce SSO increase directly with the number of SSOs produced. This has nothing to do with a SS2, Black Armadillo or so. May be that it is required to go into the details later.



II. Costs of the Passenger

Let's call

Total Costs of Operation TCOP,
Number of Passengers NP and
Costs of the Passenger CP.

Then Costs of Passenger are CP = TCOP/NP.

Let's call

Fixed Costs of Operation FCOP,
Variable Costs of Operation VCOP and
Total Costs of Operation TCOP.

Then Total Costs of Operation and Variable Costs of Operation are functions of the
Number of Passengers:

VCOP = VCOP(NP)

TCOP = FCOP + VCOP(NP)

So Costs of the Passenger are

CP = TCOP/NP = (FCOP + VCOP(NP))/NP = FCOP/NP + VCOP(NP)/NP.



III. Costs of Operation

Fixed Costs of Operation FCOP include:

Fixed Costs of Vehicle FCV
Pilot FCP
Fixed Costs of Launch Site (runway, launch pad, launch personal etc.) FCLS
Fixed Costs of Company Administration FCCA
Fixed Costs of Propellant Storage FCPS
Else Fixed Costs FCE.

Variable Costs of Operation VCOP(NP) include

Propellant Costs of Passengers VPCP(NP)
Propellant Costs of Pilots VPCPI(NPI)
Costs of Cleaning the Vehicle VCCV(NP + NPI)
...

So TCOP = FCV + FCP + FCLS + FCCA + FCPS + FCE + VPCP(NP) + VCPI(NPI) + VCCV(NP + NPI)

Lets say FCLS + FCCA + FCPS + FCE = FCR (Remaining Fixed Costs) for a while to be able
to concentrate on FCV, FCP, VPCP(NP), VCPI(NPI) and VCCV(NP + NPI) currently.

Then TCOP = FCV + FCP + FCR + VPCP(NP) + VCPI(NPI) + VCCV(NP + NPI). Consequently
CP = FCV/NP + FCP/NP + FCR/NP + VPCP(NP)/NP + VCPI(NPI)/NP + VCCV(NP + NPI)/NP



IV. Degression of Costs

Fixed Costs - of Vehicle FCV, of Pilot FCP and Remaining FCR - don't vary by variations
of the Number of Passengers NP. So Fixed Costs per passenger decrease by increasing
Number of Passengers NP but the rate of decrease decreases too. This is called
Degression of Costs and mustn't be confused with economies of scale which are a different phenomenon.

Degression of Costs is asymptotic and is convergent to a horizontal line.



V. Vehicles of different scale

Now there may be several vehicles which differ by passenger capacity only. The vehicle with the smaller passenger capacity has Fixed Costs of Vehicle of FCV1 while the vehicle with the larger passenger capacity has Fixed Costs of Vehicle of FCV2.

Because there is more material required for the larger vehicle FCV1 < FCV2 is valid.
Lets assume that the larger vehicle has exactly twice the passenger capacity of the
smaller vehicle.

The larger volume doesn't require double the material required for the smaller vehicle
- thus FCV2 < 2*FCV1. And so FCV1 < FCV2 < 2*FCV1

Next lets assume that both vehicle use the same propellant. As long as there are no
passengers - NP = 0 and NPI = 0 - there are no Propellant Costs VPCP(NP) + VPCPI(NPI)
too: VPCP(0) = 0 and VPCPI(NPI) = 0. Then VPCP(NP) includes the Propellant Costs of
both these vehicles. VCCV(NP + NPI) = 0 too then.

Important also: Each vehicle needs a pilot - and two of the smaller vehicles means two
pilots required.

If now the number of people to be carried is twice the capacity of the smaller vehicle then at least one of the following situations will be real:

Lets call the passenger capacity per vehicle PCAPV - the smaller vehicle has a capacity
of PCAPV1 then while the other has PCAPV2. Then the considered Number of Passengers is twice the capacity of the smaller vehcile then: NP = 2*PCAPV1

a) Two of the smaller vehicles are used:

TCOP1 = 2*FCV1 + 2*FCP + FCR + VPCP(2*PCAPV1) + VPCPI(2) + VCCV(2*PCAPV + 2)

b) One larger vehicle is used:

TCOP2 = 1*FCV2 + 1*FCP + FCR + VPCP(2*PCAPV1) + VPCPI(1) + VCCV(2*PCAPV + 1)

Now because of FCV1 < FCV2 < 2*FCV1 AND the non-requirement of the second pilot b) is advantageous over a).

This is called Sub-Additivity.

In concrete the Fixed Costs of Vehicle FCV include Propellant Costs to lift the weight of the vehicle which is called Dead Weight. So the larger vehicle saves propellant compared to the use of two smaller vehicles. Large and small is a difference in scale.
Obviously the larger vehicle has less costs than two smaller vehicles if NP = 2*PCAPV1.

Regarding VCCV(NP + NPI)

1. less passengers cause less dirt but
2. especially the cleaning people first have to get into the vehicle(s).

So if the cleaning people have to enter two vehicles this tends to require more time and if they are payed per time VCCV is larger for the two smaller vehicles than it is for the larger vehicle - even if NP + NPI would be the same numbers in both cases.

The difference in time is due to the fact that for SSO at least first the wing has to be climbed and then the people hace to enter the vehciel by a small entrance.

Because of this VCCV(NP + NPI) and FCV1 < FCV2 the larger vehicle has more Fixed Costs but less Variable Costs than the smaller vehicle.

As a consequence the Costs of the Passenger of the larger vehicle are below the Costs
of the Passenger of the smaller vehicle at LARGE NUMBERS OF PASSENGERS but above the Costs of the Passenger at LOW NUMBERS OF PASSENGER.

This is called economies of scale.

You can construct an example very easyly by choosing a function Y1 = A1/x + M1 and
another function Y2 = A2/x + M2 with A2 > A1 and M2 < M1. Y1 would represent the
smaller vehicle while Y2 would represent the larger vehicle. Let Excel calculate the values for x = 1, 2, 3, ..., 100 (or higher) and create a diagram using lines. The curvatures intersect each other at a certain point. You can add more such functions.

So the comparisons of these vehicles reveal economies of scale in operating of flights
as service(s)

In this example A1/x represemts the Degression of Costs of Y1 while A2/x represents the different Degression of Costs of Y2.

The economies of scale would be represented by a function that fulfills the following two conditions in parallel:

1. f(y;x;p) = 0
2. Derivation of f(y;x;p) by p = 0

A tangent to a function fulfilling these two conditions would be tangent to the CP-curvature too. Currently I don't know how to derive the function of economies of scale
from the two conditions but it is possible to draw the curvature of economies of scale
into the Excel diagram manually - it only must touch one and only one point of Y1 and Y2.
Add as much Yi as you want which must be touched by the economies of scale-curvature at one and only one point too. The economies of scale-curvature is an enveloppe which must look similar to the CP-curvatures.



(going to be continued by my next post)



Please feel free to ask questions about this.



Dipl.-Volkswirt (bdvb) Augustin (Political Economist)

(Continuation)

VI. Costs of the Flight
VII. Costs of the Single Flight
VIII. Costs of the Vehicle
IX. Costs of the Propellant
X. Steps or Stages of Production
XI. Integration and Non-Integration
XII. No Links to Demand or Price
XIII. Diagrams
XIV. Degression of Costs/Economies of Scale and Decisions
XV. Structure of Costs

Costs of the Flight

Above the variable costs are a function of the number of passengers. The function hasn't
specified. Since tickets will be sold each passenger will have to pay the same price.

But is this proper really? If not then recalculations must be assumed to be required or
measures for adjustments have to be applied.

To answer the question let's look at the Flight Costs.

Let's call

Number of Flights NF and
Costs of the Flight CF.


Fixed Costs of Flight include all those Fixed Costs included in the Costs of the Passengers.

Variable Costs of Flight include

Propellant Costs of Flights VPCF(NF).

Total Costs of all Flights would be TCOP = FCV + FCP + FCR + VPCF(NF) then and
CF = FCV/NF + FCP/NF + FCR/NF + VPCF(NF)/NF.

Obviously nothing special can be seen up to now.

But the Costs of the Flight CF have been calculated it here whereas the Costs of the
Passenger CP have been calculated above.

CF = CP could be valid only if only one passenger would be flown per flight. To do so would
mean that there are no economies of scale at the passenger level.

CF = CP is invalid if more than one passenger is flown per flight. If the number of
passengers is kept constant permanently then the less flights are required and possible the
more passengers are flown by one flight.

So in principle CP = CF/NP is valid it seems.



Costs of the Single Flight

Engineers might miss something very important up to now. Vehicles, pilots and passengers
have weight and the weight has to be lifted. This is the cause of the Propellant Costs
VPCP(NP), VPCPI(NPI) and VPCF(NF). The problem that some of the propellant is required to
lift propellant is not considered here because Propellant Cost aren't the focus.

Let's call

Weight to be Lifted WL,
Weight of the Vehicle WV,
Weight of the Pilot WP and
Costs of the Single Flight CSF.

Then

FPCWV are the Fixed Propellant Costs of the Weight of the Vehicle,
FPCWP are the Fixed Propellant Costs of the Weight of the Pilot and
VPCW(WL) are the Variable Costs of Weight to be Lifted.

So CSF = FPCWV + FPCWP + VPCW(WL) is the cost function for the single flight. Then the
Costs of One Unit of Weight to be Lifted COUWL are

CSF/WL = FPCWV/WL + FPCWP/WL + VPCW(WL)/WL.

And this now is a portion of the sum of functions VPCP(NP) + VPCPI(NPI) and of the function
VPCF(NF).

Since passengers have different weights their weight have to averaged to do correct
calculation of Costs of the Passenger CP plus it could be tried to keep the weight of each
passenger within certain margins - by dietary work for example, space camps and so on. The
costs of all this may be considered to be included into VPCP(NP) and VPCF(NF).

But still very more important than this is the Vehicle



Costs of the Vehicle

The Total Costs of Operation TCOP include the Fixed Costs of Vehicle FCV. These can be
broken up into Costs of Maintenance of the Vehicle FCVM, Other Costs of the Vehicle FCVO and
the Costs of the Vehicle Itself FCVI.

Then FCV = FCVI + FCVM + FCVO.

Under V. Vehicles of different scale it has been said that FCV varies if scale varies
because of the different amount of material required.

This seems to indicate that there are Variable Costs of the Vehicle FCVI - and they really
are there but they don't have to do with this diffrence in scale.

Instead the Variable Costs of the Vehicle VCVI are an analogon to Propellant Costs of
Passengers VPCP(NP) - the higher the Number of Vehicles of one special scale NV are
produced the higher the Total Costs of Production of Vehicles TCPV.

The production of vehicles requires machines, tools etc. too. These cause costs that are
independent of the Number of Vehicles and thus Fixed Costs of Production of Vehicles FCPV.

So TCPV = FCPV + VCVI(NV). Then FCVI = FCPV/NV + VCVI(NV)/NV.

Obviously the last function looks very similar to the function giving the CP - which means
that Degression of Costs will occur here too. And then economis of scale are to be expected
also.

Integration of the function of FCVI into the function of CP leads to

CP = (FCPV/NV + VCVI(NV)/NV + FCVM + FCVO)/NP + FCP/NP + FCR/NP + VPCP(NP)/NP + VCPI(NPI)/NP + VCCV(NP + NPI)/NP

As already explained an increasing Number of Passengers NP can cause economies of scale to
occur - but if the Number of Passengers increases further this may cause the purchase of
additional vehicles of a scale already in use for flights. This would cause degressions of
costs and later in economies of scale in the production of vehicles.

In other words an increasing Number of Passengers NP can cause economies of scale in two
different relations in parallel - a cascade of degressions and economies of scale can occur.



Costs of the Propellant

The Costs of the Passenger CP, the Costs of the Flight GF and the Costs of the Single
Flight CSF all include Costs of the Propellant CPR. What are these Costs of the
Propellant?

Concerning Flight Costs the energy required to achiebve a certain velocity, a
certain amount of thrust or a certain acceleration is considered mostly. This energy
is got out of the Propellant and the amount of Propellant to be consumed is the
amount of real costs of that flight - but these are not the Costs of the Propellant.

Additionally the amount of Propellant to be consumed mostly is calculated then by the
monetary costs per unit of Propellant or by the price the unit of Propellant can be
bought by - these too aren't the Costs of the Propellant.

So again the question: What are the Costs of the Propellant?

To produce Propellant equipment, machines, tools etc. are required and again a
machine has costs that are independent of the amount of propellant produced. This is
so because machines themselves have to be produced too. So Propellant has Fixed Costs
of Propellant FCPR.

Next Propellant has to be made out of other materials - water to be electrolysed for
example. These materials are Variable Costs of the Propellant VCPR which depend on the
Amount of Propellant produced AP.

So the Total Costs of the Propellant are TCPR = FCPR + VCPR(AP). Then
CPR = TCPR/AP = FCPR/AP + VCPR(AP)/AP are the Costs of Propellant CPR.

And once again there is degression of costs and economies of scale are to be expected
if the scale of the machines etc. used is increased - analogous to what has been said
about vehicles of different scale.

This can be inserted into the function for the Costs of the Single Flight CSF:

CSF = FPCWV + FPCWP + VPCW(WL)

FPCWV = WV * CPR = WV * TCPR/AP = WV * (FCPR/AP + VCPR(AP)/AP) =
WV * FCPR/AP + WV * VCPR(AP)/AP

FPCWP = WP * CPR = WP * TCPR/AP = WP * (FCPR/AP + VCPR(AP)/AP) =
WV * FCPR/AP + WV * VCPR(AP)/AP

VPCW(WL) = WL * CPR = WL * TCPR/AP) = WV * (FCPR/AP + VCPR(AP)/AP) =
WV * FCPR/AP + WV * VCPR(AP)/AP

So CSF = WV * CPR + WP * CPR + WL * CPR =
WV * (FCPR/AP + VCPR(AP)/AP) + WP * (FCPR/AP + VCPR(AP)/AP) + WV * (FCPR/AP + VCPR(AP)/AP) =
FCPR/AP + WV * VCPR(AP)/AP + FCPR/AP + WV * VCPR(AP)/AP + FCPR/AP + WV * VCPR(AP)/AP.

Supposedly this includes a little bit too much linearities but it illustrates the
thinking sufficiently.

As already has been said - this requires the calculation of an average to get
passenger-related costs instead of weight-related costs.



Steps or Stages of Production

These considerations started at the terminating step of production which is the
ticket of for the passenger for his participation in a flight. That step includes
several cost factors which aren't included in the consideration of flights. Not
included in the flight costs are

Fixed Costs of Launch Site (runway, launch pad, launch personal etc.) FCLS
Fixed Costs of Company Administration FCCA and
Else Fixed Costs FCE.

These are parallel to the flight costs an may be considered later perhaps.

One step before the terminating step of production is the step of producing flights -
and one step before that step is the step of producing vehicles and propellant. These
both are at the same step but their production is not linked to each other and they
both can have degressions of costs and economies of scale independently.

The next step down could be the production of engines, nozzles, hulls, seats, delivery
of water or other material for producing propellant and so on.

The functions would become more and more complex then



Integration and Non-Integration

The considerations above don't include prices - they are done as if all steps of
production would be done in one and the same company. Some of the XPRIZE teams are
talking as if they will really do so. And this valid too for Blue Origin.

But there is at least one case where this is different -Scaled Composites/Virgin
Galactic. The first produces the vehicle and sells it then to the second. In that case
it is required to do a break and fill in the profit margin(s).



No Links to Demand or Price

None of the functions has is impacted by demand or price - the functions are valid
regardless of demand being zero or infinte or somewhere between both these extremes.
The curvatures are valid allways.

In a diagram with an Y-axis showing units of money and the X-axis showing the amount
of commodities produced there would be cost-curvatures only and the units of money on
the Y-axis would mena monetary costs - and it would be impossible to determine what
amount will be produced really. It isn't the purpose here to do that. It would be
enabled by a function of demand and adding its curvature to the digram plus adding
the marginal costs.


Diagrams

Each function CP, CF, CSF, FCVI and CPR requires its own diagram because the X-axis
would represent different comoodities in each diagram - Number of Passengers NP in the
diagram for CP, Number of Flights NF in the diagram for CF, Weight to be Lifted WL in
the diagram for CSF, the Number of Vehicles NV in the diagram for FCVI and AP in the
diagram for CPR



Degression of Costs/Economies of Scale and Decisions

Without the demand function or its curvature no decison about the amount produced is
possible - but other decisons are possible.

It turned out that degressions of costs as well as economies of scale can occur at
different steps of production. The prodcution of many small vehicles can cause
economies of scale of vehicle production which may be not achieved to that degree if
a few large vehicles would be produced instead. But the large vehicle can lead to
other economies of scale themselves. This means that economies of scale at one step
of production may be substituted by economies of scale at another step.

This means that there are different stretgies regarding costs, capacities and so on.
So decsions can and must be done about the strategy regardless of the demand or the
price.



Structure of Costs

During all these considerations a difference givenm by nature between costs has been
applied - Fixed Costs and Variable Costs. And this difference is responsible for
degression of costs and economies of scale.

The Total Costs consist of both these kinds of costs - and so have a structure.

The steps of production are such a structure too.



(going to be continued)



Which questions do you have?


Dipl.-Volkswirt (bdvb) Augustin (Political Economist)

At a level "below" or "inside" the subject(s) of Political Economics costs are considered a different way that finally leads to similar results.

One of the main differences between the two ways is that Political Economics consider markets and economies which means that all commodities - products and services - are already produced or in production while Enterprise Economics consider what's going on within enterprises, companies etc.

The subject(s) of Enterprise Economics can't be considered to be at a level below or inside Political Economics but to be crossing with the subject(s) of Political Economics.

Before a company begins to produce something it has to allocate all what's required fot production, sales, storing, delivering and managing the company. Allocation includes planning, scheduling, ordering, storing, financing, investing, hiring and much more.

Most companies need to earn a profit, get increased market shares etc. Consequently plus given what I said above about allocation profits and market shares must be planned. Please note urgently: In the case of private companies planning means the design of an intention merely.

Planning profits etc. can't be done without planning the costs. The planning of costs is based on the data about the capacity of the equipment of the company, procurement prices, wages, interests of credtits and investments and the like. all these data can be inserted into formulars - resulting in optimal amount to be ordered, optimal time of ordering, optimal amount causing an order and the like. It can be done by Personal Computer - amd the formulars have the tendency to look different in each company.

The way begins at the data about what is allocated and lead to prices, profits and the like - it's the opposite direction compared to Political Economics.

Necessaryly this direction is valid too regarding the product. While Political Economics sees the product Enterprise Economics and companies don't do so - they can't and they mustn't. The idea of a new product/service or a modification of a product/service necessaryly is prior to production and so on. This one of the cores of entrepreneurship -to create soething new, thus taking a significant risk and pushing it to the market(s).
This is what's going on within the teams and companies competing for the XPRIZE CUP and the ASP.

This forces the companies to avoid nearly each estimation like done in Political Economics and to calculate the present costs instead. Present costs means costs probably to be valid within the next six months to the next two years.

They need to do a project about the properties of the new product - reusable rocket, spaceplane, expendable rocket etc. - and to look what it's going to cost. Next they have to compare the result to the financial ressource (credit lines etc.) and - likely - to modify the design in order to optimize costs as well as the new product and the production method.

For this reason they have to analyze which costs they can control and which not.

Nothing of this is estimation no way. ...


(to be cotinued later)



Dipl.-Volkswirt (bdvb) Augustin (Political Economist)

PS: This can't be described the way I have described the comsideration of costs by Political Economics because this would result in a simple but long list of formulars and a table of methods - which botth will explain nearly nothing.

In the thread about tankers etc. I initiated in the Technology section recently there was a post saying that the term "cheap" used in another post of that thread will be meant in the meaning of energy required or consumed. I have understood that term economically earlier.

Because of that I should add a simple but important remakr of theoretical kind here which is of fundamental meaning.

Costs as they are discussed here don't have nothing to do with consumption of energy stored in propellant that is not consumed yet - they don't have to do especially with the propellant costs.

Propellant costs - the costs of the propellant are the costs of mining or producing the propellant only. Nothing else.

Energy consumption by a flight is opportunity costs only. Opportunity costs are the loss or impossibility to consume something for another purpose once it has been consumed for one special purpüose of several possible purposes. For example oxygen consumed as propellant for a flight has the opportnity costs of no longer being available for breathing, vehicle atmosphere, station atmosphere.

Such opportunity costs haven't been considered during this thread up to now.



Dipl.-Volkswirt (bdvb) Augustin (Political Economist)

One important aspect has to be added regarding opportunity costs: If there are chances to get revenues then to take one of these chances means that this causes opportunity costs which consist of missing the revenues to be got by the other chances.

So energy consumed by a space flight and missing revenues to be got by a chnaces that hasn't been tken both are opportunity costs.

That's very complex compared to what has been explained in this thread up to now - and it is very abstract. That's the very reason why I don't considere it here.

And it is a reason to not base any cost considerations on energy consumption.



Dipl.-Volkswirt (bdvb) Augustin (Political Economist)

The article "The Mega-Module Path to Nowhere (Or: How to Eliminate Human Space Flight With an HLV)" ( www.space.com/adastra/adastra_mega-modules2_051013.html ) which serves as illustration of the theoretical issues of this thread explicitly mentions an additional structure of costs: costs = capital costs + labour costs.

Capital costs are interests and depreciations mainly - plus what is paid to external consultants.

Labour costs are the wages etc. of employees of the producer or servicer.

Both capital and labour costs are fixed costs - but they differe from each other. The capital costs can be reudced or avoided and have the tendency to fall apart once they are depreciated - the labour costs never fall apart like that. Additionaly labour costs per unit of product or service can drop by learning effects - the capital costs can't.

Important also is that learning effects cause economies of scale - they reduce the labour costs per unit of product or service while they may force the company to increase the wages.

I wilol think about working this out and integrate it into the functions etc.



Dipl.-Volkswirt (bdvb) Augustin (Political Economist)

To go on separating the costs into capital costs and labour costs I should concretize what I said in the previous post.

The equations in all the previous posts included Fixed Costs. The Costs of the Passenger have been considered and so the Fixed Costs have been divided by the total number passengers finally - after haveing gone through all the levels of causes and equations.

The Fixed Costs included the vehicle - its investment costs - , the propellant required to lift the additional weight of the pilots and the costs of cleaning the vehicle after flight.

These Fixed Costs now are structured themselves - some of them may terminate one day while others never will terminate.

The investment into the vehicle might terminate. It is got back from the passenger by depreciation and it may turn out that the vehicle still works well after it is totally depreciated.

The propellant to lift the pilots never will terminate unless the requirement of pilots is removed

The costs of cleaning never will be removed I suppose.

Of these the investment into the vehicle is capital costs. Even if it is the own capital of the owner of the vehicle it has to be considered to require the expense of interest money. It mustn't be expected that the use of this own capital isn't paid while the use of someone else's capital has to be paid.

So a virtual interest - "kalkulatorische Zinsen" - have to be included here.

Labour costs up to now are hidden in the Pilot FCP, Fixed Costs of Company Administration FCCA and Else Fixed Costs FCE. And some can be suspected to be hidden in variable costs.

It can't be avoided to include the time as a variable here now.



Dipl.-Volkswirt (bdvb) Augustin (Political Economist)

Before I go on with capital costs and labour costs something important requires to be mentioned urgently.

Al the cost functions alread described, explained and used in this thread consider relations between the amount of commodities - flights, vehicles, propellants - and the ingredients and inputs into the production only.

This mustn't be misunderstood as if the amount of commodities would be produced at once altogether. So the costs don't occur in sum altogether.

It' sdifferent: All the production facilities - vehicles are facilities to produce flights, fabrics are facilities to produce vehicles or propellants - have limited production capacities only. These limits limt the amount of commodities produced per unit or period of time while the amount the actual costs are related to may be much higher than this limit.

There can be several homogenous production facilities in parallel - but they then need to be distributed over a an area, a rgeion or even the whole world. This induces additional costs like transportation which aren't considered here yet.

So the amounts of commodities considered by the functions used here don't mean to be produced neither at the same time nor at the same place. Two or more flights may be distributed over the whole world - and then the costs will be too. What the functions used up to now consider is the sum of all the costs distributed over the world as well as the sum of the amounts of commodities distributed all over the world.

Furthermore all the costs don't need to be actual. I know what it will cost to drive by my car from Hamburg to Stade - but I don't intend to do that trip, I don't intend to use my car today. The costs are real and valid thought - I simply don't make them actual costs but leave them potential ones.



Dipl.-Volkswirt (bdvb) Augustin (Political Economist)