# Costs functions

In order to give a survey of the costs, cost functions are made for the following cost types, as shown in figure 1.6.1 and 1.6.2

o Total variable costs (TVC), which expresses the joined variable costs.

o Total fixed costs (TFC), which expresses the joined fixed costs

o Total costs (TC), which expresses the joined fixed and variable costs

Figur 1.6.1: Samlede omkostninger i forbindelse med bilen pr. är

Figur 1.6.2: Samlede omkostninger i forbindelse med bilen pr. är

The figures above illustrate my uncle's total costs concerning the car, as a function of the mileage. Figure 1.6.1 shows the costs concerning the loss of value due to mileage and the costs of fuel consumption as well as the costs of changing the tires, service check-ups, and maintenance. Owing to these factors, the curve "jumps," and thus illustrates the costs. Figure 1.6.2 on the other hand shows the costs after spreading the variable costs over each driven kilometer. This means that the curve is flattened, which owes to the fact that the costs of service check-up, change of tires and maintenance are treated as a cost of each driven kilometer.

The cost functions mentioned above provides a highly simplified picture of reality, as it is often necessary to make a number of more or less reasonable assumptions, before such functions can be defined.

# Explanations and assumptions

Explanations and assumptions regarding the above figures:

o The TVC curve with "jumps" (figure 1.6.1):

o The even rise of the curve owes to the fact that each kilometer causes costs of 80 0re for fuel (12,000 DKK / 15,000 km) all the while the car loses 23 0re (3,500 DKK / 15,000 km.) of value per driven kilometer.

- Service check-ups, it is assumed as mentioned earlier that these are being carried out each 7,500 kilometers and cost 1,200 DKK. Furthermore it is assumed that the last check-up was carried out 2,500 kilometers ago, which is why the curve makes a 1,200 DKK "jump" at 5,000, 12,500, 20,000 and 27,500 kilometers.

- It is assumed that the tires were last changed 7,500 km. ago, which means that the curve makes a 3,880 DKK "jump" at 22,500 kilometers.

- Furthermore it is assumed that all the maintenance costs are realized at one time at an expanded 10,000 km service check-up, including the necessary repairs, which is why the curve makes a 13,498 DKK "jump" at 25,000 km.

o The TVC curve without " jumps" (figures 1.6.2):

- Figure 2 is a development of figure 1, and the variable costs have simply been calculated as total variable costs for 30,000 km. and then divided with 30,000 km., which yields 1.77 kr./kilometer. This method is reasonable as the indirect variable costs are spread over the cost bearing kilometers. E.g. it is reasonable to distribute the costs of changing tires on the kilometers that wore them down.

o The TFC curve both with and without "jumps" (figures 1.6.1 and 1.6.2):

- As mentioned earlier, the fixed costs are not affected by the mileage, and thus they are 29,077 DKK, regardless of the quantity of kilometers driven.

o The TC curve both with and without "jumps" (figures 1.6.1 and 1.6.2):

- The TC curve shows the joined costs, which is why the curve is a vertical addition of the TFC and the TVC curves. Resultantly, the curve starts at 29,077 DKK and matches the tendencies of the TVC curve afterwards.

Moreover, the cost model has been simplified such that no considerations are made for the greater value loss incurred by the initial kilometers. Likewise no considerations have been made regarding the fact that the maintenance costs are increasing during the period, due to the fact that the risk of damages and wear and tear are less pr 10,000 km between 70,000 and 80,000 km, than 10,000 km between 80,000 and 90,000 km.

So, what do I tell my uncle? Still an open question.

# Situation dependency of the cost function

There are a number of issues other than the stated assumptions, which influence the costs, and result in the cost function being less than completely accurate; e.g. maintenance costs, tire and fuel are highly dependent on the manner in which the car is driven. Driving at 130 km/h results in higher fuel consumption than driving at 80 km/h. Driving in cities causes relatively more wear and tear on brakes than driving on a country road. Driving on salted roads during the winter in Denmark, causes higher value loss than driving on dry roads in summer.

# The product "a driven kilometer"

Cost functions with the number of kilometers as measurement unit Q is problematic for the car case, as the purpose of owning and driving a car is not just the generating of mileage. The purpose, on the other hand, is to be able to drive wherever you want, whenever you want to. As a result, the product I borrow from my uncle depends on the circumstances; e.g. the product "one driven kilometer" in a city differs from a long trip on the highway, one kilometer at high speed is quite different from a kilometer driven safely, a kilometer by an unskilled driver is different from the same distance driven by a skilled driver. Moreover, the value of having a car is dependent on the condition of the public roads. The costs vary based on all these circumstances.

# Decisions and costs

In connection with defining my uncle's costs of letting me borrow the car the specific decision-making situation is of great importance (= opportunity costs). In order to give an insight into this line of thought, a number of decision-making situations are presented, where the costs are to be treated differently:

o I am at a Christmas lunch at my uncle's, and all the family except me has had too much to drink. Suddenly my girlfriend calls and asks me to pick her up. In this case, my uncle's costs of letting me borrow his car can be regarded as the variable costs of the trip as the time horizon is quite short and he is not able to drive anyway because of his drinking.

How much should I pay?

o I have just been offered a four week job, with relevant for my education, requiring me to spend every afternoon on a location outside Ringsted, where it is impossible to go with public transportation (I live in Copenhagen). My uncle tells me that I can borrow his car, despite the fact that he himself would have liked to use it in the same period. As a consequence of this, my uncle's costs of letting me use his car are regarded as the variable costs as well as a part of the fixed costs, e.g. the fixed costs divided into 365 days and multiplied by 28. Furthermore it would be appropriate for me to pay my uncle for "owning" his car during this period.

How much should I pay?

o If the situation above is changed so that my uncle is on vacation and has no use of the car, the costs of letting me borrow the car are changed as well. Then the costs would be regarded as being the variable costs plus potential opportunity costs, in case my uncle could have rented the car out to a friend.

How much should I pay?

The decision-making model 1.6 is generated in order to structure the above thoughts into a more general way, so that the model is applicable in different decision-making situations.