Demand Elasticity and Cost Analysis of Building a Pipeline
Utility In order to understand how consumers make purchasing decisions, we must understand their utility. Utility is the happiness or enjoyment that consumers
derive through the purchase of goods or services. We use the term "util" as a
unit of measurement for utility. Consumers will have different utilities for
different items and will also have different utilities from other consumers.
Imagine a hypothetical economy with only two goods: soda and pizza. Our
hypothetical consumer Sarah has a preference for pizza, so let us assign four
utils to a slice of pizza. One may think that Sarah would eat pizza all day,
every day based on this preference, but we know this would not happen in
real life. This is because of the law of diminishing marginal utility. After
Sarah eats one slice of pizza, she is very happy and has achieved four utils.
However, she is not as hungry when she eats the second slice of pizza, so
she may only derive three utils. The third slice of pizza will not be as satisfying
as the first or the second slice, so she may only derive two utils. If she is full
after the third slice, a fourth slice of pizza would yield zero utility. If she
continued to eat a fifth slice and got a stomachache, she would receive
negative utility as the fifth slice is bringing her discomfort, or disutility.
Looking at the table below, the law of diminishing marginal utility is apparent,
as the marginal (or additional utility) derived from additional consumption of
pizza decreases over time. If we add up the marginal utilities, or the utility
derived from each piece of pizza, we will obtain total utility in the third column.
Total utility increases, but at a decreasing rate due to the law of marginal
utility. Once marginal utility becomes negative, the total utility will start to
decrease. Therefore, her total utility is maximized at the third slice of pizza.
This is called consumer equilibrium, when a consumer has no incentive to
change the amount of goods or services consumed, because satisfaction has
been maximized.
No. of Slices MUP TUP
1st 4 4
2nd 3 7
3rd 2 9
4th 0 9
5th -2 7
We can elaborate on this scenario by adding a second commodity, soda, to
our hypothetical economy. Sarah likes soda half as much as pizza, so we can
assign two utils to her first soda. We know that the marginal utility of soda will
also decrease, so soda will always provide less marginal utility than pizza.
Based on this, one may assume that Sarah would still eat three slices of pizza
and also drink two sodas every day, as this combination would yield the
highest total utility possible at 12 utils.
No. of Slices MUP TUP
No. of Sodas MUS TUS
1st 4 4 1st 2 2
2nd 3 7 2nd 1 3
3rd 2 9 3rd 0 3
4th 0 9 4th -1 2
5th -2 7 5th -3 -1
However, consumers have a limited amount of funds available, called a
budget, and must operate within this budget constraint. Assume the price of
pizza is $3, the price of soda is $1, and that Sarah has a budget of $8 for
lunch. She cannot afford the previous combination at a total cost of $11.
In order for Sarah to maximize her total utility, given this budget restraint, she
will need to compare the marginal utility derived per dollar spent on both pizza
(MUP/$P) and soda (MUS/$S). The equation below will give Sarah a new
consumer equilibrium, assuming that the marginal utilities per dollar for the
last goods purchased are equal, and that she has spent her last dollar.
MUA/$A = MUB/$B = … = MUZ/$Z
Sarah makes her first choice between a soda and a slice of pizza, with the
first soda giving the highest marginal utility per dollar at two utils per dollar.
The choice now lies between the first slice of pizza and the second soda, so
Sarah will buy the pizza next to gain 1.33 utils per dollar. Sarah reaches the
point where the MUP/$ = MUS/$ at the second slice and the second soda.
She also spends her entire budget of $8, so she has reached consumer
equilibrium.
No. of Slices MUP/$
Total Price
No. of Sodas MUS/$
Total Price
1st 4/3 = 1.33 $3.00 1st 2/1 = 2 $1.00
2nd 3/3 = 1 $6.00 2nd 1/1 = 1 $2.00
3rd 2/3 = .67 $9.00 3rd 0 $3.00
Costs of Production Just as all consumers have a common goal to maximize happiness, or utility, producers also have a common objective—to maximize profits. In order to do
so, they must consider the various types of costs they will face. The following
formula gives the profit, π, obtained by a firm when subtracting total costs
(TC) from total revenues (TR).
π = TR - TC
Each firm will have different costs of production, depending on input costs.
There are four types of inputs, or resources, which include anything that is
necessary to produce a good.
1. Land—includes natural resources such as timber or fisheries.
2. Labor—includes skilled and unskilled labor, as well as physical and
mental labor.
3. Capital—includes money and physical assets such as machinery,
buildings, and vehicles.
4. Entrepreneurship—includes the function of gathering and allocating
the other resources to produce a final product.
Some of these costs will be fixed in the short-run, meaning that they must be
paid regardless of how much the company is producing. For example, if a firm
stops producing, they will still need to pay for rent, loan payments, utilities,
etc. On the other hand, variable costs fluctuate with the level of production
and are completely eliminated when the company shuts down. A moving
company will spend more money on gas as they increase offerings of their
service, whereas this variable cost will be zero if there is no production.
Other important costs are:
1. Marginal Cost—the additional cost of producing an additional unit.
MC = ∆ output / ∆ input
2. Total Cost—the sum of total fixed and total variable costs.
TC = TFC + TVC
3. Average Fixed Cost—the average fixed costs per unit of output.
ATC = TFC / Q
4. Average Variable Cost—the average variable cost per unit of output.
AVC = TVC / Q
5. Average Total Cost—the average total cost of the good or service.
ATC = TC / Q
ATC = AFC + AVC
The graph below shows a hypothetical cost table, which has several apparent
patterns. Notice that the total fixed cost remains the same, regardless of
production. If you increase or decrease production of a good, your fixed costs
such as rent and loan payments will remain the same. Even with zero
production, fixed costs still need to be paid. Conversely, total costs do vary.
Total costs increase with production and are zero when no production is
taking place. The total cost is the sum of the two costs in columns two and
three.
The average fixed cost is determined by averaging the total fixed cost per
quantity of output, or column two divided by column one. We also take the
average of total variable cost in column three and divide by column one to
obtain the average variable cost in column six. Average total cost is the sum
of columns five and six. Notice that average fixed costs decrease as output
increases, while average variable costs increase with production. This causes
the average total cost curve to increase initially, and then decrease.
The marginal cost column to the right is calculated by looking at how the total
costs in column four change, divided by the change in total output (column
one). With zero output, total cost is initially $20, but increases to $40 when
output increases to 10 units. The change in total cost is 20, divided by the
change in total output of 10, yielding a marginal cost of 20/10 = 2. As
production moves from 10 to 20 units, total cost increases from $40 to $60.
The change in total cost is 20, divided by the change in output of 10, yielding
20/10 = 2. Next, we see that total cost increases from $60 to $90, as the
output increases from 20 to 30 units. The change in total cost is 30, divided by
the change in output of 10, yielding 30/10 = 3. You could continue this
calculation in the same manner to obtain the last column.
Total Output TFC TVC TC AFC AVC ATC MC
0 20 0 20
10 20 20 40 2.00 2.00 4.00 2.00
20 20 40 60 1.00 2.00 3.00 2.00
30 20 70 90 0.67 2.33 3.00 3.00
40 20 100 120 0.50 2.50 3.00 3.00
50 20 160 180 0.40 3.20 3.60 6.00
60 20 260 280 0.33 4.33 4.67 10.00