A major court case just concluded threatening to significantly change the way Realtors in the United States are paid for their services. The fallout from this change is a matter of controversy. Some claim that the coming changes will be detrimental to low income buyers while others vehemently disagree.
As is usually the case, it is pretty easy to tell which side of the debate someone is on by considering which section of the market they are affiliated with. I am not making any judgements with that statement. I am positive that the majority of people on both sides find themselves there earnestly. However, the lack of a truly trustworthy authority to lean on makes it really hard to sort through the noise and develop your own conclusions on the matter.
This is the first part in a multipart series where I am going to start from scratch and analyze this problem using the rigorous approach of an economist. Throughout the series I will start from the very basics and carry on to layer necessary complexities into our analysis as we progress.
In this first part we are going to go through a brief primer on some key concepts and tools in economics that we will be using in our study.
In part 2 we will create a simple economic model that will be used as the foundation for all of our future analysis. This model will be overly simplistic on purpose. The goal is to create a clean pallet void of unnecessary complexity to give us a solid starting point.
In part 3 will assess the components of the aspects of the market that are most pertinent to this particular study and enhance our simple model to enable us to better observe those components as we progress through our analysis.
Further parts will dive into the various arguments presented by key commentators and analyze them through the lens of our model. In the end, we will coalesce what we have learned at form our own conclusions where we can and highlight the areas that we still remain uncertain.
The Three Core Assumptions of Economic Theory
In order to create generalized models economists start with three core assumptions:
- People have rational preferences among outcomes that can be identified and associated with a value.
- Individuals maximize utility (as consumers) and firms maximize profit maximize profit (as producers).
- People act independently on the basis of full and relevant information.
Now, I am sure you read those assumptions and scoffed. It only took four words for you to think to yourself “I know plenty of irrational people” and I agree with you. However, these assumptions are not meant to be perfect. They are meant to be useful and to be close enough that we can rely on them to build our models and conduct the majority of our study. But before we settle on our conclusions we will discuss how our results might be effected if our assumptions are wrong, for example the lack of perfect information will be a key player in our study.
Key Term: Utility
Next we need to define a new term, Utility. Utility is the total satisfaction or benefit an individual experiences or receives as the result of a transaction. It is an abstract unit that encompasses a wide variety of concepts.
For example, a man, Kevin, is sitting at a restaurant and considering what he wants to order. He has narrowed it down to two options: the $40 rib eye steak or the $20 pork chop. He will definitely enjoy the rib eye more, but $20 more? This is where the abstract concept of utility comes into play. Kevin is comparing the abstract idea of how much more he will enjoy the rib eye steak over the pork chop to the more concrete idea of the value of $20. In economics we lump all of that under a single term, Utility.
Economist’s Toolbox: The Utility Function
From there we go a step further. In order to really understand the decision Kevin is making, we can build a Utility Function, a mathematical formula that captures the logic from the paragraph above into a generalized format that we can study.
For our example we have two components to the utility function of customers of this restaurant such as Kevin: the price of the meal and how much enjoyment the customer gets from eating the meal.
\Large
U_c = E_m - P \\
\\
\phantom{U} \\
\footnotesize
\begin{aligned}
U_c &= \text{Customer's overall utility} \\
\text{Where,} ~E_{m} &= \text{Enjoyment the meal provides,} \\
P &= \text{The price of the meal}
\end{aligned}This function tells us that the more Kevin enjoys eating the chosen mean the more utility he receive and the higher the price of the meal the less utility he receives. A restaurant owner could use this utility function when making choices about what to offer on their menu. Based on this, the more enjoyment a meal provides, the more a customer is willing to pay. So they can replace less enjoyable meals with more enjoyable meals and charge higher prices.
A Better Utility Function
In reality, that utility function is probably too simple to be of much use to the owner though. “Enjoyment” is way too vague of a concept that should probably be broken out into more components such as how tasty a meal is, the size of the portions, presentation, etc. On top of that, different customers will have different preferences on what is most important to them. For some customers the tastiness of the meal will be the most important. For others the portion size is. Furthermore there are components completely missing from the simple utility function such as how easy it is to make that meal at home vs only get when out at a restaurant treating yourself.
\Large
U_c = \alpha(T) + \beta(V) + \lambda(S) + \omega(D_h) - P \\
\phantom{U} \\
\footnotesize
\begin{aligned}
U_c &= \text{Customer's overall utility,} \\
\alpha &= \text{Preference for a Tastier meal,} \\
T &= \text{Tastiness of the meal,} \\
\alpha~ &= \text{Enjoyment the meal provides,} \\
\beta &= \text{Preference for a more Visually Appealing meal,} \\
\text{Where, } ~~V &= \text{Visual appeal of the meal,} \\
\lambda &= \text{Preference for larger Portion Size,} \\
S &= \text{Portions Size of the meal,} \\
\omega &= \text{Preference for a meal that is Difficult to Make at Home,} \\
D_h &= \text{How difficult the meal is to make at home,} \\
P &= \text{The price of the meal}
\end{aligned}A good utility function is one that finds the balance between adding enough relevant complexities while remaining simple enough to actually be used. Identifying which components are important to an individual’s utility function and how to represent them mathematically is the art within the science of economics.
A Note on Notation
There are no hard and fast rules for the notation that economists use, there are a few common guidelines I will be using that are worth touching on.
- Variables (such as T for time) are typically italicized to distinguish them for regular text.
- Greek letters (\alpha, \beta, \gamma, ...) are typically used to represent parameters that modify other variables. For example, a person’s preference for tasty food is a parameter that modifies the tastiness of a specific food when calculating utility.
- Subscripts (e.g. the i in U_i, V_i, and T_i) are used to add specificity to a variable. For example in C_b and C_s the variable represents Costs, and the subscripts _c and _b specify that the cost is associated with the buyer, C_b, or the seller, C_s.
- Shorthand for signifying that a variable is dependent on other things is expressing that variable as if it were a function. For example U_c(T, V, S, D_h, -P) indicates that the Utility of a customer ,U_c), is depended upon the tastiness T, visual appeal, V, portion size, S, at home difficulty, D_h, and price, -P, of the food. The - associated with the P illustrates that price has a negative effect on the customers utility.
Using a Utility Function
Hopefully by now you have started to accept that utility functions can be quite useful. You may still be thinking to yourself that you hate math and this is teleporting you back to 10th grade algebra and you want to pull your hair out, but bear with me.
The first use case for a utility function is to apply it in a fully generalized manor. You use it as a road map to understand, conceptually, how changing different variables will affect the outcome of things.
In our restaurateur example, they can use the utility function we made to guide their decision making. When considering which of two potential options to add to their menu they simply look to the utility function to know which features of the two options are important to consider. Their first instinct to simply pick which meal tastes best is not enough, they also have to be sure to consider portion sizes, etc.
In more complex situations, such as the sale of a house, having utility functions can prove invaluable to navigate the theoretical affect different options have.
The second use case brings us beyond theoretical and allows us to actually measure the world around us.
Sticking with our restaurateur example, they can use this function to design a survey for their customers. In the survey they can ask each customer how much each of the key aspects of the meal options matters to them. They can use the results of that survey to fill in values for each of the preference parameters (\alpha, \beta, ...) in the utility function and make even better decisions about their menu. If their customers really don’t care about visual appeal and care a LOT about portion size, then they know which types of meals to focus on for their specific customer base.
The last use case is in using the utility functions, which focus on specific individuals involved in one off transactions, to extrapolate more comprehensive models of the entire market. Supply and demand curves.
Up Next in Part 2
In the next part we will use the tools introduced in this part to start to explore the economics around realtor commissions. We are going to build a simple utility function for each of the key players involved in the sale of a house upon which we will expand and explore in part 3 and beyond.