Calculus has many real world uses and applications in the physical sciences, computer science, economics, business, and medicine. I will briefly touch upon some of these uses and applications in the real estate industry.
Let’s start by using some examples of calculus in speculative real estate development (i.e.: new home construction). Logically, a new home builder wants to turn a profit after the completion of each home in a new home community. This builder will also need to be able to maintain (hopefully) a positive cash flow during the construction process of each home, or each phase of home development. There are many factors that go into calculating a profit. For example, we already know the formula for profit is: P = R – C, which is, the profit (P) is equal to the revenue (R) minus the cost (C). Although this primary formula is very simple, there are many variables that can factor in to this formula. For example, under cost (C), there are many different variables of cost, such as the cost of building materials, costs of labor, holding costs of real estate before purchase, utility costs, and insurance premium costs during the construction phase. These are a few of the many costs to factor in to the above mentioned formula. Under revenue (R), one could include variables such as the base selling price of the home, additional upgrades or add-ons to the home (security system, surround sound system, granite countertops, etc). Just plugging in all of these different variables in and of itself can be a daunting task. However, this becomes further complicated if the rate of change is not linear, requiring us to adjust our calculations because the rate of change of one or all of these variables is in the shape of a curve (petshub.xyz)? This is one area where calculus comes into play.
Let’s say, last month we sold 50 homes with an average selling price of $500,000. Not taking other factors into consideration, our revenue (R) is price ($500,000) times x (50 homes sold) which equal $25,000,000. Let’s consider that the total cost to build all 50 homes was $23,500,000; therefore the profit (P) is 25,000,000 – $23,500,000 which equals $1,500,000. Now, knowing these figures, your boss has asked you to maximize profits for following month. How do you do this? What price can you set?