In this video, we will look at real estate markets: rent, vacancy, and equilibrium. We will explore these markets in terms of both the short-run and the long-run.
To begin, let’s consider a real estate market for a specific kind of property. This real estate may be for residential, industrial, commercial or for a number of other uses. However, for any of these markets, we will consider the real demand, Q sub d, and the real supply, Q sub s, in quantities of usable square feet.
If the available square footage is not sufficient, additional quantities can be added at a market price notated as small Greek letter kappa for the cost of construction. In effect, this cost for an additional square foot is a marginal cost.
As the value of real estate is determined by the net returns from it, over an estimable period of time, we need to define the useful life of the property. Therefore, we can determine useful life in terms of one divided by delta, where delta is a coefficient that reflects the average amount of value that is used up in a given year. For example, if delta equals .025 (2 and a half percent), the estimated useful life would be calculated as one divided by 2.5 percent, which equals 40 years.
In respect to Supply and Demand, we can consider Rent as the Price and Square Footage as the Quantity. Total Rent received before any adjustments or deductions are made. The net return from a property is referred to as Net Rent. In turn, Net Rent equals Gross Rent minus all Expenses not covered by the tenant.
When Expenses are deducted from Gross Rent, D sub g, the remainder is Net Rent, D sub n. In our graph of demand for real estate, we find that Demand moves downward and to the left as Expenses are subtracted from the gross. The slope of the demand curve remains the same. However, the vertical intercept decreases by an amount equal to the Expenses, which we assume as fixed in this example.
Let’s go a bit deeper into this matter. First, we assume that the Demand for vacant land before improvements are made is inversely related to Net Rent. In other words, the quantity of vacant land demanded increases as Net Rent decreases.
Because of this inverse relationship, we can consider Net Rent as the opportunity cost of holding space off the market, keeping it vacant for a given period of time. In other words, renting land out to a tenant represents the next best use of the land in comparison to the owners holding and perhaps using the land themselves.
Before constructing a real-estate market model, let’s define and give symbols for the variables that we will use. These are: K, the total square footage of that exists in a specific market; Q, the square footage currently occupied by tenants; V, the square footage in the market that is currently vacant; r, the discount rate for determining present value; delta, the rate of depreciation for any structures (note: land itself does not depreciate); R, the rent per square foot for occupied space; kappa, the construction cost of an additional square foot of improvements; v, the vacancy rate defined as the vacant square footage divided by the total square footage in the market; Theta, the occupancy rate defined as the square footage occupied by tenants divided by the total square footage in the market; and C, the annual cost of using capital. In respect to this last item, we note that C is a function of construction cost per square foot, the discount rate, and the depreciation rate. Furthermore, as the depreciation rate goes to zero, the annual capital cost will be equal to the product of the discount rate and the construction cost per square foot.
Therefore, K, the total inventory of property in a market equals the sum of V, the square footage of vacant land, and Q, the square footage of occupied space. We note that as percentages of K, the total inventory, the sum of the vacancy rate plus the occupancy rate must equal 100%.
Working with v, the vacancy rate and Theta, the occupancy rate in respect to K, the total inventory of property, we can graph contrasting demand curves. D sub Theta, the blue line descending to the right from the vertical axis to a point along the red line K, represents the demand for occupied property. In contrast, D sub v, the blue line descending to the left from the uppermost point on the line K, represents the demand for vacant property. These two demand curves intersect at the equilibrium point identified by the coordinates R*, the equilibrium Rent, and Q*, the equilibrium quantity in square feet. The curved green line represents the annual cost of capital per the occupancy rate. In respect to long-run equilibrium, this capital cost function must come into concurrence with the two demand curves at the point of equilibrium.