My editorial
This time, in the educational stream of my blog, I am addressing the students of 1st year undergraduate. This update is about microeconomic and management. Regarding your overall educational curriculum, these two courses are very much complementary. I am introducing you now into the theory of markets, and, in the same time, into the managerial concept of business model. We are going to consider a business of vital importance for our everyday life, although very much unnoticed: energy, and, more specifically, electricity. We are going to have a look at the energy business from two points of view: that of the consumer, and that of the supplier. If you have a look at your energy bill, you can basically see two lines: a fixed amount you pay to your supplier of energy, just for being connected to the grid, and a variable amount, which is, roughly speaking, the mathematical product: [Price of 1 kWh * Quantity of kWh consumed]. Of course, ‘kWh’ stands for kilowatt-hour. On the whole, your expenditure on electricity is computed as:
E = Fixed price for connection to grid + [Price of 1 kWh * Quantity of kWh consumed]
P1 P2 Q
From the point of view of the supplier of energy, their market is made of N consumers of energy. We can represent this market as a set made of N elements, for example as N = {k1, k2, …, kn}, where each i-th consumer ki pays the same fixed price P1 for the connection to the grid, the same price P2 for each kWh consumed, and consumes an individually specific amount Q(ki) of energy measured in kWh. In that set of N = {k1, k2, …, kn} consumers, the total volume Q of the market is computed as:
Q = Q(k1) + Q(k2) + …+ Q(kn) [kWh]
…whilst the total value of the market is more complex a construct, and you compute it as:
Value of the market = N*P1 + Q*P2
Most consumers have a more or less fixed budget to spend on electricity. If you take 1000 people and you check their housing expenses every month, you will see that their expenditures on electric power are pretty constant, unless some of them are building spaceships in their basements. So we introduce in our model of the market a budget on electricity, or Be, specific to each individual customer ki. Hence, that budget can be noted as Be(ki). Actually, that budget is the same as what we have introduced earlier as expenditure E, so:
Be(ki) = E = P1 + P2*Q(ki)
This mathematical construct allows reverse engineering of individual power consumption. Each consumer uses the amount Q(ki) of kilowatt-hours, which satisfies the condition:
Q(ki) = [Be(ki) – P1] / P2
In other words, each of us has a budget to spend on electricity bills, from this budget we subtract the fixed amount of money P1, to pay for being connected to the power grid, and we use the remaining sum so as to buy as many kilowatt-hours as possible, given the price P2. This condition is a first approach to what is called the demand function, on the part of the consumers. Although this function is still pretty sketchy, we can notice one pattern. The total amount of electricity Q(ki) that I consume depends on three parameters: my budget Be(ki), and the two prices P1 and P2. In economics, we call this an elasticity. We say that the quantity Q(ki) is elastic on: Be(ki), P1, P2. How elastic is it? We can calculate it, if we now the magnitudes of change in particular factors. If I know that my consumption of electricity has changed from like 40 000 kWh a year to 42 000 kWh, and I know that in the meantime the price P2 of one kilowatt-hour has moved from 0,1 euro to 0,12 euro, I can calculate something called deltas:
delta [Q(ki)] = ∆ Q(ki) = 42 000 – 40 000 = 2 000 kWh
delta (P2) = ∆P2 = €0,12 – €0,1 = €0,02
The local (i.e. specific to this precise situation) elasticity of my consumption Q(ki) to the price P2 can be estimated, in a first approximation, as
e = ∆ Q(ki) / ∆P2 = 100 000 kWh per €1
The first thing to notice about this elasticity is that it is exactly contrary to what you see in my lectures, and what you can read in textbooks, about the demand function. The basic law of demand says something like: the greater the price, the lower the consumers’ willingness to buy. Here, we have something contrary to that law: greater consumption of energy is associated with a higher price, through a positive elasticity. I am behaving contrarily to the law of demand. In science, we call such a situation a paradox. Yet, notice that it is a local paradox: I cannot keep on increasing my personal consumption of electricity ad infinitum, even in the presence of a constant price. At some point, I have to start saving energy and increase my consumption just as much, as the prices possibly fall. So, generally, as opposed to locally, I am likely to behave in conformity with the law of demand. Still, keep in mind that in real life, paradoxes abound. It is not obvious at all to peg down a market equilibrium exactly as shown in textbooks. Most real-life markets are imperfect markets.
Now, if you look at this demand function, you can find it a bit distant from how you consume electricity. I mean, personally I don’t purposefully maximize the quantity of kilowatt-hours consumed. I just buy stuff powered by electricity, like a computer or a refrigerator, I plug it in, I turn it on, and I use it. Sometimes, I vaguely practice energy saving, like turning off the light in rooms where I am not currently staying. Anyway, my consumption of electricity Q(ki) is determined by the technology T I have at my disposal, which, in turn, consists of a set M = {g1, g2, …, gm} of goods powered by electricity: fridge, computer, TV set etc. We say that each j-th good gj, in the set M, is a complementary good to electricity. I can more or less accurately assume that an average refrigerator consumes x1(fridge) kWh, whilst an average set of house lighting burns x2(lighting) kWh. We can slice subsets out of the set N of consumers: N1 people with fridges, N2 people with air conditioners etc. With Q(gj) standing for the consumption of electricity in a given item powered with it, I can write:
Q(ki) = N1*Q(g1) + N2*Q(g2) + …+ Nm*Q(gm) = [Be(ki) – P1] / P2
It means that, besides being elastic on my budget and the prices of electricity, my individual demand for a given amount of kilowatt-hours is elastic on the range of electricity-powered items I possess, and this, in turn, means that it is elastic on the budget I spend on those pieces of equipment, as well as on the prices of those goods (with a given budget to spend on houseware, I am more likely to buy a cheaper fridge rather than a more expensive one).
Now, business planning and management. Imagine that you are an entrepreneur, and you want to build a solar farm, and sell electricity to the people living around it. Your market works as shown above. You know that whatever you want to do, your organisation will have to satisfy the needs of those N customers, with their individual budgets and their individual elasticities in expenditures. The size of your organization, and its structure, will be significantly determined by the necessity to maintain profitable relations with N customers. Two questions emerge: what such organizational structure (i.e. the one serving to build and maintain those customer relations) would look like, and how could it be connected to other functional structures in the business, like building the solar farm, maintaining it in good technical state, purchasing components for construction and maintenance, hiring and firing people etc. You certainly know one thing: you have a given value of the market = N*P1 + Q*P2 and you have to adapt your costs (e.g. the sum total of salaries paid to your people) to this value of the market. Thus, you know that:
Average salary in my business = [(N*P1 + Q*P2) – The profit I want – Other costs] / the number of employees
In other words, the size of my business, e.g. in terms of the number of people employed, as well as my profit and the wages I can pay, will be determined by the value of my market. Now, let’s go along a path at the frontier of economics and management. I want to know how much capital I should invest in my business. I posit a condition: that capital should return to me, in the form of profits from business, in 7 years. Thus, I know that:
My initial investment = 7* My annual profit = 7*(N*P1 + Q*P2 – Current costs) = N*Be(ki) – current costs = N*E – current costs = N*[P1 + P2*Q(ki)] – current costs
This is how the size of my business, both in terms of capital invested, and in terms of the number of people employed, is determined by, or is elastic on, the prices I can practice with my customers, the sheer number of those customers, as well as on their individual budgets.
