For the purposes of this article in the series, I will be focusing on the relationship between my Grandfather (Economics) and I (Finance). Economists, so far as they are in the grandfather role, are not exactly ignored. But, rather, ”selectively heard” by the other family members. The information that is derived from the Economist, ends up being twisted around and turned into finance. Before you know it, the Economics behind it is gone and it is just finance.
This is an understandable phenomenon. Due to the large degree of assumptions and a lack of specificity, that come packaged with Economic models or explanations, it is completely reasonable to favor to more tailored, Finance-based, point of view when determining department or firm profitability.
I would argue though, that Economics is discarded a little too much in this case. Economics possesses the potential to show profit prospectus for a firm or department better than Finance. This is especially true in the case of determining the minimum profitability acceptable from a potential department addition. As well as the optimum number of employees and wage rate, for that department. The added benefit of Economics is more time expansive with less alteration than Finance. In essence, Economics possesses the simplicity define basic minimums with ease. Not getting too bogged down, as it were, like Finance often does, in the exact details. In short, Economics was made to be generic, Finance was not. Below, I go through my logic for the above process of adding a department to a firm. It must be said that the particular economic model used, is not absolutely applicable to all businesses or departments. Therefore, I selected a single model for analysis. I will use the model for a firm in a monopolistic competition industry. I chose this model due to its neutrality compared to the major alternatives and its simplicity. The potential alternatives, such as using perfect competition, monopoly, oligopoly (with and without cartel) and so on. But for the sake of any sort of brevity I will stick to one for now and most likely approach the rest in a supplement.
How To Make The Two Sides Equal
Alright, now for the good stuff! First, we need an example. Since I have seen a lot about the profitability of Social Media Advertising and its return on investment to the firm, I will use a related example. I saw this question posted on Linkedin a little while back:
How much time do I spend on Social Media in marketing for my business?
Using this question as a foundation, I will show through economic modelling, how to calculate the optimum amount of time to spend on Social Media for marketing. As well as how that time variable relates to profit maximization in the short run and long run.
Brief Economics Lesson:
An industry in monopolistic competition is characterized by:
- Products are imperfect substitutes and therefore, the competition is also imperfect.
- There are multiple consumers and producers with no absolute market price.
- Producers have proportional control over market price.
- There are limited entry and exit barriers. (Not really important for us)
- Economic Profit exists only in the short-run due to the duality of control of industry market price.
- Can be inefficient (i.e. loss to producer/consumer surplus or cause of excess, respectively) when a firm produces where Price(p) = Marginal Cost (MC) or if a firm produces a profit maximizing Output (Q*) < Output at minimum Average Cost (ACmin)
- Profit maximization occurs when Marginal Revenue (MR)= Marginal Cost (MC)
When using the monopolistic competition industry model in our case. I replaced the word “industry”, with “division” and the word “firm”, with “department”. So, we then have a Social Media department in the Marketing division as opposed to a firm in an monopolistic competition industry.
It also, made sense to me because the two relationships are very much alike in the way they interact with each other, derive price and so on. Therefore, we can assume a Social Media department would yield a short-run profit so long as MR=MC and Q*>ACmin.
Now, since our example is slightly more specific (How much time should you spend on social media?), we need to convert the variable, “time”, into economic terminology. So, we assume “time” is equivalent to Labor Hours (Lh), which then we monetize using Wage (w) and quantify by number of related employees (Ln). Finally, we isolate the cost of “time” by assuming the only calculable direct cost of Labor (L) is Wage (w) and that “time” is only applicable to Labor Hours spent us Social Media.
Note: It is important to recognize that due to the nature of our problem Quantity (Q) is substituted for Labor Hours (Lh) and Price (P) is substituted for Wage (w). This is due to our examination of the, per unit or per hour, cost of Labor.
Therefore, we calculate:
Marginal Cost (MC) = ΔTC/ΔQ = Δ[(w)(Ln)] / ΔLh
Total Cost (TC) = (w)(Ln)
Average Cost (AC) = [(w)(Ln)] / Lh
Marginal Revenue Product of Labor:
This one was a little more difficult to determine, which was only fitting seeing as it has been a heated topic of debate to determine the return from time spent on Social Media.
- The Marginal Revenue (MR) and Average Revenue (AR) curves are downward sloping in this model,
- The MR curve has exactly 2x the slope of the AR curve, and
- The AR curve = Demand (D).
In order to determine the revenue from the social media associated labor, we need to use the Marginal Revenue Product of Labor (MRPL). The MRPL = Marginal Product of Labor (MPL) x Marginal Revenue (MR). A maximizing firm will pursue an MRPL = Wage (w), due to an inefficiency that would occur for the firm if MRPL<W.
Note: The same condition applied to cost exists here where Quantity (Q) is measured in Labor Hours (Lh). But here we further specify variable Labor (L) to Number of Department Laborers (Ln).
Since MRPL is an increase in Revenue per unit increase in Labor, we can find that:
Marginal Revenue (MR) = ΔTotal Revenue (TR) / Δ Number of Department Laborers (Ln)
Marginal Product of Labor (MPL) = Δ Labor Hours (Lh) / Δ Number of Department Laborers (Ln)
MRPL = ΔTR / ΔLn
As stated before, increases in Total Revenue relative the Number of Laborers (Ln) will cause an increase in MRPL. Since, equilibrium is such that MRPL = w, this increase would either need to be matched by a higher wage or an increase in the Number of Laborers (Ln).
This relationship can be used to find MR as a function of wage and MPL:
MR(MPL) = w
MR = w / MPL
We can conclude from the above calculations that the equilibrium value will exist at a point equivalent to:
MR = MC
ΔTR / ΔLn = Δ[(w)(Ln)] / ΔLh
ΔTR / ΔLn = Δ(w) Δ(Ln) / ΔLh
Now, to find the amount of “time” one would need to spend on Social Media marketing they would simply need to input the desired Total Revenue (TR) per Laborer and solve for Lh.
Note: Be sure, that during any calculations, all time periods are kept constant across variables to maintain negation. For example, Total Revenue could equal revenue for the day or for the month so long as the Lh are divided by number of periods (pd.) then the calculation will retain significance. Otherwise, one might end up with a calculation of 1000 Labor Hours and be frightened when, in fact, if taken annually, comes out to 2.7397 Labor Hours per day.
Say that my Grandmother, the Marketer, wants a Total Revenue of $30,000 per year to be sourced from Social Media Marketing. Since she is operating a sole proprietorship she will have to do all of the Labor herself, but her wage is equal to Revenues earned. How long would she have to work, per month, to achieve this? Note: We do not include taxes for we do not know too many other variables and this calculation is only intended to find a baseline average. Not provide exact, “bankable”, values.
Well, first we need to divide TR and W by 12. We also know that she is the sole laborer. So, Ln = 1
ΔTR / ΔLn = Δ(w) Δ(Ln) / ΔLh
($30,000/12) / 1 = ($30,000/12)(1) / (Lh/12)
2500 = 2500 / (Lh/12)
(2500Lh / 12) = 2500
2500Lh = 30000
Lh = 12 hrs per month
This seems highly doable and I would tell Granny to go for it!
Graphs (courtesy of en.wikipedia.org):
Remember: For our purposes Q = Lh and P = w
Short Run Equilibrium under Monopolistic Competition (Economic Profit displayed in Gray Area)
Long Run Equilibrium under Monopolistic Competition (No Economic Profit)
I promise I will keep this part brief but an interesting fact that I ran across while I was freshening up on all this stuff was that:
1) Economic Profit = Net Income (Y) – (Marginal Product of Labor (MPL) x Labor (L)) – (Marginal Product of Capital (MPK) x Capital (K))
2) Accounting Profit = Economic Profit + (MPK x K)
Just thought this was a great illustration about why the above would be useful in calculating segmented profit as not all industries are effected largely by Capital Gains as a determinant for Profit.
If you have any questions, comments or anything in between, feel free to email me at firstname.lastname@example.org. Or just leave a comment below. Thanks for reading!
Economics Wizard Danny
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