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Situation

I hope I'm asking in the right place. I'm writing a paper on the application of quadratic functions in economics and intend to use the Total Revenue function as well as the Profit function for a specific product in order to derive conclusions and whatnot. For the moment, all that I require is the price (or demand) function of a given product in order to find the rest out. For the price function:

p(Q) = m - nQ

in order to find out what m (the slope) is, I would require coordinates (Q, p). Q being the quantity demanded (or sold apparently according to this link) and p being the price per unit sold.

I require the price function in order to make the TR (Total Revenue function).

Attempted Solutions

I have looked online for methods to derive the number of units sold from financial statements made by the company but I find that:

  1. I need the price per unit for this (that that I do not have)
  2. financial statements pertain to all products sold by the company and as such are an inaccurate representation of the price function for that particular product

For the profit function which requires the cost function, I have managed to find the solution from the financial statement but once again point 2 still stands. I think that if I find a business that exclusively sells one product, I will manage to derive the second cost function from the financial statements but once again, I do not have a solution for the first one.

Question

I am really lost in regards to what I should do in order to obtain data that I can use to analyze and ultimately demonstrate the application of mathematics in economics (specifically two sets of price per unit and number of units sold). I really hope that someone can help me with these questions and provide not necessarily the aforementioned solution that I desire but any solution to the situation I am in.

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  • $\begingroup$ You are unlikely to find price per unit in financial statements. But could you perhaps focus on companies that sell directly to the public and look at their websites or advertising to find prices? $\endgroup$ – Adam Bailey Mar 13 at 20:08
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What you are trying to do here is estimate the demand curve of a firm. Broadly speaking, even if you got data on price and quantity, you would not be able to estimate this because your right-hand-side variable (quantity) is also determined by the supply curve. This is what people call the 'simultaneity' form of the problem of endogeneity.

The way to resolve this is to find a credible instrument that allows you to model movements in quantity that arise from changes in supply. For example if you found data on changes in the oil price, and found that they affect the quantity of goods purchased in the market you are estimating the equation for, you would essentially be able to 'trace out' the demand curve.

However, reading between the lines of your query, I suspect you are not particularly familiar with econometrics so the above may not be useful to you. If this is a school project (as opposed to university or other higher level of education), I think you could take the approach you are suggesting and then get additional points if you can explain what I just did above.

Company annual reports should contain the information you need, so long as you focus on companies that sell 'real goods' as opposed to services (think automobile manufacturers rather than tech companies or law firms). For example, page 71 of the Daimler annual report (see here) contains data on number of cars sold, and page 228 contains total revenues. If you want to break this down by type of vehicle sold, see page 253 for revenue by type of vehicle.

In general (i.e. when you look at other annual reports) you will find that:

  1. You will find volumes sold somewhere in the text of the annual report (before the financial statements start)
  2. You will find revenues at the start of the financial statements (p.228 in the above report example)
  3. Further breakdown of revenues can be found in the notes to the financial statements (i.e. some point beyond p.228 - the note I refer to on p.253 is the note on revenue in that annual report, so naturally breaks the revenue out. You can find out which notes refer to which items in the financial statements by looking at the financial statements on p.228 - there you will see a '4' next to revenue which means you want to look at note 4)

I would recommend of doing a mix of looking through annual reports for a given company over time, and also multiple different companies' reports.

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