Hi! I'd like to understand how to model consumer demand given a price I set for a good. Therefore for a specific good I'm given the current prices of competitors and maybe some historical values for number of goods sold by competitors and me at a specific price at previous times. I would like to understand what will happen to the amount sold if I increase or decrease my current price. My background is fairly mathematical and I hope someone can point me to a reference where I can read up an approach?! Ideally it should be intended for a mathematical audience, therefore not too wordy but detailed instead. What is this topic called if I want to research more information?
You would be attempting to plot a "demand vs supply" graph from the data you have and some sort of assumption about how the population behaves and what is governing the market. Have you already searched "demand and supply" and "market modelling".
The "have some sort of assumption about how the population behaves" is the tricky part here. Also the competitors prices might never be the same, so that strictly speaking I have no perfectly identical historical points. Some kind of interpolation would be needed. So I'd need some insight from markets/consumer theory to enrich the information. However Googling economics terms is highly unsatisfactory, since it usually yields some "waffle" which doesn't get to the point how to actually calculate the perfect price given only the information I stated. I'm hoping for a reference which gets down to results and actual numbers/equations.
You will want a microeconomics lecture series then? It depends how non-wafley you want it, but there is no shortcut here. Presumably different competitors will have slightly different products too? If they have been in the market for a long time, and it is a free(ish) market, then their pricing can be expected to be close to the equilibrium price - plotting the different prices vs sales for a particular time will produce a blob if that is the case. The actual maths in economics tends not to be all that hard BTW.
I'm currently checking microeconomics lecture series. Even better would be a textbook or a specific article. The whole point is to find something concrete and mathematical since my search results are shadowed by too much waffle information. So I'm hoping someone can identify a detailed source among the more "general" texts. I can imagine empirical results for connections between population income distribution and price elasticity. Or even interpolation from other competitors prices. I think most helpful would be an empirical or theoretical model for price elasticity which I could fit to the data. Anything that could improve the above problem which I could state in very few lines of mathematics. (Competitors have similar products, but slightly different quality/popularity I suppose.)
Most free market models assume identical goods and no brand proliferation - adding brand value can be tricky. Where the goods are identical, then the difference in price would be attributed to consumer perception of the brand. IRL the full free market model does not apply - and you need more data to work a decent model. Ultimately markets are chaotic - so to advise you properly we would need to know what the model is to be used for: what is the context? Note: it is not just a question of what price you offer, but also how many units are available and consumer demand. From what you are describing, the market is saturated so any movement will be at the expense of the other competitors?
I don't know so much of the economics terminology. Basically my problem is fairly similar to "hotel pricing". You have competitors which offer the same hotels, but there might be a (somehow constant?) bonus for brand. Moreover, demand depends on season - I hope this only leads to some overall "scaling" rather than completely different demand distributions. For simplicity units available are not limited. But (for the current prices) the market is saturated and movement is most likely at the expense of competitors (but not completely since a very low price might attract new customers). Given historical data and making some empirically valid assumptions about constancy about parameters (season scaling, constant brand influence, ...), I'd like to get as close as possible to an optimal solution.
Gerenuk, I would get an Economics textbook and plow through the microeconomics chapters. That would at least get you up to speed on the basics of supply-demand curves, price elasticity, and the different kinds of markets (monopolies, oligopolies, and competitive markets). I found the text by Krugman & Wells useful, but there are others out there too.