<p>This sort of very generic and stylized problem is not easily applicable to real life situation.</p>
<p>However, this being said you could parametrize the problem. For the costs, you can find maximum possible cost of production for the product <span class="math-container">$c_{max}$</span> (you could proxy this with highest cost among all firms in sample, or use some other method) and then divide the cost of the firm you are looking at by <span class="math-container">$c_{max}$</span> (i.e. use <span class="math-container">$c_i/c_{max}$</span>), which will guarantee  that the cost for any arbitrary firm is <span class="math-container">$c \in [0,1]$</span>. However, note that <span class="math-container">$c$</span> in economics should include opportunity cost which is very difficult to measure empirically. You can't just take the raw data for accounting costs reported by firms. You should try to estimate opportunity cost and add it on top of the accounting costs (you could estimate it by trying to see what wage business owners could earn if they would become employed in related field).</p>
<p>In order to make <span class="math-container">$p$</span> comparable to <span class="math-container">$c$</span> you can take the market price <span class="math-container">$p_m$</span> and also divide it by <span class="math-container">$c_{max}$</span>, this will give you <span class="math-container">$p=p_m/c_{max}$</span> that will give you price relative to cost meaning it will make sense to do arithmetic with <span class="math-container">$p$</span> and <span class="math-container">$c$</span>.</p>
<p>This way you get <span class="math-container">$p$</span> and <span class="math-container">$c$</span> you could plug into the equation in principle. However, in practice it is extremely difficult to calibrate such model for any large firm as outside single person firm measuring opportunity cost of production gets very tedious.</p>
<p>Furthermore, you should note that the simple stylized model would likely be too simplistic for any real world application. Such models are usually used to teach students some important insight or concept so they are oversimplified.</p>

CC BY-SA 4.0
2022-04-01T13:53:26.013Z
"How would **sellers** of oranges or cars know..."
Giskard
CC BY-SA 4.0
2022-04-01T14:12:42.100Z
@Giskard they could check official statistics? I am not sure what you are hinting at. Typically there are statistics available for market prices and nowadays you can get data even on micro costs. Other things would have to be estimated
1muflon1
CC BY-SA 4.0
2022-04-02T03:48:37.430Z
My point is: if you are selling oranges for \$2 each, you probably know their price is \$2 without sampling.
Giskard
CC BY-SA 4.0
2022-04-02T09:22:03.513Z
@Giskard oh I see, well my thought process was that sellers of oranges are price takers so when new seller comes to market the seller checks prevailing market price and sells at it
1muflon1
CC BY-SA 4.0
2022-04-02T09:23:33.227Z
This is a possible answer to the question; but above you are addressing a stasticians problem.
Giskard
CC BY-SA 4.0
2022-04-03T02:36:54.590Z
Thank you very much, I was thinking along these lines too. I guess we could also use the maximum reservation price as a baseline for parameterization as it has to be equal to the costs (D=1). Do you have an example where this is done?
Karl A
CC BY-SA 4.0
2022-04-03T08:33:39.503Z
@KarlA no I do not have an example of such simple model being parametrized. As mentioned in my answer for such exercise people use more advanced models. I know only of textbook examples where parameters are made up. This would be like asking for a physics example of parametrization of some simple model for projectile that ignores friction and weather conditions, that’s fine for 101 physics class but people who actually want to actually have useful predictions will have to add that friction and weather conditions in and won’t bother parametrizing mode without them
1muflon1
CC BY-SA 4.0
2022-04-01T13:44:27.493Z
2022-04-01T13:49:36.117Z
2022-04-01T13:49:36.117Z
1muflon1
<p>I have a very general question about the application of the very beginning of every microeconomics textbook. When solving a profit maximization problem, we take some general parameters that might be bound between 0 and 1 to make it as general as possible.</p>
<p>But how could that be transferred to real life?</p>
<p>For example, a profit function of a seller with demand following a uniform distribution <span class="math-container">$D=1$</span> and costs <span class="math-container">$c\in[0,1]$</span> will look like <span class="math-container">$\pi = \int_x^1(p-c)dx$</span> and therefore <span class="math-container">$\pi=(1-c)^2/4$</span>.</p>
<p>How would sellers of oranges or cars know what their <span class="math-container">$p$</span> and <span class="math-container">$c$</span> are? How would a seller calibrate in practice? Is it in relation to the maximum willingness to pay or should they take another starting point?</p>

<microeconomics><calibration>
Calibration of parameters in a general microeconomic model
Karl A
# Calibration of parameters in a general microeconomic model

(Asked by: username_0 on 2022-04-01)

I have a very general question about the application of the very beginning of every microeconomics textbook. When solving a profit maximization problem, we take some general parameters that might be bound between 0 and 1 to make it as general as possible.

But how could that be transferred to real life?

For example, a profit function of a seller with demand following a uniform distribution $D=1$ and costs $c\in[0,1]$ will look like $\pi = \int\_x^1(p-c)dx$ and therefore $\pi=(1-c)^2/4$.

How would sellers of oranges or cars know what their $p$ and $c$ are? How would a seller calibrate in practice? Is it in relation to the maximum willingness to pay or should they take another starting point?

**Tags:** microeconomics, calibration


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## 1 answers

### Answer by username_1 on 2022-04-01. Score: 1 | Accepted answer

This sort of very generic and stylized problem is not easily applicable to real life situation.

However, this being said you could parametrize the problem. For the costs, you can find maximum possible cost of production for the product $c\_{max}$ (you could proxy this with highest cost among all firms in sample, or use some other method) and then divide the cost of the firm you are looking at by $c\_{max}$ (i.e. use $c\_i/c\_{max}$), which will guarantee that the cost for any arbitrary firm is $c \in [0,1]$. However, note that $c$ in economics should include opportunity cost which is very difficult to measure empirically. You can't just take the raw data for accounting costs reported by firms. You should try to estimate opportunity cost and add it on top of the accounting costs (you could estimate it by trying to see what wage business owners could earn if they would become employed in related field).

In order to make $p$ comparable to $c$ you can take the market price $p\_m$ and also divide it by $c\_{max}$, this will give you $p=p\_m/c\_{max}$ that will give you price relative to cost meaning it will make sense to do arithmetic with $p$ and $c$.

This way you get $p$ and $c$ you could plug into the equation in principle. However, in practice it is extremely difficult to calibrate such model for any large firm as outside single person firm measuring opportunity cost of production gets very tedious.

Furthermore, you should note that the simple stylized model would likely be too simplistic for any real world application. Such models are usually used to teach students some important insight or concept so they are oversimplified.

> **Comments:**
> **username_2**: "How would **sellers** of oranges or cars know..."  
> **username_1**: @username_2 they could check official statistics? I am not sure what you are hinting at. Typically there are statistics available for market prices and nowadays you can get data even on micro costs. Other things would have to be estimated  
> **username_2**: My point is: if you are selling oranges for \$2 each, you probably know their price is \$2 without sampling.  
> **username_1**: @username_2 oh I see, well my thought process was that sellers of oranges are price takers so when new seller comes to market the seller checks prevailing market price and sells at it  
> **username_2**: This is a possible answer to the question; but above you are addressing a stasticians problem.  
> **username_0**: Thank you very much, I was thinking along these lines too. I guess we could also use the maximum reservation price as a baseline for parameterization as it has to be equal to the costs (D=1). Do you have an example where this is done?  
> **username_1**: @username_0 no I do not have an example of such simple model being parametrized. As mentioned in my answer for such exercise people use more advanced models. I know only of textbook examples where parameters are made up. This would be like asking for a physics example of parametrization of some simple model for projectile that ignores friction and weather conditions, that’s fine for 101 physics class but people who actually want to actually have useful predictions will have to add that friction and weather conditions in and won’t bother parametrizing mode without them  

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