The ratio X/Y for the fictitious company, Teslala, that produces a single type of electronic vehicle, Model Z is 10/pY.
<h3>What is a mathematical model?</h3>
A mathematical model is the model which is used to explain the any system, the effect of the components by study and estimate the functions of systems.
Consider a fictitious company, Teslala, that produces a single type of electronic vehicle, Model Z.
The demand for Model Z depends on the gasoline price (q) because customers tend to purchase an electronic vehicle as a substitute for vehicles that run on gasoline when the gasoline price increases.
The demand for Model Z is estimated as
![D(p) = 180 + 10q - 4p](https://tex.z-dn.net/?f=D%28p%29%20%3D%20180%20%2B%2010q%20-%204p)
Here, <em>p</em> is the price of Model Z.
Consider the following two statements:
- 1. When the average gasoline price q increases by $1, the revenue-maximizing price p" increases by $X.
![D(p) = 180 + 10q - 4p\\D(p) = 180 + 10(q+1) - 4(p+X)](https://tex.z-dn.net/?f=D%28p%29%20%3D%20180%20%2B%2010q%20-%204p%5C%5CD%28p%29%20%3D%20180%20%2B%2010%28q%2B1%29%20-%204%28p%2BX%29)
- 2. When the average gasoline price q increases by $1, the demand at the revenue-maximizing price (i.e., D(p*)) increases by a factor of Y.
![D(p)+Y = 180 + 10q - 4p\\(D(p)+Y) = 180 + 10(q+1) - 4(p+X)\\Y= 180 + 10(q+1) - 4(p+X)-D(p)\\](https://tex.z-dn.net/?f=D%28p%29%2BY%20%3D%20180%20%2B%2010q%20-%204p%5C%5C%28D%28p%29%2BY%29%20%3D%20180%20%2B%2010%28q%2B1%29%20-%204%28p%2BX%29%5C%5CY%3D%20180%20%2B%2010%28q%2B1%29%20-%204%28p%2BX%29-D%28p%29%5C%5C)
Put the value of demand at the revenue-maximizing price as,
![Y= 180 + 10(q+1) - 4(p+X)-(180 + 10q - 4p)\\Y= 180 + 10q+10 - 4p-pX-180 - 10q + 4p\\Y= 10 -pX\\1=\dfrac{10}{Y}-\dfrac{pX}{Y}\\\dfrac{10}{Y}=\dfrac{pX}{Y}\\\dfrac{10}{pY}=\dfrac{X}{Y}](https://tex.z-dn.net/?f=Y%3D%20180%20%2B%2010%28q%2B1%29%20-%204%28p%2BX%29-%28180%20%2B%2010q%20-%204p%29%5C%5CY%3D%20180%20%2B%2010q%2B10%20-%204p-pX-180%20-%2010q%20%2B%204p%5C%5CY%3D%2010%20-pX%5C%5C1%3D%5Cdfrac%7B10%7D%7BY%7D-%5Cdfrac%7BpX%7D%7BY%7D%5C%5C%5Cdfrac%7B10%7D%7BY%7D%3D%5Cdfrac%7BpX%7D%7BY%7D%5C%5C%5Cdfrac%7B10%7D%7BpY%7D%3D%5Cdfrac%7BX%7D%7BY%7D)
Thus, the ratio X/Y for the fictitious company, Teslala, that produces a single type of electronic vehicle, Model Z is 10/pY.
Learn more about the mathematical model here;
brainly.com/question/4960142
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