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rosijanka [135]
2 years ago
11

Consider a fictitious company, Teslala, that produces a single type of electronic vehicle, Model Z. The demand for Model Z depen

ds 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, where p is the price of Model Z. Consider the following two statements: 1. If the average gasoline price q increases by $1, the revenue-maximizing price p" increases by $X 2. If 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 What is X/Y?
Mathematics
1 answer:
grin007 [14]2 years ago
5 0

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

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)

  • 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)\\

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}

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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