When we first encounter parametric equations, they can seem like an abstract mathematical technique. We are introduced to equations such as x(t) and y(t), and it may not immediately be clear why we need them. A good way to understand parametric curves is to start with a simple question: What if two quantities are changing at the same time? This situation occurs … [Read more...] about Parametric Curves in Economics, Marketing, and Finance: Understanding the Idea from Scratch
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the investor changes their portfolio allocation. As the allocation changes
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y(t)
usually represented by t. For example: x(t) = 2t y(t) = t² Here
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two marketing campaigns might eventually reach the same advertising expenditure and sales values
we describe both x and y in terms of another variable. That variable—the parameter—allows us to describe not only where a system is
x(t)
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y(t)) where t is time. Its horizontal position might be: x(t) = 0.5t and its vertical position: y(t) = 90 + 0.2t − 4.9t² At each moment
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these represent velocity components. But in business
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t = 2 gives one point
time determines the pumpkin's horizontal and vertical position. In economics
time can determine how advertising expenditure and sales evolve together. In finance
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they can seem like an abstract mathematical technique. We are introduced to equations such as x(t) and y(t)
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we get a particular combination of coffee and tea. For example: Price of coffee
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the consumer's chosen combination moves from one point to another. The resulting path can be viewed as a parametric curve. The important insight The parameter is not necessarily time. Here
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t is the parameter. Let's see what happens as t changes. t
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y
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the corresponding risk and expected return change. Mathematically
which tells us how quickly y is changing. In the pumpkin example
t = 3 gives another
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