Calculus: Taking a Derivative

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From the course by University of Virginia

Cost and Economics in Pricing Strategy

150 оценки

University of Virginia

Cost and Economics in Pricing Strategy

150 оценки

Course 1 of 4 in the Specialization Pricing Strategy Optimization

How much should you charge for your products and services? Traditionally, businesses have answered this question based on the cost to produce or provide their goods and services. This course shows you the economic factors behind pricing based on cost and the pros and cons of a cost-based pricing approach. Led by Darden faculty and Boston Consulting Group global pricing experts, the course provides the practical and research-based models and methods you need to set prices that maximize your profits. By the end of this course, you’ll be able to: --Apply knowledge of basic economics to make better pricing decisions --Recognize opportunities for price discrimination—selling the same product at different prices to different buyers—and recommend strategies to maximize sales and profits --Calculate three types of price elasticities to determine the impact of price on demand --Analyze and apply different pricing models -Cost-plus pricing -Marginal cost-plus pricing -Peak-load pricing -Index-based pricing --Evaluate the impact of channel intermediaries and customer lifetime value on pricing

From the lesson

Common Pricing Metrics: Elasticities

This week we'll dive deep into the world of demand modeling. We'll start with a brief overview of regressions--what they are, why they're useful and how to calculate them using Excel. Then you'll get a chance to use regressions as you learn about three types of elasticities--relationships between demand and price or other factors--and the drivers of these elasticities. We'll finish with a price optimization based on demand models--a truly useful method for pricing based on economic factors. By the end of this week, you'll be able to impress your colleagues and friends with your knowledge of mathematical models and how to use them to inform your pricing strategy!

Price Elasticities8:33

Cross-Price Elasticity6:53

Income Elasticity4:32

Drivers of Price Elasticity3:16

Drivers of Price Elasticity: Market Share4:22

Drivers of Price Elasticity: Competitors' Prices4:48

Calculus: Taking a Derivative3:58

Price Optimization Considering Demand8:12

Price Optimization Example4:00

Meet the Instructors

Jean Manuel Izaret
Senior Partner and Managing Director, Leader of BCG’s Global Pricing Practice
Thomas Kohler
Associate Director, Pricing
Marketing, Sales & Pricing Practice
Ronald T. Wilcox
NewMarket Corporation Professor of Business Administration & Senior Associate Dean for Degree Programs
Marketing

Remember back in week one?

I introduced the idea of calculus and

that we would need it later on to do price optimization.

Well, we have now come to that point.

Now calculus you might know is,

one of the great intellectual achievements of mankind.

So if you can spend some time learning more calculus, have at it.

I think it is a wonderful way to spend your time.

Today I am going to take a more limited approach,

we are going to learn how to take a derivative.

Some of you may know this already.

If you don't, I will teach it to you and this is what you have to do the price

optimization that I will be doing momentarily.

Now, I am going to write down a function and then in particular,

I am going to write down Y equals 6x at its most most basic level.

What a derivative is, is a measurement

of how quickly a function changes relative to the variable.

In this case, the variable is x.

So you might look at that and say well,

if x goes up by one, how much will y go up by.

I think the answer is pretty clear, right?

The answer is six.

Every time x goes up by one Y goes up by 6,

that is the rate of change of the function.

So if I formalize that,

I can formalize that by taking the derivative of the function.

And this little squiggly thing out in front of the Y,

if you've never seen that before, that's just a derivative sign.

And I'm saying, I'm taking the derivative of y with respect to x.

And it turns out, that that is equal to that six.

How do I get that?

Well, there's a little rule in taking a derivative.

And that says, when you're taking a derivative and you've got a constant,

that six is a constant and you've got a variable.

That x is a variable.

Then taking a derivative with respect to that variable

is just equal to the constant, okay.

So, the derivative of y with respect to 6x is just six.

If it were 8x there, it would be eight.

All right, so

if you understand that, the next thing I'm about to tell you is very straightforward.

Suppose you have a situation where y = Three and

you ask the question, what's the derivative of y with respect to x.

Well, there's no x in the equation.

That function doesn't change as x changes, because there's no x there.

So the derivative of y with respect to x is zero.

And in fact, the derivative of y equal to any constant,

whether that's four, or five, or 17, is simply going to be equal to zero.

Now, there's one other thing I've got to show you.

This is the only thing that's even slightly tricky, but

I'll walk you through it.

Suppose you have a little more complicated function here.

Lets say you have y equals 2x to the 3rd power and

you ask the question what is the derivative of y with respect to x.

Well, here's how you do that.

Remember, you're measuring the rate of change of a function and

mathematically, here's how you handle something like that.

You take the number that send the exponent, right?

The power number sitting out there and you multiply it by the constant upfront.

So in this case, we'd have three times two, you insert the x and then,

you subtract one from the exponent, so it's 3- 1.

So in this case, the derivative of y with respect to x is 6x squared.

So again, you just take the exponent, multiply it by the constant out front and

subtract one from that exponent and you're done.

And that's really all you need to know to do the price optimization coming up.

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