3.5 Linear Demand and Revenue - notes

3.5 Linear Demand and Revenue - notes - Objective [3.5]...

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Objective [3.5] – Notes Use a linear or exponential demand function to create a revenue function and then find the optimal price (the price that gives the maximum possible revenue). The Revenue Relationship really has two inputs, price and quantity. The “model” for the revenue relationship is simple, it’s linear in both price and quantity. You know this to be true because when you go to the grocery the revenue the store makes when you say buy energy bars is simply the marginal revenue(unit price) of the bar times the quantity you purchased (quantity demanded). In functional notation it looks like this. ( , ) R p q pq (recall: linear p in means wherever p occurs on the RHS it to the first power or simply just p, same with q ) It is totally ok that a relationship has more than one input, but in this course we need to limit ourselves to functions of just one input. The good news is that since price has an effect on demand we can replace q in the above with the demand as a function of price. When that is done the q ”g oes away and we have now revenue only as a function of price! Note: we could do like economists and have price as a function of quantity and thus get rid of p instead leaving revenue as a function of quantity , but we won’t! () ( , ( )) ( ) ( ) ( ) q D p R p D p pD p R p pD p Now here is the cool part. The demand function Dp can be any model. It can be linear, exponential, logistic, or something else. Whatever it is you will just multiply back by p and thus make the revenue function.
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3.5 Linear Demand and Revenue - notes - Objective [3.5]...

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