Based on sales data over the past year, the owner of a DVD s...

Question

Based on sales data over the past year, the owner of a DVD store devises the demand function D(p) = 40 - 2p, where D(p) is the number of DVDs that can be sold in one day at a price of p dollars.

Find the elasticity function for this demand function.

Accepted Answer

Welcome back, everyone. In this problem, a local coffee shop models the daily demand for their coffee using the function QFP equals 60 minus 4%, where QFP represents the number of cups sold daily at a price of $5. What is the price elasticity function for this demand function? A says it's 4% divided by P + 15, B 4% divided by P minus 15, C P divided by P + 15, and D P divided by P minus 15. Now how can we figure out the price elasticity function for this demand function? Well, let's first ask ourselves, what do we know that relates the price elasticity function to the demand function? We recall that the elasticity of demand e of P is given by the formula that says it e equals the derivative of the demand function with respect to the variable in this case p multiplied by P divided by the demand function q. So, we already know what Q is, OK? So if we can figure out the derivative of Q with respect to P, then we should be able to solve for the elasticity function. So let's go ahead and do that. We know that Q. R QFP OK. Is equal to 60 minus 4P. OK. So that means then that the derivative of Q with respect to P is going to be equal to the derivative of both of our terms here. And when we differentiate 60, it equals 0 because it's a constant. We can differentiate -4P using the poor rule, which leaves us with -4. Thus, the derivative of Q with respect to P equals -4. Now we can substitute it into our elasticity of demand function because no put that back in black here. That means EFP. Is going to be equal to -4 multiplied by P divided by Q, which is 60 minus 4 P. Now, let me just clean this up here. Notice here that we can factor -4 out of our denominator. That's gonna leave us with -4 multiplied by P divided by -4 multiplied by -15 plus P. And no, we did that because we can cancel -4. And thus that leaves us with P divided by negative 15 plus PR P minus 15. Thus P divided by P minus 15 is the price elasticity function for this demand function. If we look back at our answer choices, that means D is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

Based on sales data over the past year, the owner of a DVD store devises the demand function D(p) = 40 - 2p, where D(p) is the number of DVDs that can be sold in one day at a price of p dollars.
Find the elasticity function for this demand function.

Key Concepts

Demand Function

Elasticity of Demand

Calculating Elasticity

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