Question
16.P is in dollars and is the number of units. Find the elasticity of the demand function Ip + 84 ' 191 at tbe price = S20
16.P is in dollars and is the number of units. Find the elasticity of the demand function Ip + 84 ' 191 at tbe price = S20
Answers
Find the price elasticity of demand for the demand function at the indicated -value. Is the demand elastic, inelastic, or of unit elasticity at the indicated -value? Use a graphing utility to graph the revenue function, and identify the intervals of elasticity and inelasticity. $$ p=\frac{100}{x^{2}}+2 \quad x=10 $$
We're trying to find the price elasticity of demand given this demand function and the specific hex value. We're trying to plug in here. So formula for that is P over X divided by P. Prime. So that's going to be equal to 20 minus 200.0 02 X. All divided by X. And divided by a negative 0.2 All right. So then go ahead and plug in 30 into that. We have 20 minus 0.2 times 30 over 30. Divided by a negative 0.2 This is approximately equal to 9970 Just definitely greater than one. So we have that terrorism and it's elastic at X equals 23. Okay, X equals 30. Sorry. Right. Okay. So from here, what we're going to do, let's take a look at the revenue function. So we've got that the revenue function is equal to X times P is equivalent to X times 20 miles 0.0 serial two X. Ask us to graph and take a look at what that graph looks like here. Take a look at that. It's going to look this where the right most endpoint is 100,000 not to maximum is actually achieved. Uh huh. X equals 50,000. So because the revenue function is increasing from zero to 15,000, then we say that it's elastic from zero less than X less than doesn't. And then we say it's an elastic from 50,000 two 100,000 since it's decreasing. And that is our solution for the second part.
We're trying to find the price elasticity of demand for this given p annex. So to do that we have to do P over X. Divided by p prank respect tax. So yeah, basically when we do that plug that in, well I end up having a 600. What's wrong with you? Sorry? 400 uh minus three X. Oh rex. And divided by negative three. Okay, so when we plug in 20 into that we have 400 and it's 600 over 20. And then since we're divided by negative three, that's equivalent to multiplying by one over negative three. So that's equivalent to it's 460. Okay, so based 3 40 over 60 here and we're taking the absolute value of this, we could see that 3 40 or 60 is definitely greater than one. So we have that it's elastic at X equals X equals 20. Okay, so that's the first part of it. Then it asks us to graph what this would look like for the revenue function. So the revenue function is able to X. Times P. And so that's going to be equal to 400 X minus three X. Squared. And so from here, when we graph this what we see here, it looks something like this, zero and this would be 403. And this middle part here, it's 200 over three. It's actually where achieves the max there. And so based off of this, we can tell that from zero to 200 over three. Since it's increasing for the revenue function here, that that would be elastic. So from 0 to 200 or three it's elastic here and then since it's decreasing from 200 over three, two, 400 over three, then it's an elastic And so ever done.
X. Equal to f O B. Equal to 10,000 negative 100 90 time p. So here in this kitchen we have to use price demand equation to find E F B the elasticity of demand. So here we know that E F P equal to Maggie do be time derivative of fsp upon fo fee. So first of all, we have to find the derivative of F of P. So here you can see that We get first term is constrained. So here we get the derivative of 10,008 0 and the second term is negative 190 time P. So here the derivative of 190 time P is negative 190. So now we put that value here so we get E. Are free equal to negative be time Negative 190 upon 10,000 negative 190 time be. So now we simplify this and we get of P equal to be dine 190 upon 10,000 negative 190 Time P. So it is our final answer.
X equal to I for fee equal to 4800 negative full time. Piece Choir. So in discussion we have to use the price german equation to find E. P. The elasticity of demand. So you can see that here E f E equal to negative be time the value of F of fee upon fo feet. So first of all we have to find the very bottom of fo fee so you can see that first room is constant. So we know that the constant rooms The derivative of the concern is zero. So now we have to solve the second term which is 98 times p because the delivery of 90 Be four times the square is 98 times b. So now we put that value here negative P time negative eight times p upon 4000 800 negative four times the Squire. Now we simplify this and we get E. or three equal to piece choir eight times piece choir upon 4800 negative full time be square so it is over. Final answer.