Find the elasticity of demandfor the given demand function at the indicated values of= Is the demand lastic, inelastic or neither at the indicated values?9=407 _ 0....

Find the elasticity of demand (E) for the given demand function at the indicated values of p. Is the demand elastic, inelastic, or neither at the indicated values? Interpret your results.
$q=300-2 p$
a. $p=\$ 100 \quad$ b. $p=\$ 50$

Instructions for six point three. Number twenty six Tell us to find the elasticity of demand, which is E for the given demand function that indicated values of pee. And then we need to decide the demand is elastic in elastic or neither at the given P dies, so we do need to find e First is equal to negative p over Q times. Dick you dp So we do need to go to the side and find d. Q. DP first, this is our cue function, which means Dick you DP is going to be equal to negative three. So we have an e equal to this is negative. Negative p over Q five forty minus three p times Negative three, which was the derivative that we found Simplification. We have three p over five forty minus three p. You can factor out the threes here, which gives us a final E equal to P over one hundred and eighty minus p. Now that we have this evil you we're going to plug in R and B's for P. So with e equal to P over one eighty minus p and a, we had P equal to eighty, so Now we have e equal Teo eighty over one eighty minus eighty, which is equal to point A. So we haven't e equal to point A, which is less than one when e is less than one. We're gonna have in elastic supply in elastic supply because he is less than one. So this basically means you can change the price by a little bit and it won't change the demand. Okay, so a percent change in the price will not have a drastic percent change in the demand For part B, we have p equal to one hundred, which gives us an E equal to one hundred over one, eighty minus one hundred. This is going to be equal, tio one point two five, which is greater than one. So we haven't e equal to one point two five, which is greater than one. That means we have elastic here. So we have an elastic demand. And you, Khun, let's put demand here instead of supply. You have elastic demand because our E is greater than one. That means that a increased like if you change the price, it's just going to drastically change what the demand is. So this price is this is a little bit more sensitive to your prices, as opposed to the inn elastic over here.

In this question, we are given a quantity demand that earth is price for a nation. In this gaze, Q equals 4500 minus. He square were asked to find a MME. The a necessity in elasticity at two price points being 30 and $50. So that's first figure out. What are you necessity is? Remember the general Former lives negative. Be over Q. Times D. Q. P. Let's figure out, uh, what the GPS Q P equals first remains a constant, so it doesn't contribute, and the second term deserved it. With native B. Squared is native to pee scape, knowing that we can figure out he's with negative. He divided by 4500 minus B squared times native to pee. Or, in short, we get to be squared defined by 4500 minus 25 minus B square. Right? So a what happens when P is $30? Well, um, putting in $30 for eat, so e equals two times 30 square, divided by 4500 minus 30 squared. Um, so you could do this by hand? Um, it's actually no, that the numbers work out quite nicely. So the talk 30 square is 900 so the top becomes 1800. The bottom through spirit against its 900 4500 is no. Well, there's a 45 100. Minus 900 is 3600 which is twice 1800. So this will get you 1/2. Uh, anyway, you do it so you can do this with the calculator, Um, or by hand, surprisingly easy some. But the conclusion is, this guy is less than one. So did the man is in elastic. And this is just the definition. So when it's called elastic, elastic necessity is less than one. It's not the elastic or in the last on, because it is basically means price doesn't affect the man very strong. So for B were asked to compute the necessity at the price point of $50. Well, in this case, he is two times if he squared, divided by 4500 minus 50 squared. So again, you can work this out your calculator or play, uh, had the top becomes 5000. The bottom becomes 2000. So this will be for laughs, which is more than one and get you a on elastic good one of the things you can say is that if you would increase the price, the man would fall so much that your total revenue would go down. So in this case you should procreate. Beeker show price, but it's gold elastic, good at $50.

For question number 25 to demand function is Q equals 400 minus Goingto he squirt. And since he is equal, cool, negative be over. Q. By que TV? We need to get the first derivative of the demon function with respect to price. So the queue who DP would be equal to minus or in four he So now we can substitute in e equals negative B 400 minus going toe D squared, multiplied by negative 0.4 p, which would be I went for P squirt over 400 minus point to he squared so he would be equal toe to be square over 2000 Linus be squirt. So for a price be equal $20 he would be equal to two multiplied by 20 square over 2000 minus 20 square, which is one have. And for e less than one. The demand is and elastic, which means the revenue will increase only if the price increased. So to increase revenue, you need to increased price. Okay. Now, for a price, p equals $40 e value would be equal toe you must light by 40 squared over 2000 minus 40 squared which is eight and for e greater than one. The demand is, in this case, elastic, which means in order to increase revenue, we need to decrease price. So if we want to increase revenue, we need to lower the prices. Thank you very much.

Defying problem, we want to compute the elasticity with the exponential function D. F. P. You go to A each, the negative et R. B. P. Status 29. Um and er positive real numbers, we want to know for what prices is the demand elastic and inelastic. So you see it's going to be elastic for P Greater than one ever be Because it was greater than one over B. And we see that one over B would give us one, but if it's greater than that, that means that this is going to grow and faster or shrink at a faster rate. And that's gonna be in elastic when we have zero is less than key, which is less than one over B. Because then it's not going to um it's not going to slow down.