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Question 2 (5 points): For the demand function D(x) = (4500- 9x). findElasticity 0f Demand Is the demand elastic or inelastic at x= At what price X will give unit e...

Question

Question 2 (5 points): For the demand function D(x) = (4500- 9x). findElasticity 0f Demand Is the demand elastic or inelastic at x= At what price X will give unit elasticity Or maximum revenue

Question 2 (5 points): For the demand function D(x) = (4500- 9x). find Elasticity 0f Demand Is the demand elastic or inelastic at x= At what price X will give unit elasticity Or maximum revenue



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. $$ p=\frac{500}{x+2} \quad x=23 $$

Elasticity of demand. Professing e off X demand. The off X decoration is e off X equals negative x times that anybody with me up x armor, the up X so the price elasticity defined, or the man It's a measure off the chains in the the quantity demanded or parties off product in relation to its price change. So in the given, we have que or the quantity in the D C equals toe the demand are the the function of the man. The X that is equals to 500. Mine was two x so and then we have the day of exists calls toe by bonds with my two x so that it's the rib and it's even Mallya that iss Mexico's toe to seven. So we have to determine the elasticity off the one first weekend. How we have to the differentiated the off ex the day off The prime X It's equals two negative, too. So we have now that the derivative of X that this or did the relative of two x negative two x Because negative toe that they won the relative demand exits cause negative too. So substitute this formula of elasticity off the demand. So e off x that is equals toe capacity to x Ober by 100 minus two x So now we have to need to find a derivative of them with the punk. Right? So this is negative two x So the functions your plexus goes toe to over 200 people. The minus two substitution off Mexican sweep 17 Impression off X. So we have toe to times. But first we simplify this one. The But both sides dominated denominator by two. So we have X over typically minus X. So we have that It's the simplified the X and then first. Now that's, um this is the everybody you have. Now look, the e off people have been This equals toe people to say Ben all blur 250 my nose 57 and then we have people, said Ben Cobbler 193. So this is less than one so that the money is in elastic. We have the value of X for which is equals to one. This is the maximize the total revenue. So so we have from a park show that it's x over 2 50 minus X that is equals to one and then we have extra physical studio 50 my nose X and then we transpose the X to the others. Negative extra other side of equation. So we have expressed X So we have two x equals 2 50. So the revenue maximum profit will be closed toe excessive goes toe 125 in this in dollars so the value off profiting or the Max ISS 125.

So the elasticity off the month this expression on it's a mathematical league. Bye e x c equals two negative x times the derivative of them and function over the dairyman function x the elasticity off the month, he said. Measurement off the changes in the quality demanded off parties is spare product in relationships, primes, price change that can be in good services. So and there is a poor kind off last 60 months Price elasticity, top pros, elasticity. Thank um, even arrested city. And also we have nah part one advertising or promoting elasticity of demand. So in the given, you have you Sequels toe the off off X. But this good door 5 100 minus X and the ex points so Turk to eat. So the last city, the last seat elasticity. So here you have to find a derivative off the X good with a deep primex. But this equals toe. I got the one. As you can see, we have not The prime X that is supposed to negative one substituted in the electricity they won doesn't, um, be off X. But the Sequels to since it is negative and this negative to help positive X over 500 minus X. So we substitute the value off X here to get the elasticity at the given price. Statistical security now So e off 38 we have. So the equation The X was x over 500 of X. So now the value of X observing price at 38 Humber 500 minus 38. So we have the dates over 482. So we have to have lost term this divide dominating the nominator off too. So we have 19 over 281. Take note. This value is less than one. So it is an elastic the month. Then what is the point or price in which the maximizing the daughter Um you know, when the existing goes to one. So here we have he said the of extra testicles to one so one equals x over by 100 minus x, then transposed. So we have by 100 minus x or, of course, multiply that so 100 minutes x Paul's X So we have 100 equals two x, so x equals toe 2050 In order to maximize the profit. The business said to be at the Taliban know when X or the prices he goes toe 250 dollars. So this is the answer for maximizing that opinion. So executes Tata pity.

Elasticity of demand. It's representative. Mathematically, in thesis is off X calls negative x times the prime X over the X that the X present the man off function. So the price elasticity of demand is a measure of the change in the quantity he demanded, or parties off product in relation to its price change. Then we have a G. Ben that is a price at X s equals to one and the wan da que that is equals to the demand function or the op X that is equals toe 100 over the quantity X plus three scrag And then we have to do reputation shit off this equation. First, we set up the d o X on the fractional from exponents. So we have 100 times X plus three. We're gonna get to use the power. Very. But if the power did it The day everybody's is the off you to the end Sequels to and times you times I toe the end minus one have steady body off you. So here we have 100 times negative, too. Times the quantity express three face to the negative three time for the everybody pop extra t c equals toe one so that this is the t prime off X. So the deep prime off X sequel store Negative 200 over the quantity X plus three Cube. So this is the derivative. We accepted the function off the prime X. That access was the one or this is not a deep prime X is this, um I This is this prime X So we now have the deep prime X and that the XO was substituted Integration of e up X so eop X that is equals toe negative x times the negative 200 over X plus three. So it become positive. So we have 200 x all ober X plus three The doc you and that the the day off X that ISS equals toe 100 uber X plus three. So simplifying we have e up prefer buying? We have eat off X. This equals two. You have talks, Kulbir and then we have this one. Is he squared? Then you have two over X plus three. This is because stressed one because thesis can sell and can sell. This has become to then Also we have can cancel your cancel years. This is to consider this is become one. And also she is two x over X plus three. This is a great show for them. Letter A for X s equals to one. So substitute the off X that it's Sequels off one. So we have to over three. Therefore, this is less than one. So this is in elastic in a in a plus. Then set the value off me off X. That is equals toe one because that the prophet will become maximum. So we have one is equals toe toe X over X plus three. So we cross multiply it. We have X plus three. This is equals toe to x and then we have the value off expertise equals toe one are have the access equals toe three. So then the answer is access calls to train at one

So trying to find the price elasticity of demand for this specific demand function and X. Value that we're given here. So to do that we need to plug into the formula of P. R. X divided by P. Prime. And so that's going to be equal to five minus 50.3 X divide by X. All over negative 0.3 Not plugging in 100 into that, we get five minus three over 100. It's going to be at times negative one order 0.3 So that when we multiply that out, we're going to get to over negative two or three, they can have some value of that. You can see that that's less than one. In which case it's an elastic at X equals 100. Okay, so that's the answer to the first part here. Now let's go ahead and take the revenue function into account here. And so we have X times the demand function. So the X equals, I'm sorry the revenue is equal to five X. Last 0.3 X squared. So graphing that what we'll end up having here is something like this, where the point over here is 500 or three. The other one is zero. The maximum occurs at X equals to 50/3. And so what we see here is that since the revenue function is increasing up until 2 50 or three, we've got that it's elastic from zero 22 50 or three and that it's going to be in elastic. It's it's decreasing from 2 50/3, 2, 500 over three. And this is our answer to the second part.


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