Supply curve is modeled bY the equation600 0.403/2, find the producer surplus when the selling price is $1000_Need Help?ReadTalk to TutorSubmit AnswerPractice Anoth...

If a supply curve is modeled by the equation $ p = 125 + 0.002x^2 $, find the producer surplus when the
selling price is $625.

Okay, so here we have the demand curve, and here we have globally line right here. We have the price of $16 so we just seem to see where they're going to intersect, which is about 3727. So now what I need to do is integrate dysfunction. The demand function from zero 2 3727 No B e negative X over 5000 over X plus 20,000 d X. So you'll you'll. You'll want to use a computer at algebra system for this one, such as Wolfram, and then whenever you do, you will get about $37,753.

So in this problem, we're given a demand curve. P is equal to 450 divided by the quantity X plus eight and were asked to find consumer surplus when the price So consumer surplus on this graph is going to be this area in green Now, To find it, we have to integrate this demand curve up to the value it corresponds it 10 and then subtract out the area of this box. So to begin first, we need a value where I have placed that red dot. So to get it, we're going to take 10 which is a value of P and said it equal to 450 over the quantity expose. So if we multiply both sides by expose, we're going to get 10 eggs. Course, can you equal to 450 and then subtracting 80 from both sides. We get 10 x is equal to 370 and x his equal 2 37 So 37 units is what we have for X now to get the green area, which is our consumer surplus that is going to be equal to the integral from zero 2 37 of 450 over X plus eight d X and then subtracting off 10 times 37 which is going to be the area of a rectangle in red. So this integral right here, we'll evaluate 2 450 And since we have a X to the power of one term and the denominator, we'll get the natural log of X plus eight evaluated at zero and 37. In most cases, you have to put absolute value bars around the argument for the natural log. But here, if you plug in zero, you get positive. Eight. If you book in 37 you get positive. 45 and so you will never go negative. So you can just put parentheses in this situation, and then we're going to subtract off 370. So we get for 50 times dear natural log of 45 minus the natural log of eight minus our 370. So 450 just to simplify for the exact form, slightly weaken right as 45 over eight and then again minus 3 70 So this would be the answer in exact form, and then to approximate this first term 450 times. The natural log of 45 of her eight is approximately 777 0.25 And so subtracting off we get 407 dollars and 25 cents for consumer surplus.

So here we have the following function on the top for demand and this bottom one for supply and meaning to find supply surplus. Well, first we did not avenue to find its equilibrium quantity and price. In order to do that, we need to set the two equations they call to each other as we've done over here and solving for it by moving the tuning around. And this number around here, We get 86 days ago to 0.03 x or X is equal to 2000. And that's really important. Now using that, let's come down here. Okay, so this line going down is the curve is a function for demand and the one going up is for supply. This area down here, it's going to be our uh supply surplus. So we have the equilibrium quantity 2000 now, we need to find their ca Librium price. So the equilibrium price For that, we need to plug 2000 back into our equations. If you plug it back into uh supply, we get that, it's going to be tiny plus 0.02 times X. Or times 2000. And that is going to give us um party. I'm sorry. That's gonna give us 60. I don't make sense. That's going to give us 60. Um It's a very equilibrium prices that's sexy. So now all they have to do is to find this area, well the area is height or changing Price, which is $40 times the quantity at equilibrium, which is 2000, right this sidelines or let me use a different color for it. The silence over here is just actually this quantity 2000. So Our area is going to be 40 times 2000 over two or $40,000.

Okay And discussion a price supply function is given that S. P equals two X cubed plus X plus 10. Okay. And where X Is the supply that isn't 1000 units? And P is the price per unit? That is in dollars? Okay. And now we have to find out we will have to draw a supply car. Okay? So we will take X. That is on X. Axis and C. That is priced well don't via access. So let's take some points. Okay? When X equals to zero, P will be this will zero. So we will be 10. Okay. At same attack supposed to one? The price will be 12 exposed to it will be 20 exposed to three. It will be 14 exposed to four. It will be 78. Okay. So using these points we can draw or we can escape the graph on the coordinates. Okay. So we will draw. I already do on the graph for you that is like this. Okay. And when you see this this will be the graph Okay at X equals to zero. Okay please. 10. Okay. And you can see this is the point when X equals to it. It will be 78 this point. Okay so and X equals 23 It will be 40 like here. Okay so this is the X axis. That is the supply. Okay. Supply. And why access that is price function or we can say test price. And this is the graph of P equals two X cubed plus X plus 10. Okay so answer of part of the graph that is in red color. Okay. And now we will go to the party of discussion that is okay. We have given the supplier will make 2000 units so X is given okay, X is given to because it is already in 1000 and we have to find out the price per unit. So we have to find out B. So now we will take price function that is X cubed plus X plus 10. And now we have to find out we at X equals to two. So we will put X equals two to where it will be to cube plus two plus 10 and P. Two. It will be to cube that is eight plus two plus 10 and eight and 2 10 and 10 and 10 20. So we do it will be 20. And the unit for the price per unit is given. That is dollars. $20 will be the final answer of discussion. Thank you.