Suppose the supply for a certain textbook is given byp=14q2 and demand is given by p=−14q2+10, where pis the price and q is the quantity. Find the equilibrium...

Find the equilibrium quantity and the equilibrium price. In the supply and demand equations, $p$ is price (in dollars) and $x$ is quantity (in thousands). Supply: $p=181-.01 x$ Demand: $p=52+.02 x$

Are you ready for some algebra? Because this question is going to require us to do some algebra. We're told that quantity demanded is equal to 500 minus 50 p. We're also told that quantity supplied is equal to 50 plus 25 p. Remember that the definition of equilibrium is that quantity supplied, equals quantity demanded and were asked, What is the equilibrium? Well, we have equations here for quantity demanded and quantity supplied. So let's set them equal to each other. We'll say that 500 minus 50 p equals 50 plus 25 p. Now, if we add 50 Pete, both sides, we get 500 equals 50 plus 75 p. Let's subtract 50 from both sides to get 450 equals 75 p. And now we just have a simple division problem, which I would recommend you use a calculator for 450 divided by 75 is six soapy equals six. We have our equilibrium price. We're halfway there. And to find our equilibrium quantity, we will just take this equilibrium price and substituted into one of these equations. So let's take this supply equation. 50 plus 25 p Well, we know that P is six. So quantity Excuse me. Quantity supplied equals 50 plus 25 times six, 25 times six is 150. So quality supplied equals 50 plus 150. Thus quantity supplied equals 200. So we have found our equilibrium price We have found our equilibrium quantity We can finally right out that are equilibrium P Comack you is equal to six as the price and 200 as the quantity.

Right here. We want to solve this as a system of equations. Now, since P is equal to both of these things, we can just set these things able to each other. 25 axis of 40 minus 1.15 acts. Let's add 1.15 back stateside. So we get two x 0 40 goodbye to when we get access 20. So the equilibrium quantity is access 20. Got to find the equilibrium price. Plug it back in. He is 0.85 x so he has 0.85 times 20 so ps 17.

Here. We basically want to solve this system of equations. Now, since P is equal each of these things, that means these two things must be equal to each other. That's the 300 minus 30 x his 80 plus 25 x So it's add 30 x on your side. Subtract 80 So we get to 20 on the left, 55 x on the right ride by 55. We should get access for So that's your equilibrium. Quantity. Your eagle of your price. We played it back in. I'm gonna use that equation. So it's 80 plus 25 times for five times for hundreds. This is 80 plus 100. So the equilibrium, equilibrium price there's $180.

Here we want the equilibrium, quantity and the equilibrium price. I just mean solve this system of equations Now, since P is equal to both of these things, we just set these things able to each other. So it's that 1.4 acts might a 0.6 even a of two X plus 3.2. And so then I need to add to actually inside. I need to add 0.6 on your side. It was just me. 3.4 Acts on the Left doesn't mean 3.8 on the right when you're 3.4 axes with 3.8, divide by 3.4. But you know, like you stole it. Divide by 3.4. That's what, a 3.8 by 3.4 that goes is about 1.18 Yes, waxes 1.18 no. We also need to find or equilibrium price. So P is native to X plus 3.2 so P is native to times 1.18 plus 3.2. And so if you take native two times 1.18 is this negative? 2.36? Well, it's 3.2, so the equilibrium price is 84 cents