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The supply and demand for a product are given by 2p − q = 70 and pq = 200 + 20q, respectively. Find the market equilibrium point....

Question

The supply and demand for a product are given by 2p − q = 70 and pq = 200 + 20q, respectively. Find the market equilibrium point.

The supply and demand for a product are given by 2p − q = 70 and pq = 200 + 20q, respectively. Find the market equilibrium point.



Answers

Find the point of equilibrium of the demand and supply equations. The point of equilibrium is the price $p$ and the number of units $x$ that satisfy both the demand and supply equations. Demand $\quad$ Supply $p=140-0.00002 x \quad p=80+0.00001 x$

So here we are given a pair of supply and demand functions. We want to put both on the same axes find the point of market equilibrium. And we also want to identify which one is the supply and which one is the demand function. So if we have P plus ax equals 100 we can just move the X to the other side, giving us P equals negative X plus 100. Well, right off the bat, we know this is gonna be the demand function because we know that the demand decreases as X increases. So anytime you have a negative slope and you're trying to determine which ones which we know that's going to be the demand function. So that our supply function is going to be P equals 7/2 x Uh the over two, which is 30. Yeah. Stop. Right. There is going to give us our supply function. We see that our point of market equilibrium is going to be 15.556 84.444. It will be our final answer.

Wasn't very calling about the equilibrium which need to send that the man function. Hey, got to the supply function here in this question were given the man function ico June the 8800 minus that the X and a supply function Ego Juna 7000. My plus 15. Thanks. Yeah, we want to find an equilibrium. So we need to send the d X You go to the S e X and it means that we have the 8800 minus 30 X They go to the 7000 plus 15 x on. Then I'm going to move on the X to one side, the constant to the other side It will be equal to, you know, just when we get to go churned up 18 100 Now it will go to the 45 x So my X and we go to 1800 dividing by the 45. Don't get Geico too for the so when they execute you thought that you can look into the Let's say I'm looking to the supply now during it into your 7000 plus 15 times 40 and we can t go with you. I was 15 and then plus 7000 so he could get a 7200. They found the equilibrium pond. Will you go to execute to 40 and value equal to a 7200?

So here we want to look at the um supply and demand function of a portable cd player. Now it's going to be p equals 190 -15 x and Equals 75 plus Iraq's how the supply and demand function works is we see if demand is too great and supply is too little, then um we're going to lose money or if the supply is too great and the demand is too little that we're going to lose money. So we want to find this equilibrium point that occurs at the intersection. So we see that the supply and demand meat when X. Is the number of units. So five is the number of units And then 115 Is RP values that stands for 100. Uh So X being the p being the price in dollars, that would be 100 and $15 each and five is in hundreds of thousands. That means 500,000 units.

Given a demand of p equals 140 -0.00002 x. And a supply of p equals 80 plus .00001 x. We're going to determine where the equilibrium is. The equilibrium is where the demand and the supply intersect with one another. So this is a system of equations and we want to find the point of intersection. We know p equals this whole thing. So we can substitute that in for p. c. 140 -0.00002 x equals 80 plus 0.1 X. We're going to add 0.00002 X to both sides. And we get 140 equals 80 plus 0.00003 x. Subtract 80 from both sides And we get 60 equals 0.00003 x. I want to divide both sides by 0.00003 60, divided by 0.00003 is two million. So the quantity, the equilibrium quantity is two million units to determine the equilibrium price, we're gonna say P equals 140 minus 0.2 times X, which is two million, P equals 140 minus 1400.2 times two million, gives me 40. So we got 140 -40, Which is just 100, Making the Equilibrium Price 100.


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