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In this video, we're going to go over a question that asks us that given a demand and a supply curve, we would like to find the equilibrium price of the good, and eventually we would like to find the consumer and producer surplus at that equilibrium price.
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So let's begin with finding the equilibrium price and quantity.
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Here we're given two demand and supply curves, and we know that the equilibrium price and quantity is the place at which these two intersect.
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So let's note that down, where d and s intersect is the equilibrium position.
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So let's actually equate these together, and then we can solve for x.
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And by plugging that x value into one of these curves, we will find the demand.
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And or the supply curve.
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So by doing so, let's see here, 50 minus 1 over 20 x is equal to 20 plus 1 over 10.
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To make our life easier, i'm going to convert these into decimals just for temporarily.
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So let's just note that down.
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1 over 20 is 0 .05 and 1 over 10 is of course 0 .1 .1.
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That'll just make our division easier.
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So with those changes we have 50 minus 0 .05x will be equal to 20 plus 0 .1x.
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Now let's get all of the x to the other side.
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We'll get that 30 is equal to 0 .15x and that means that x will be equal to 200.
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That means that it takes 200 units to reach equilibrium.
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Now, by putting 200 into, let's say, the demand curve into the demand curve, we will get that 50 minus, and converting this back into a fraction, will have 200 over 20 or result in $40.
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So we can conclude that the equilibrium price is $40 at 200 units of the price sold.
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All right.
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Now, part b asks us to find the consumer and the producer surplus.
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In order to do that, let's first look at the graph of the regions that we have two that are given by the curves.
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And we'll also draw the equilibrium price line.
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The equilibrium price line is this green line, and we know that's $40.
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From basic coordinate geometry, we can very easily draw the demand and the supply curves.
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I'll draw the demand curve in red, which should look like this.
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And the supply curve, which will look something like this.
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Now, we know that they have to intersect at some point.
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So i'll call this the demand, not the demand curve, this is the supply curve.
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This is the supply curve, and this will be the demand curve.
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With that being said, we know that the area in between the area in between the equilibrium and the demand is the consumer surplus.
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So let's note that down...