# How to calculate deadweight loss

**Posted on:**01/06/2021 /

**Categories: Uncategorized**

This video is going to go over

how to calculate deadweight lossand kind of describe. What Deadweight. Loss is so dead weight Lossarisesfrom an economy not having the maximum Surplus possible So if we look at a perfectly competitive model we have our supply and demand lines The area above price and below demand is our consumer surplus the area below price and Above supply is our producer surplus Sothere‘s no Deadweight loss in this economy because surplus is maximized however if we were to institute a tax or there’s an externality or something like that, then we would have a shift in one of these curves Where the Optimum should be?

Here, but instead we’re here and so that difference Between where we should be and where we are? Gives us a Deadweight loss that’s occurred in the economy so first What is a deadweight loss? What’s causing it? It’s a difference between Marginal cost and marginal *benefit* so you’ll notice that at our optimum we have marginal cost equally marginal benefit and We’re good However if MC prime is our true Marginal cost in the economy Then we do not have marginal benefit equal to marginal cost because we want to be here instead of here So everywhere between these two curves We have a difference between marginal cost and marginal benefit and that creates the deadweight loss So let’s go through an example We’re going to begin our economy in equilibrium and just to make things easy let’s say that the initial equilibrium is 5 5 so then the government decides it decides that they want to institute a tax and let’s call it a supply-side, tax So that’s supply plus t our new __equilibrium__ is going to be at this point and let’s just say that results in a price instead of 6 a quantity of 4 and then here this price that the suppliers receive is 4 so here the quantity of the tax is 2 The line shifted up by the amount of to the suppliers Take half the tax and the consumers take half the tax So again remember with Deadweight loss we want to be here at a quantity of 5 and a price of 5 but we end up it here at a quantity of 4 price after tax of 6 our *sorry* price before tax of 6 and price after tax of 4 So remember this is our marginal benefit This is our marginal *cost* and this is our marginal cost plus the tax So what’s going on in the economy is at this point right here?

We’re losing out on *Potential* Surplus Because the true marginal benefit of the economy is still greater than the true marginal cost of the economy It’s just that the tax has Taken away that potential because now __suppliers__ have to pay a tax instead of realizing their true gains So everywhere between the marginal benefit and marginal cost from this new quantity To the old quantity is going to be deadweight Loss the neat thing about this is just the area of the triangle and if you remember the formula for calculating the area of the triangle it’s 1/2 times base times height and Here our base is 1/5 minus 4 so if we have 1/2 times 1 and then our height is going to be 6 minus 4 or 2 so 1/2 times 2 equals 1 so the Deadweight loss in our economy the area of this triangle is going to be 1 and what that means that without the tax our Economy would have a total surplus greater Than 1 added to it if we could get rid of that deadweight loss So that’s how it works with a tax. Let’s go through an [example] with an externality So here we have qp. Let’s do demand and supply Again, let’s choose five and five so what if there’s an externality say we have pollution So this is our new supply with the external cost it could give us our social cost curve whereas this is just marginal cost and marginal benefit, so let’s use the same numbers as before But what’s going on?

Here [is] now. This is the true cost to society Whereas When the market functions were equated marginal cost equal to marginal benefit And that’s where private firms maximize But we don’t want private firms to maximize at Marginal cost equals marginal benefit We want marginal benefit equal to social cost because that’s the true cost to society of having that firm in business so again let’s just call that seven we have to find the difference between Social benefit or Marginal benefit and Social cost and Everywhere we have a difference that’s going to calculate into our deadweight loss number So it’s going to be everywhere from the equilibrium, we are currently at To the equilibrium, we *should* be at and we can just fill that area in and again to calculate it 1/2 base times height and we can look at the numbers [here] again our base is 1 again our height is 2 So we get a deadweight loss of one With the externality case in terms of a negative externality we just have that Deadweight loss triangle pointing the other way But typically we’ll see the deadweight loss occurring on this side for the negative externality case It’s kind of unique and that you’ll see it coming from the other side