How to calculate deadweight loss - YouTube

This video is going to go over how to calculate deadweight loss and kind of describe. What Deadweight. Loss is so dead weight Loss

arises from 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

So there'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