when we talk about economic policy one of the main things that separate conservatives and liberal is how they view the Lord of government especially how big it should be People have a strong opinion on this But what I of notice is that they jump into conclusion without really understanding what's at the core of the disagreement That's what we are going to explore today We are going to use welfare economics to better understand tax policy and see how it impacts different groups in the economy Our main tool will be surplus analysis Just to recap total surplus is made up of consumer surplus and producer surplus Right but when we introduce tax into the mix we also include the government tax revenue So now total surplus becomes sum of consumer surplus producer surplus and levenue collected by government Let's start with the free market low taxes involved In this case the market reach equilibrium price based on supply demand This is equilibrium price Consumer surplus is area below demand curve above the price So triangle A B C right what about producer surplus it's below price above supply curve right so triangle D E F together so total surplus is sum of all that ABC plus D E F that give us most efficient market outcome Now let's see what happen when tax is introduced So we have a tax w here tax create wedgie between the price buyer pay and price seller receive This wedgie is the size of tax t In this example the government now collects tax revenue represented by this pink rectangle which equals tax rate T times quantity sold QT right so T * QT that's this pink box right it can be rewritten this way Yeah this is just tax rate price buyer pay minus price seller receive But tax also change behavior quantity force right from QE to QT buyers pay more seller receive less So now consumer surplus shrink to area A below demand above price they pay PB right up to QT So just A is consumer surplus Similarly producer surplus shrink to area F below price seller receive above supply curve up to QT Tax revenue is as discussed B and D right So total surplus in this case a consumer f producer BND tax revenue but what happened to this CN this yellow triangle that is a dead weight loss the value that's lost to the economy because few trade happened these are mutually beneficial transaction but they don't occur anymore more because of the tax Yeah To summarize tax reduce market efficiency yet create deadway loss right which is not captured by buyer seller or government just gone Let's try this with some numbers Stay in a free market So price is $200 and quantity sold is 100 right we calculate both consumer and produce surplus using area of a triangle half time base times the height So consumer surplus half times what well 400 minus 200 right times quantity 100 Then we come up with 10,000 You can do the same for producer surplus It looks symmetric Yeah it's 10,000 and total surplus becomes sum of those two 20,000 Now let's say there is a $100 tax imposed So you can have a tax wedge right here Then buyers now pay 250 Seller receive 150 The quantity sold dropped to 75 Right do consumer and product surplus both shrink So you can have a consumer surplus here and produce surplus here Right using the formula Yeah You can have half times now base 75 times the height that is 150 right yeah 400 minus 250 Then you come up with this number Same is the case for producer surplus right and tax revenue is this revenue box tax rate 100 * 75 so revenue become 7500 total surplus is now the sum of all these number so two of this plus 7500 then total surplus become this number you can also calculate that weight loss Right Yeah This triangle now half times the base is tax rate 100 excuse me the height is 25 right then you come up with this number or you can subtract this number total surplus with the tax from 20,000 Okay now let's ask what determine how big the dead weight loss is Even though tax have cost they are necessary we need them to pay for things like roads school public safety in general public good So the key is minimizing the economic calm So it's necessary evil in some sense Then how can we minimize economic calm that way loss is smaller when supply or demand is inelastic That is when buyer and seller don't change their behavior much in response to price So let me show you if supply is steep right it's inelastic text doesn't change quantity much right here is just one possible text w then as you can see yeah this that way lo triangle is rather small right What if now this time supply curve is flat so quantity changes a lot with the tax So loss as you can see this that loss triangle becomes bigger The same goes for demand steep demand small loss and flat demand that's associated with a big loss like this Right so steep demand flat demand you can see the difference of impact of tax So ideally we want to tax good and services where supply and demand are more inelastic In extreme cases if the supply or demand is perfectly inelastic as a vertical line the text cause no distortion and no dead weight loss This brings us to deeper question How big should the government be yeah If someone believes that the cost of taxation especially deadway loss is high they are likely to favor smaller government that's the conservative view if someone believe the cost is relatively small they are less concerned about expanding government services that leans more liberal to really understand this we need to look at where tax revenue comes from about 47% of US federal tax revenue comes from income tax paid by workers Right another 33 comes from payroll tax split between employer and employee But as we discussed in previous lecture workers tend to bear most of the burden So in total about 80% of tax federal tax revenue is tied to the labor market So the question comes down to elasticity of labor supply How elastic or inelastic is labor supply this is big question Many economists too especially more liberal one believe labor supply is inelastic meaning workers don't drastically change their behavior in response to ch uh taxes That implies the dead weight loss from taxing labor is small which supports the case for larger government But other economists too often more conservative disagree They argue labor supply might be more elastic than it appears in short-term data People might adjust to how much they work retire earlier or not take a job at all if taxes are too high That means that weight loss could be larger than we think Yeah this is where real disagreement lies It's not just about ideology It's about how people view the cost of taxation especially in relation to labor supply Let me end with one final point How does that weight loss change as tax rate increase imagine small triangle representing deadway loss from small tax t right So this is initial deadway loss double the tax rate then yes you see triangle just to doesn't double right it gets a lot bigger with the two * t with the now triple right it grows even faster so this show dead weight loss increase exponentially with the size of tax So here is a just practical takeaway from this analysis Instead of imposing very high tax on small number of good or services it's often better to spread the tax more broadly That helps reduce overall economic distortion