Saturday, April 26, 2014

The effect of a tax

Danny wrote:

Hi Professor, 
In regards to taxes, I have seen that in your video, that you name the vertical axes either the selling price or the buyer price and am I correct in saying that depending on whether the tax is levied on buyers or sellers is what determines what you name your vertical axes and thus determines which curve you shift. I have never seen it been done this way. I've always seen the vertical axes to just be denoted price. 
Since the burden of the tax is shared (doesn't have to be equally shared of course right) between buyers and sellers, does it really matter what curve you shift (demand or supply) when either the buyer pays the tax or the seller pays the tax? Is it correct to shift either one of the curves? The way my lecturer has demonstrated it is to draw a tax wedge between the supply and demand curves,however I get confused to how this is used or can be used to answer questions. Because there will be two intersections given a particular quantity with both the supply and demand curve, so how do you know which one to look at?

My lecturer has said he does not prefer shifting the supply or demand curves because that is not actually what is happening, it is just 'construction lines' to depict the tax levy and drawing a tax wedge is much more simpler and achieves the same thing, however I have difficulty grasping the tax concept. 
Furthermore, my lecturer and other online videos suggest that the price to the buyer is equal to the price to the producer PLUS the tax? (Pb = Ps + Tax) 
However isn't that only correct if we are assuming that the consumer PAYS the tax? What if the producer pays the tax, does that mean this equation (Pb = Ps + Tax) is invalid? And rather it should be the price to the producer equals the price to the consumer plus the tax? 
Or because the tax burden is shared between buyers and sellers, that it doesn't really matter? So in these cases, how do you know which curve to be shifting or to be looking at when determining the new tax equilibrium?

I hope that makes sense and would appreciate some help. 
Thank you so much,

My response:

In the presence of the tax, the buyer pays more than what the seller receives.  The difference is the tax.  That much is fundamental.  If Pb is what the buyer  pays and Ps is what the seller receives, then the equation Pb = Ps + Tax or Ps = Pb - Tax (which is the same equation rewritten) is always valid.   
The rest is on how to represent this graphically, going from no tax to a tax or going from a tax to then raising the tax.  What happens in these cases is called the comparative statics of competitive equilibrium with respect to the tax. You can do this as I have done in my video or via the wedge that your instructor prefers.  An advantage of the wedge, as your instructor has noted, is that the underlying demand and supply curves are not changing.  A disadvantage is that you may not be able to eyeball the vertical distance between demand and supply for a given quantity or, conversely, to eyeball the quantity where a given vertical distance is attained.  


  1. Thanks for that, one further question, what did you mean by: A disadvantage is that you may not be able to eyeball the vertical distance between demand and supply for a given quantity or, conversely, to eyeball the quantity where a given vertical distance is attained

    I'm not sure what this means.

  2. The curve shifting approach determines the new output as the intersection the shifted curve (for example shifted supply curve) with the original curve from the other side of the market (in this case the original demand curve). In the wedge approach, you must determine the new output by eyeballing where the vertical difference between demand and supply equals the tax.

  3. Great, thank you Professor!

  4. May I ask if it would be possible to make a video that demonstrates the difference between the two approaches with two simple examples (one where the buyer is paying the tax, and the other where the seller is paying the tax). I think this would better aid my understanding of taxes, I would appreciate it a lot.

    1. I can see you are not understanding, but I don't believe there are two approaches It is simply a matter of representing the new equilibrium (after the tax) and the old equilibrium (before the tax) in the same diagram. In general, if P* is the old equilibrium price then in the new equilibrium Pb > P* > Ps and both sides of the market pay some of the ax. In one "razor edge" case, Pb = P* > Ps and the entire tax is borne by the sellers. In another razor edge case, Pb > P* = Ps and the entire tax is borne by the buyers. I encourage you to try to draw those razor edge cases with pencil and paper to see if you can understand what is going on.

    2. Sorry, may I ask what does it mean a 'razor edge' case? Since you refer to them as the tax being borne by one side (either seller or buyer), are you talking about drawing either the supply or demand curve as perfectly inelastic? Otherwise, I'm not sure what Pb = P* > Ps and Pb > P* = Ps means. Thank you for the help

    3. If you go back to the video and read the description there is a link to Google Docs where the Excel workbook is. Download it as an Excel file. The video is based on the second worksheet.

      There are three push button controls. Push the one to the right, which sets the size of the unit tax. Start with a situation where the tax is sufficiently large that it is noticeable in the graph. Then the original equilibrium price is what I called P*. In the graph P* is $50. In the equilibrium after the tax the buyer pays a price more than $50, the seller gets a price less than $50 and the difference between what the buyer pays and the seller gets is the tax. The amount of the tax paid by the buyer is Pb - P*. The amount of the tax paid by the seller is P* - Ps.

      The other controls vary elasticity around the original equilibrium. The control at the left is for the demand elasticity. The control in the middle is for the supply elasticity. Make demand more elastic at the original equilibrium, with a positive tax. What happen to Pb and Ps as a consequence?

      The controls only allow a limited range of variation for the elasticity of demand and the elasticity of supply. What would happen if demand were perfectly elastic? perfectly inelastic? That's one way to get at the razor edge cases.

      The other way is to look at supply. What happens when supply is perfectly elastic? Perfectly inelastic?