Estimating Demand Elasticity

Joseph wrote:

Dear Sir/Ma,

I am a research student currently conducting a study to determent the price and income elasticity of demand for fuel products in Nigeria, using a Quadratic Almost Ideal Demand System. I am using a cross sectional data (Harmonized National Living Standard Survey, 2009) obtained from the statistical agency in Nigeria. Currently, I face a challenge estimating the price elasticity of demand for fuel product because prices are constant across household units in the survey period (2009). The survey data contains information on expenditure of various fuel products, but no information is available on the price and quantities of fuel products purchased. However, I obtained the price of each product in 2009, but it is constant across all households, as a uniform price is applicable in Nigeria. This poses a challenge in estimating the price elasticity of demand for fuel products. To circumvent this problem, some studies have used quantities of each product to divide expenditure of each product. This will create the needed variability in prices. This approach seems impossible to me since my data set has no quantity of fuel products purchased. I humbly write to seek for more clarification on how to obtain variability in prices of each product across various households units in the survey. Thanks Joseph O.

My response:

I'm afraid I can't offer any further insight to what you've already said.  I don't do empirical work and as you said, you don't have the data do produce estimates here.  It seems to me the best you can do is some survey on what others have found.  After a quick search I found this paper by Boshoff.  You are probably aware of it already.  But in case not, on page 48 (page 6 of the pdf) there is a table with other estimates provided.  And then, of course, there are his own estimates later in the paper.  Those are for South Africa, not Nigeria.  In the absence of data about your own country, however, you should find what else is known about gasoline demand elasticity elsewhere.

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.