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Economics/MicroEcon Tax Incidence

Question
I'm a beginning MicroEcon student. We just recently covered the subject of Tax Incidence. On a recent quiz I took, the Professor asked a question for us to show the effects of a Tax over the span of 5 years. I'm in disagreement with this question. From what I've learned, Tax Incidence is used to show the tax burden on the supplier or customer and how it affects supply and demand. I don't ever recall it being used to predict the passage of time, such as Taxes of over a period several years.

Can Tax Incidence be used to predict the Taxes over a period of time? The professor said it could through Elasticity.

Hi Robbins,

I am very sorry that I was extremely busy with some research work, and I am still working on it, and so I couldn’t write to you earlier. Even though I am busy now, I think it has been quite some time, and you must be wondering about the reply. I always want to help students, and I would like to help in in connection with the question your professor has posed.

It appears from your question that you are a perceptive student and you have a good ground on incidence of tax on (a) producers (or, as you say, supplier) and (b) consumers (or, as you say, customer).
I believe you already know that tax will cause the supply curve to shift upward and leftward. That means, prices charges to consumers/customers rises by the amount of tax imposed. Now the question is: who pays the tax? You may have seen on diagrams that, with an upward-sloping supply curve and a downward-sloping supply curve, as the supply curve shifts upward and leftward, the equilibrium point of intersection  “shifts” northeastward. This shows that part of the burden falls on supplier and part on customer.

Please do not forget we are talking of “unit tax,” not “ad valorem” tax: In case of ad valorem tax the supply curve will NOT “shift parallel” [This problem in a question once occurred in the examination under University of London exam, and students were mystified, and even some teachers were flabbergasted; later I showed that to their Chief Examiner, and then they sent a note of correction in the next year. Hopefully your professor is not asking a question on ad valorem tax; even if he does, that can also be solve for prediction but would require more advanced math which may not be suitable for you –and you may discuss this matter with your professor, if your professor is very good in economic theory.]

Now, once you know that the vertical distance between the “supply+tax” curve and the “initial demand curve” at the new level of “output bought and sold” (which point is to the left of the initial point when intersection was between “supply +no tax” and demand”), you see that the shares of burden DEPENDS ON THE SLOPES OF BOTH THE DEMAND CURVE AND THE SUPPLY CURVE. You probably also know that SLOPE is not the same as ELASTICITY.

Next you can safely say the shares or burdens of tax fall on supplier and customer depending on the elasticities of demand for and supply of the product on which tax has been imposed. Here are a few things:

(a)   If elasticity of demand is zero, the entire burden falls on customer  [supply curve is upwardly sloping and demand curve is “vertical”]
(b)   If elasticity of demand is infinite, the entire burden falls on seller  [supply curve is upwardly sloping and demand curve is “horizontal”]
(c)    If elasticity of supply  is zero, the entire burden falls on seller  [supply curve is vertical and demand curve is “downward sloping”]
(d)   If elasticity of supply  is zero, the entire burden falls on customer  [supply curve is vertical and demand curve is “downward sloping”]

So we find that the incidence of tax finally depends on both the elasticites of demand and supply.
FINALLY, HOW CAN YOU SHOW EFFECT OF TAX OVER A SPAN OF 5 YEARS? This is, as now you know, is NOT an entirely invalid question, though this question is rather vague.  At your level, I don’t think you are studying econometrics. Hence let us leave the question of quantitative measurement at this moment. Then how should you answer the question.

You can draw 3 curves –one original downsloping demand curve, one original upsloping demand curve, and one new upsloping supply+tax curev, where the “vertical distance” between the supply and the supply+tax curves is the “amount of tax.” As you move along the horizontal (quantity ) axis, you can measure up the vertical axis.

Your professor’s question is rather vague. However, if the amount of tax imposed is for one year, then you just multiply the “relative burdens” five times, and you see the effect relatively is unchanged.
This answer requires a bit of geometry and some equations. If you need further assistance you will have to send me your question via email, because on this page mathematical explanations are not always possible.

I hope you are on a better ground now to tackle this question. Best of luck.

Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Thank you Mr.Raza for you response. I much appreciate your answer. Regards, Cory Robbins

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Economics

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Eklimur Raza

Expertise

It appears some students in this website are confused about elasticity of demand and the slope of the demand curve when they are trying to figure out why rectangular hyperbola comes up in case of unitary demand curve. First, they don't know that RH can be depicted in a positive quadrant of price,quantity plane. Secondly, they make the mistake that the slope of RH is constant at -1. Two points could help them: first, e=1 at each and every point of the RH, because the tangent at any point shows lower segment=upper segment (another geometric definition of e); yet slopes at different points,dQ/dP, are different; second, e is not slope but [(Slope)(P/Q)]in absolute terms. Caveat: only if we measure (log P) along the horizontal axis and (log Q) up the vertical axis, can we then say slope equals elasticity --in which case RH on P,Q plane is transformed into a straight-line demand curve [with slope= -tan 45 deg] on (log Q),(logP) plane, and e= -d(log Q)/d(log P). [By the way, logs are not used in college textbooks --although that is helpful in econometric estimation of elasticity viewed as an exponent of P, when demand equation is transformed into log-linear form.] I have not found the geometrical explanation I have given in any textbook followed in undergraduate and college classes in Canada (including the book followed in a university where I taught for a short time and in the book followed in George Brown College, Toronto, where I teach.

Experience

About 11 years' teaching economics and business studies, and also English, history and elementary French.Practical experience in a development bank, working with international donor agencies like the World Bank and the ADB. Experience in free-lance journalism, including Canada's "National Post."

Organizations
I teach micro- and macroeconomics at George Brown College (continuing education), Toronto, ON, Canada.

Publications
Many articles and editorials, on different subjects, in English newspapers. Recently an applied Major Research Paper, based on a synthesis of the Solow growth model and the Lewis two-sector model, has be accepted by Ryerson University, Toronto. Professors Thomas Barbiero and Eric Cam, Ryerson University, accepted the paper.

Education/Credentials
Master degree in Interantional Economics and Finance and diploma with honours in Business Administration from Canada.

Awards and Honors
Received First Prize in an inter-university Literary Contest.