Friday, June 6, 2014

A question about health insurance

James asked:

I saw your Youtube video on Demand for Insurance and it led me to here. With that said, there are many articles written about health coverage choice e.g.National Institute of Health: http://economics.mit.edu/files/7870
Beginning on page 5 and,

Urban institute: http://www.urban.org/UploadedPDF/412471-Health-Insurance-Policy-Simulation-Model-Methodology-Documentation.pdf
Beginning on page 12.
RAND Compare has an overly complex model, but for discussion purposes, will use NIH's example.
NIH is taking into consideration (i) Risk aversion utility maximization (ii) expected healthcare needs (iii) variance in OOP cost from a set of health plans with consideration of variance in premiums for the health plans.

Is there a model or someone who can help me create a supplemental excel model that reflects the NIH's Model? In this model, they are using limited data such as Age, Income, and gender to impute a cost (lognorm function?)

There is so much written about this subject, however, I am having a very hard time modeling what is being discussed. If you could point me in a direction to someone who can help or may be interested in taking this on as a project, I would appreciate your feedback.

My response:


The video of mine that you mention just considers risk aversion and then only in the two-state case: loss or no-loss. So it is done very simply in that model.  I have another video on adverse selection, that looks at the problem graphically in a simple model and one on moral hazard that does it algebraically.  (It is really a model of the principal and agent, but that is essentially the same as an insurance model with moral hazard.) 

The MIT paper that you mention puts all these factors together in one model by considering two periods, where in the second period there is moral hazard, given the insurance policy choice in the first period.  Then, understanding the second period solution, they fold it back and look at the selection problem in the first period.  And the do this noting that demographic characteristics of the insurance purchaser will impact both the moral hazard and the selection problems.  This is substantially more complex then any of my videos.  It is also more realistic.   

Whether you can build an Excel model that imitates the MIT paper, I'm not sure.  But why would you want to do that?  To understand the MIT paper because it is too hard to work through the equations that are presented there?  Please not that papers published in the AER are meant for an audience of professional economists and assume the reader has crossed a prior threshold of understanding - both on the issues and the math modeling.  I would not teach this paper to an undergraduate class.  

Saturday, April 26, 2014

Comparative Advantage

Danny wrote:

Hi professor, 
For example, given two countries and two outputs such as trains and planes, when determining which has the comparative advantage, do you compare within the country itself or between countries? That is, should you be comparing whether producing one particular good has a lower opportunity cost than the other in that same country? Or comparing whether producing one particular good has a lower opportunity cost in another country relative to your own country? 
In other words, are the comparisons of opportunity costs performed horizontally or vertically? I am confused. 
For an example, please see: https://www.youtube.com/watch?v=z9SAzSm24qg&index=7&list=PLA46DB4506062B62B At 2:00mins, the instructor suggests comparing between countries, however, isn't comparative advantage and opportunity costs compared within the same country? Or is it because the introduction of trade changes it around? Not really sure. 
Thanks for any help

My response:

The question that might help you to understand this is this.  Suppose trade between the two countries can occur and is costless.  Then an efficient production plan that produced a given amount of trains would maximize the number of airplanes produced.  How should production be divided across the two countries to attain an efficient production plan? 
If the efficient production plan entails one country specializing in production, for example say that country A produces Trains only while country B produces Trains and Planes, with the result an efficient plan, then we say that country A has a comparative advantage in producing Trains.   
Further, if you considered a different efficient production plan with a bit less production of Trains and a bit more production of planes, then the way to get from the first to the second is by having country B reduce its production of trains and increase its production of planes and have country A continue to specialize in the production of trains.  

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.  

Externalities and Curve Shifting

Danny wrote:

Hi Professor Arvan,

Can externalities be either on the production or consumption side? That is, for example, a negative externality, does it matter whether you shift the supply curve leftward/inward or the demand curve leftward/inward?

For example, when dealing with a good such as for example, a cologne that is extremely repugnant, is the negative externality related to the consumption or production of the good?

It could be argued from both perspectives, right?

Hence how would you know which curve to shift in order to find the socially optimal quantity? (If you shift either, they do however end up at the same socially optimal quantity, however the prices differ (if you shift the supply curve inward, the new equilibrium would be higher, and if you shift the demand curve inward, price would be lower)

I would appreciate your comments on this.

Thank you.

Regards,
Danny


My response:

There can certainly be externalities in consumption and they can be either positive or negative.  For example, sometimes there is a desire to be "part of the crowd."  If many students wear bluejeans to class, other students might want to wear them for that reason.  This is a positive consumption externality that is sometimes referred to as a network effect.  Advertisers understand this and one economic rationale for advertisement of a certain sort is to encourage the market to congeal on that product.

I didn't quite get the example with the cologne.  Presumably a person wears a scent to attract others.  If the cologne were generally repugnant, that would seem to be a product without a market.  But one might consider a scent that most others like yet that a few are allergic to.  There would be a negative externality in that case in causing the allergic reaction.

One can a little nitpicking on products that are durable by separating out purchase from use.  The bluejeans mentioned about don't contribute to the network effect if they hang in the person's closet.  The networks effect only arises when the person is seen wearing them.  Something similar can be said for the cologne.  Normally we are not so finicky in making our analysis and assume purchase and use are strongly correlated.

The last point I'd make is to be careful about discussing curve shifting in the presence of the externality.  In the textbook case of a factory that is polluting the air as a byproduct when operating the plant, neither the supply curve nor the demand curve shift as a consequence of the externality.   Normally we analyze this case by saying the marginal social cost shifts inward (from the original supply curve) where social cost includes both the production costs and the abatement costs.   In contrast, in the presence of network effects the demand curve itself actually shifts.

Tuesday, March 11, 2014

Estimating Demand Elasticities and Compensating Variation

A student posed the following question:

Hi Respected Sir,
I am writing a report on Compensating Variation (CV) in case of more than two goods say 8 goods. My question is how can we estimate it in case of more than 2 goods.
Another Question is How can we write the equations for 8 commodities in Almost Ideal Demand System (AIDS) to calculate Own , Cross and Expenditure Elasticities of demand.
In which software both of the methods can be calculated?
I am waiting for your reply.
Thanks in anticipation

My response:

This question is more econometrics than it is intermediate micro.  So I am only going to provide a partial response and stick to the economic theory part, though I must say I'd only teach what I discuss below at the graduate level. 
The traditional approach to consumer choice is to start with preferences, specified by a utility function, u, and combine that with a budget constraint, that depends on a price system p = (p1,p2,...,pn) that specifies the prices of each good or service, and the consumers income y.  Together the price system and income determine the budget set.  The consumer's choice, or demand, or optimum, call it x*(u,p,y) solves the problem of maximizing utility subject to the budget constraint.   
There is an alternative approach called the duality approach, which is useful conceptually and in laying the foundation for the econometrics.  Two value functions are determined.  One, measured in dollar terms, is called the Expenditure Function.  It is analogous to the Cost Function developed in the theory of the firm.  The expenditure function maps indifference curves (or when there are more than two goods, level sets of the utility function) and price systems into an expenditure level - the least expenditure it takes to reach that indifference curve at the given prices.   The other value function, measured in utility terms, is called the Indirect Utility Function.  It maps budget sets into utility levels.  Alternatively, it gives the utility attained at the consumer's choice. 
One of the powerful results from duality theory is that you can recover the consumer demand's from these value functions.  The compensated demands (these measure the substitution effect only) are given by the first partial derivatives of the Expenditure Function with respect to the specific price.  The ordinary demands can be obtained in a similar way from the Indirect Utility Function, though the result, known as Roy's Identity, is a bit more complicated.   
Let me close with the little I know about the Almost Ideal Demand System.  Deaton and Mulbauer start with the Expenditure Function, express it in log form, and then linearize it locally, assuming it is some average of the expenditure at subsistence (the worst possible point) and bliss (the best possible point).  This makes it suitable for estimation. 
Good luck on your paper. 

Thursday, September 5, 2013

The effect of a tax - curve shifting

Vu asked:

Dear professor Arvani have a questionWhy when a unit tax is levied directly on consumers, this make the demand curve shifts downwards? and what could be the causes of this shift ?
Thank you very much

My response:

The tax is levied in some market for a good or service.  Typically, buyers pay some of it and sellers pay some of it as well.  The tax creates a wedge between what the buyer pays and what the seller receives, with the difference being the tax.  If in the diagram the price represented is the seller's price (so the supply curve remains the same) then the demand curve shifts down by the amount of the tax.  In this way if you add the tax to the seller's price, you get the price really does pay so the quantity demanded should be exactly what it was before at this higher price.

Monday, July 8, 2013

Comparative Statics of Consumer Choice

Judy asked:

using well labele diagrams show the total effect,income effect and substitution effect due to a price fall of good x1 assuming that the consumer baskets has only good x1 and x2. The price of good x2 remains constant.

My Response:

I encourage you to watch my video on income and substitution effects.  There the goods are labeled x and y (instead of x1 and x2) and it is for a price increase rather than a price decrease.  I suspect you covered something similar in your class and now your instructor wants you to think through what happens when the price change is in the opposite direction.

From my video in the description there is a link to the spreadsheet.  Go to the tab labeled Income and Substitution Effects. There is a button called Raise Price of Good X.  Push on that and look at the cell next to the button.  It has positive values.  If you type into that cell a negative value, say -15, you will get the graph for a price reduction of Good X.  Note that because this was designed for a price increase, the new budget line doesn't extent all the way to X axis.  It should.

Also, your instructor may feel I'm doing your homework for you and not be happy about it.  So if you pose another question of this sort to Ask The Prof, please also include what you've tried to do in response.  This way I can help you without giving away the answer to the question.

Tuesday, April 30, 2013

Produce or Not in the Short Run?

Joe R. asks:

Working on  a question with a full chart to reference but am lost where to get the date for the answer. The question ask about the product price of $56, will this firm produce in the short run.?

My response:

There is a fairly complete analysis of the general issues in the video Short Run Cost.  The question is asking, in effect, whether there is any output level were Average Variable Cost is below $56.  If the answer is yes, then producing at that output level nets some producer surplus (the difference between revenue and variable cost), so it makes sense to produce.  If not, then it is best not to produce.

Note that the fix cost is not relevant for this calculation.  It is sunk in the short run and therefore must be paid regardless of whether production occurs.  

Your chart that you refer to may not have Average Variable Cost broken out, in which case you must compute it by dividing Total Variable Cost by Output.  If it is broken out, then it is simply a matter of eyeballing it to see if it ever is below $56.

Thursday, April 18, 2013

On the Weak and General Axiom of Revealed Preference

John asked the following:


"I have two related questions on Choice. 
I know that we can satisfy WARP but have nevertheless a violation of GARP. My question is if we can have a situation where WARP is violated, but GARP is satisfied? 
Secondly, from the definition of GARP it is always spoken of a bundle being revealed preferred to another bundle through a chain or ""sequence"" of revealed preferences. My question is, if this defined ""sequence"" can consist of only two observations, so that we have actually a direct revealed preference after all?  In other words, does ""revealed preferred"" include the case of ""direct revealed preferred""?"

My response:

The quick answers are, to the first question, no, and to the second question, yes.  In other words, GARP implies WARP and the chain can have only two elements, which is WARP directly.

A longer response would include making a comparison between revealed preference and the usual assumptions made about preference.  These are about a preference relation, R.  xRy is then read as, x is preferred to or indifferent to y.   So from R one can also define P and I by:

  • xPy if xRy and not yRx.
  • xIy if xRy and yRx.


There are three "logical" assumption about preference orderings.

R is complete.  For every x and y in the Consumption set (the set of possible consumption bundles) either xRy or yRx.  This means comparisons can be made between any two consumption bundles.  Note that neither P nor I are complete.

R is reflexive.  For every x in the Consumption set xRx.

R is transitive.  For every x, y, and z in the Consumption set, if xRy and yRz then xRz.

These properties allow one to define a choice, provided the choice set is closed.  In this case if the choice set is C then x in C is a choice (a maximal element under R) if xRy for all y in C.  Note that there is no greatest number less than 100.  If you posit it is 99, then 99.9 is greater and you can always add an additional 9 to the right.  So for a choice to exist, the choice set must be closed.  100 is the greatest number less than or equal to 100.  The choice set being closed means it includes its boundary.

To these logical assumptions, one usually adds an economic assumption - monotonicity or more is preferred to less.  This assumption rules about satiation points as well as "thick indifference curves,"  The upshot of this assumption is that when the choice problem is given by a budget set, the choice will always be on the budget line, never inside the line.

A further assumption that is frequently made is that preferences are Convex, which gives indifference curves their usual shape.  This is done do when the Budget environment changes in a small way, the choice also changes at most in a small way.  Or, if you prefer, the demands are continuous function of the budget environment.

Now, with all this machinery, what does WARP get you?  In this way of thinking, WARP is equivalent to completeness, reflexivity, and monotonicity.  You need GARP to bring in transitivity.  There is also something called SARP, the strong axiom.  It is WARP plus the assumption that preferences are strictly convex, so the choice is always unique.

I hope that helps.


Sunday, December 16, 2012

Follow Up On Measuring Utility

Jonathan came back with this:


Hi, thanks for that Professor. IMO Utility does describe the feeling, or at least the “something” that kicks-in mentally, particularly with ""money"" based decisions - when you know (or don’t) you are detaching yourself from the wholly rational course of action (expected return) to take the money on the table offered, or a sum offered with certainty that is just enough of a push - for you to cash in your chips.
Where I’m stuck – is that there is a load of books and research about the abstract pro’s and cons – but I can’t find anything anywhere on the net that explains just how to go about discovering how to assess yourself (e.g. a clear example from the grass up).
Any ideas?
Thanks again,
Jon   

My response:

If you took the standard expected utility theory at face value, then you would approximate the utility function locally with a quadratic.  The benefit of doing that is you get that for small gambles around the mean, the theory says the risk premium should be the Arrow-Pratt measure of absolute risk aversion at the mean, r, times the variance of the gamble.

For example suppose you face the gamble of $1,001 with probability .5 and  $999 with probability .5, so the mean is $1,000 and the variance of this gamble is $1, which is small relative to the mean.  You then try to elicit what amount of money for certain would make the person indifferent between having that or having the gamble.   Suppose you find the certainty equivalent determined experimentally is $999.60.  So in this case the risk premium is $.40 and hence the inferred Arrow-Pratt measure of absolute risk aversion is .4.

Now if you do this seriously, you would like to see whether the theory is really confirmed.  So you might try other small gambles with mean $1000.  For example you might consider the gamble (a) of $1001 with probability .8 and $996 with probability .2  as well as the gamble (b) of  $1004 with probability .2 and $999 with probability .8.  Each of these gambles has the same variance, $4.  So ahead of time you might guess based on what you discovered before that the measured risk premium would be $1.60, which must be the case if  the formula in the first paragraph held exactly and you measured the risk premium perfectly in the previous experiment.  You might get something close to that for the gamble (a) but you definitely won't for gamble (b) because that says the certainty equivalent is $998.40, which is lower than the $999, what is attained in the lower income state.

There are two possible source of error here: (1) measurement of the risk premium in the first experiment and (2) the formula that relates risk premium to the Arrow-Pratt measure and the variance of the gamble.   The second error becomes less as the variance gets smaller but the first error gets bigger that way.  So even if you take the theory as fully correct, you will have issues in measuring the utility function.

Let me make one more point on this.  The psychologist Daniel Kahneman, winner of the Nobel Prize in  Economics, has shown that the standard expected utility theory is wrong and that something else called Prospect Theory is closer to how we actually behave.  In that a reference point matters for evaluating gambles and then whether the outcome is a win with respect to the reference point (where the individual is then risk averse) or a loss with respect to the reference point (where the individual is then risk seeking).  Put another way, the utility function for Prospect Theory is convex-concave, with an inflection point at the reference point.   If you find this interesting you might read Kahneman's recent book, Thinking Fast and Slow.