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:
Beginning on page 5 and,

Urban institute:
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: 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.


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.