NCAA

My mom and my wife have each filled out NCAA brackets for the first time this year. They seem to be getting the feel for it already; agonizing over match ups and a growing distaste for teams. My wife struggled with any first round losses and I’ve tried to convince her to be patient. For perspective, let’s review a few characteristics of the tournament. First and foremost, there are a possible unique bracket outcomes for this tournament, ignoring the one game playoff,

For a perfect bracket, an individual needs to select the single bracket out of the total possible set. Of course, certain brackets are more likely to occur than others, and using information we can eliminate unlikely brackets and highlight brackets that are most likely. This should reduce the current odds of a correct bracket, , significantly.

Consider a crude probability model where the probability a team wins is strictly dependent on seed. One such specification is

where represents the prescribed seed for a team. For example, the probability a four seed beats the thirteenth seed is about 0.76 using this formulation. Assuming a team with the higher seed wins each game we can thus calculate the likelihood of such a bracket.

The odds of such a bracket occurring are Still not a likely prospect but it is significantly smaller then the original computation. I imagine there is even a more likely bracket that would reduce the odds even more. A more efficient probability model could find such an answer. Nevertheless, the likelihood of a perfect bracket is tremendously small.

Rational Addiction

The Becker-Murphy Rational Addiction framework incorporates two important means for describing addictive behavior: reinforcement and tolerance. The current period utility function,

states that well being is determined by consumption of an addictive good, , the capital accumulation of the addictive good, , and a non-addictive good, Reinforcement is imposed on the model if and is consistent in agents with myopic preferences. More clearly stated, reinforcement is observed in a good whose past consumption increases the marginal utility of current consumption. Tolerance requires and describes how past
consumption of an addictive good reduces current utility. In other words, a greater quantity of the addictive substance is required to receive the original euphoric effect.

Presented in this manner, steady state solutions are found and analyzed for the dynamic optimization problem. The model can describe a variety of circumstances, and the existence of unstable steady states illustrate the difference between highly addicted people who continue consuming harmful substances and those who eventually quit entirely. Two other important implications of the model are: First, individuals who heavily discount the future are more likely to become addicted, and second, reinforcement causes addictive goods across time periods to be complements.

Because robust data on illegal drug prices doesn’t exist, the implications for the model are purely hypothetical. However, the model has been empirically tested on cigarette, alcohol, and gambling consumption. From these results a permanent reduction in the price of drugs is expected to increase consumption in the short run. It is likely that addiction would increase in the long run as well. Furthermore, addiction among lower income groups and the young are likely to be affected the most.

The results are certainly not complete and a more thorough study is necessary to evaluate the impact of such a policy. Nevertheless, legalizing drugs like heroin, cocaine, and marijuana are likely to increase
consumption, particularly in low income and younger groups.

Economics of Drugs

Earlier, I discussed comments made by Gary Becker that addressed the issue
of legalizing illicit drugs. While I was unable to locate any information
regarding the effects on inner-city youth, I did find an interesting
discussion detailing the impact legalization would have on consumption.
Certainly prices would fall, but the corresponding change in quantity
demanded is the question to be answered. If this were an introductory
economics class we would analyze the change in policy through a series of
graphs. The following figure, for example, illustrates the current policy,
where legal barriers increase the risk of bringing goods to the market. The
demand curve is relatively inelastic, showing that changes in price result
in relatively unresponsive changes in the quantity demanded.

Legalizing drugs would cause a shift in the supply curve, S1 to S2; as a
result, a new market equilibrium point is determined. This new equilibrium
represents a solution corresponding to a lower market price and higher
market quantity. A simplistic representation and one that provides a
generally intuitive example. However, this static realization fails to
address the question of how much the actual quantity will change. Is it
enough to know that consumption will increase, or is it more important to
know the magnitude of such a change. One issue is the usage of a linear
demand curve. Naturally, it is generally assumed that demand functions for
addictive goods are inelastic. However, the computed elasticity for a linear
demand curve is not constant, and in fact encompasses the entire permissible
range of elasticity, . The problem can be easily addressed by
substituting a constant elasticity demand curve in place of the linear
specification. But, consumption of an addictive good has dynamic
implications as well. This is why the Becker-Murphy Rational Addiction model
is so promising. Next time we’ll discuss the implications of the Rational
Addiction model and consumption estimates for the change in policy.