Shopping for Pareto Efficiency

Shopping for Pareto Efficiency

Group members: Shelley, Xianger, Lady, Delia

Public goods are goods that must be provided in the same amount to all members of a society. Economists refer to these types of goods as “non-excludable” and “non-rival”. “Non-excludable” means there is no way to prevent another person from using and benefiting from the same public good. Public goods cannot even be withheld from those who do not pay for them. “Non-rival” means that one’s usage of the good will not decrease the amount that is available for others to use. The availability of the good is never reduced. National security, street lights, and lighthouses are all examples of public goods.

One downside is the free-rider problem. Public goods can not exclude anyone from benefiting from them. A problem that arises is that members of a society do not have the incentive to provide public goods. Instead, they have the incentive to be free riders - those who get the benefit of the the public good but do not pay for the provision of that good. A rational person would not pay for a service that s/he could benefit from without paying. However, if a free rider problem exists, public goods are not provided at their Pareto efficiency level. The following story shows an example in which public goods are provided at the Pareto efficiency level.

           

In the Mount Holyoke community, public goods can be shared among roommates.

We have four women who chose to live in an apartment in Buckland Hall.The apartment comes with a kitchen and a bathroom that they can share. In order to pay for their apartment’s public goods, the roommates all decided to chip in money for the additional utensils. Each person chipped in with $3 that will go towards buying an additional utensil for the public spaces. This amount of money is the value that roommates place individually on an additional utensil, which goes to the marginal utility of using the utensil. Assuming the equation for the cost of the amount they use the utensils is C(G)=G^2, we take the first derivative of the equation and get the marginal cost of 2G. Provided that the equation for MRS1+MRS2+MRS3+MRS4=Marginal Cost, where MRS1 is equal to the marginal utility (MU) of using the utensils divided by marginal utility of using other goods except for utensils for person 1. The same logic is applied to MRS2 which is the MU of using the utensils divided by MU of using other goods except for utensils for person 2. Similarly, MRS3 is the MU of using the utensils divided by MU of using other goods except for utensils for person 3, and MRS4 is the MU of using the utensils divided by MU of using other goods except for utensil for person 4. Since income has been spent on only one good (e.g., utensils) and the MU of using other goods except for utensils is 1, the sum of marginal utility of each person equals to the marginal cost. Therefore, the sum of the total marginal utility equals the marginal cost. This makes sense in this case when finding out the pareto efficiency level because if the sum of MU of the four students is greater than the marginal cost of buying an additional plate, then the students will keep buying the utensils. Thus, making the equation sum of MU=MC allows us to find the pareto efficiency level of the number of utensils to be bought. Since the MU for each person is $3, the total marginal rate of substitution for these four women is 3*4=2G. Solving the equation, we get  G=6. Therefore, the Pareto efficiency of the number of utensils is 6.

Similarly, this example can apply to the purchasing of additional ceramic plates. Each person chipped in $4 for buying the additional plate. Using the same equation as above, the cost of the amount they use the plates is C(G)=G^2 and the marginal cost is still 2G. Marginal cost remains MRS1+MRS2+MRS3+MRS4 and the only thing that changes is that the MRS for each person is now $4. This makes the total marginal rate of substitution 4*4=2G, resulting in G=8. In this scenario, the Pareto efficiency of the number of plates is 8. This is how the Pareto efficiency is calculated for these Buckland residents paying for additional utensils and ceramic plates.

However, sharing public goods do not always work out ideally. Most of the time, having free riders is unavoidable. One possible way to solve this problem among roommates is have all of them take a Microeconomic Theory class and learn how to maximize their utilities by studying the marginal cost equation above.