Question

1. A. Define Pareto improvement.   Using Vilfredo Pareto’s criteria, how can we confirm that a Pareto improvement has taken place? Give one brief example.

B. Define Pareto efficiency   Using Vilfredo Pareto’s criteria, how can we confirm that we have Pareto efficiency? Give one brief example.

C, D. In Ontario, Canada sales tax is 14%. Personal income taxes also are higher than in the US. Their higher sales tax and income tax funds government guaranteed medical care.   Separately answering as parts C and D, give and explain two different reasons why their medical funding methods are contrary to the objectives of Vilfredo Pareto.   (note: This question asks for Pareto’s reasoning, not your own.)

Answer 1

A. Defination of Pareto improvement

• A Pareto improvement is an improvement to a system when a change in allocation of goods harms no one and benefits at least one person. Pareto improvement is not considered an ideal method to measure improvements because it does not ensure equitable distribution of resources.

Pareto in Practice
Aside from applications in economics, the concept of Pareto improvements can be found in the fields of life sciences and engineering - in any academic discipline where trade-offs are simulated and studied to determine the number and type of reallocation of resource variables necessary to achieve Pareto equilibrium. In the business world, factory managers may run Pareto improvement trials in which, for example,

they reallocate labor resources to try to boost productivity of assembly workers without decreasing productivity of the packing and shipping workers.

Example of Pareto Improvement
Suppose an equal amount of funds are disbursed to two families, one rich and another poor. The funds help lift the latter above the poverty amount but does not make much difference to the overall income of the former. This improvement is an example of Pareto improvement.

Another example of Pareto improvement is the case of two students exchanging lunchboxes. One of the students, who does not like cheeseburger, gives his burger to another student who considers it delicious. Even though one of the students gives away his burger, no one is worse off and both students are satisfied with the trade exchange. This is an example of a Pareto improvement.

B.  Defination of Pareto efficiency

• Pareto efficiency or Pareto optimality is a situation where no individual or preference criterion can be better off without making at least one individual or preference criterion worse off.

The concept is named after Vilfredo Pareto (1848–1923), Italian engineer and economist, who used the concept in his studies of economic efficiency and income distribution. The following three concepts are closely related:

i. Given an initial situation, a Pareto improvement is a new situation where some agents will gain, and no agents will lose.

ii. A situation is called Pareto dominated if it has a Pareto improvement.

iii. A situation is called Pareto optimal or Pareto efficient if no change could lead to improved satisfaction for all parties.

"Pareto optimality" is a formally defined concept used to describe when an allocation is optimal. An allocation is not Pareto optimal if there is an alternative allocation where improvements can be made to at least one participant's well-being without reducing any other participant's well-being. If there is a transfer that satisfies this condition, the reallocation is called a "Pareto improvement". When no further Pareto improvements are possible, the allocation is a "Pareto optimum".

The formal presentation of the concept in an economy is as follows: Consider an economy with {\displaystyle n}n agents and {\displaystyle k}k goods. Then an allocation {\displaystyle \{x_{1},...,x_{n}\}}{\displaystyle \{x_{1},...,x_{n}\}}, where {\displaystyle x_{i}\in \mathbb {R} ^{k}}{\displaystyle x_{i}\in \mathbb {R} ^{k}} for all i, is Pareto optimal if there is no other feasible allocation {\displaystyle \{x_{1}',...,x_{n}'\}}{\displaystyle \{x_{1}',...,x_{n}'\}} such that, for utility function {\displaystyle u_{i}}u_{i} for each agent {\displaystyle i}i, {\displaystyle u_{i}(x_{i}')\geq u_{i}(x_{i})}{\displaystyle u_{i}(x_{i}')\geq u_{i}(x_{i})} for all {\displaystyle i\in \{1,...,n\}}{\displaystyle i\in \{1,...,n\}} with {\displaystyle u_{i}(x_{i}')>u_{i}(x_{i})}{\displaystyle u_{i}(x_{i}')>u_{i}(x_{i})} for some {\displaystyle i}i.[5] Here, in this simple economy, "feasibility" refers to an allocation where the total amount of each good that is allocated sums to no more than the total amount of the good in the economy. In a more complex economy with production, an allocation would consist both of consumption vectors and production vectors, and feasibility would require that the total amount of each consumed good is no greater than the initial endowment plus the amount produced.