representative poor person? The citizens of PlanetV cares about two things: the aerobic lessons (A) and bread (B). Each individual utility function in PlanetV is given by the following:
U(A, B) = (A^0.5)(B^0.5) or "A to the power of 1/2" times "B to the power of 1/2"
There are one million rich people and two million poor people in PlanetV. To keep the 2007 election promise, government in PlanetV has decided to provide aerobic lessons as public good. That is, everyone consumes the same amount of aerobic lessons.
Here are some other details:
1. Price of bread is $1 per loaf and the cost to the state of aerobic lessons is $2 per lesson.
2. A rich person's income is $100 while a poor person's income is $50.
3. If A lessons are provided, each individual pays a per-head tax of $2A
(i) Write down the budget constraint for the a representative rich person and a representative poor person.
(ii) Suppose the aerobics lessons are paid for by per-head tax. How many lessons would the rich prefer to have supplied? How many would the poor prefer to have supplied?
(iii) If the outcome is determined by majority rule, how many aerobics lessons will be
provided? How much bread will the rich get and how much bread will the poor get?
(iv) Calculate the utility of rich and the poor by plugging the allocations obtained in (iii).
(v) As it often happens the election promise was reneged and aerobic lessons were
privatized in 2008. No lessons were supplied publicly and no taxes were collected.
Everyone is allowed to buy as many lessons as she likes and as much bread as she likes.
Suppose that the price of bread stays at $1 per loaf and the price of lessons stays at
$2 per lesson. Compute the following in this new environment:
(a) number of aerobic lesson and bread for a rich person;
(b) number of aerobic lessons and bread for a poor person;
(c) utility of the rich and the poor.
(vi) Is privatization Pareto superior to head tax?
sorry, i really have no idea how to do these and really need help
U(A, B) = (A^0.5)(B^0.5) or "A to the power of 1/2" times "B to the power of 1/2"
There are one million rich people and two million poor people in PlanetV. To keep the 2007 election promise, government in PlanetV has decided to provide aerobic lessons as public good. That is, everyone consumes the same amount of aerobic lessons.
Here are some other details:
1. Price of bread is $1 per loaf and the cost to the state of aerobic lessons is $2 per lesson.
2. A rich person's income is $100 while a poor person's income is $50.
3. If A lessons are provided, each individual pays a per-head tax of $2A
(i) Write down the budget constraint for the a representative rich person and a representative poor person.
(ii) Suppose the aerobics lessons are paid for by per-head tax. How many lessons would the rich prefer to have supplied? How many would the poor prefer to have supplied?
(iii) If the outcome is determined by majority rule, how many aerobics lessons will be
provided? How much bread will the rich get and how much bread will the poor get?
(iv) Calculate the utility of rich and the poor by plugging the allocations obtained in (iii).
(v) As it often happens the election promise was reneged and aerobic lessons were
privatized in 2008. No lessons were supplied publicly and no taxes were collected.
Everyone is allowed to buy as many lessons as she likes and as much bread as she likes.
Suppose that the price of bread stays at $1 per loaf and the price of lessons stays at
$2 per lesson. Compute the following in this new environment:
(a) number of aerobic lesson and bread for a rich person;
(b) number of aerobic lessons and bread for a poor person;
(c) utility of the rich and the poor.
(vi) Is privatization Pareto superior to head tax?
sorry, i really have no idea how to do these and really need help