The Model
Let's imagine there are only three people living in California, but that each of them have preferences described by the following utility function:
u(x1, x2) = x1^1/10 x2^9/10
In that function, x1 is the quantity of water consumed, and x2 is the quantity of the composite good consumed (where the 'composite good' represents 'all other goods').
Details
The three people in our model all have the same preferences, but each has a different income. One of them has an income of $100, another an income of $1,000, and the third has an income of $10,000. The price of water1 is $1 and the price of the composite good is $1. The State of California must reduce the total consumption of water to 300 units.
Derive each of the consumer's demand functions for water without any taxes or rebates: x1(p)
2. Derive the total market demand for water without any taxes or rebates: X^1(p)
3. Determine the total amount of water consumed in this market.
4. Calculate the quantities consumed for each individual consumer without any taxes or rebates.
5. Calculate the level of utility consumed for each individual consumer at these quantities.