Question 1: Suppose there are 90 consumers in the market with two goods x and y. There are two types of individuals A and B. 60 of the consumers are type A and the 30 of them are type B. Type A consumers have a utility function of u(x,y)=x 1/3
y 1/3
and each of them has an income of m A
​
. Type B consumers have a utility function of u(x,y)=x 2/3
y 1/3
and each of them has an income of m B
​
. 1. Find the individual demand for type A for good x and y as a function of m A
​
,p x
​
, and p y
​
. 2. Find the individual demand for type B for good x and y as a function of m B
​
,p x
​
, and p y
​
. 3. Find the market demand for good x as a function of incomes and prices. 4. Find the market demand for good y as a function of incomes and prices. 5. Suppose price of good x is 2 and the price good y is 2. Further suppose m A
​
=60 and m B
​
=120. Find the market demand for good x and good y at the given prices and incomes.