Final answer:
The aggregate demand at each price of x can be determined by analyzing the utility function and budget constraint. At a price of $8, the demand is 10 units. At a price of $4, the demand is 20 units. At a price of $2, the demand is 41 units. At a price of $1, the demand is 55 units.
Step-by-step explanation:
The aggregate demand at each price of x can be determined by analyzing the utility function. The utility function U(x, y) = x²/⁵y³/⁵ represents the preferences of Simone and her identical sisters. To find the aggregate demand, we need to determine the quantity that each person will demand at each price of x.
Assuming that the income of Simone and her sisters is $100, we can calculate the budget constraint. Since the price of y is $1, the income can be divided between x and y. For example, if the price of x is $8, Simone and her sisters can afford $100/$9.6 = 10.42 units of x. However, since x must be an integer, they will demand 10 units of x at a price of $8.
Similarly, we can calculate the aggregate demand at each price of x. At a price of $4, Simone and her sisters can afford $100/$4.8 = 20.83 units of x, so they will demand 20 units of x. At a price of $2, they can afford $100/$2.4 = 41.67 units of x, so they will demand 41 units of x. And at a price of $1, they can afford $100/$1.8 = 55.56 units of x, so they will demand 55 units of x.