What is the relationship between returns to scale and average cost?

What is the relationship between returns to scale and prot maximizing production plan.

Can you check whether 2 utility functions represent the same preference?

Can you analyze how consumption increases or decreases due to SE and IE, when goods are ordinary, or gien, or normal, or inferior?

Can you calculate optimal utility maximizing bundle for dierent types of preferences (cobb-douglas, perfect complements etc)?

Can you check whether goods gross compliments or gross substitutes if you know utility functions?

Do you know how to calculate optimal output and prices under dierent price discrimination types?