CAN YOU PLEASE ANSWER BOTH QUESTIONS IN DETAILS

1. Suppose that we have elicited the indifference relation N and the strict prefer- ence relation > from a decisionmaker. Dene the weak preference relation >_- given relations N and >. That is, reconstruct the decision-maker's weak pref- erence statements from the decision-makers indifference and strict preference statements. 2. Are simple rules of thumb necessarily irrational? Consider a consumer who loves fried chicken. When the consumer enters a fried chicken restaurant, she does not look at the menu or worry about prices. She decides how many pieces of fried chicken to order depending on how hungry she is. Because eating fried chicken makes her thirsty} she also orders something to drink: her simple rule is to order one beverage for every three pieces of fried chicken that she orders. (a) Suppose that the unit price of fried chicken is pk, that the unit price of beverages is pd. Suppose that the consumer is hungry enough to eat K units of fried chicken on some particular day. What is the budget set B over fried chicken and beverages that an econometrician would infer that the consumer faced after observing her behaviour in the restaurant? What would be the acceptable choices 0 (B ) collected by the econometrician on that day? (b) Now suppose that the econometrician observes the consumer's choices in a number of fried chicken restaurants and constructs the corresponding choice structure (3, C ()) Does this choice structure satisfy WARP? (c) Provide a preference relation over fried chicken and beverages that ratio- nalises 0 relative to B