question 1 consider the market for a good that has 8 buyers each havin

Question

Question 1 Consider the market for a good that has 8 buyers, each having income $200. Let q
denote the amount of the good and the money left after buying the good. Buyers 1,2,3 have the
same utility function -q-q²+m. Buyers 4,5 have the same utility function a4-74-q² + m.
Buyers 6,7,8 have the same utility function us-10g-q²+m. Denote the price of the good by p.
(a) [5 points] Show that regardless of the price of the good, each buyer can always attain a utility
of at least 200.
(b) [7 points] Solving utility maximization problem, for each buyer find the individual demand.
(c) [3 points] Find the numerical value of the market demand when price p = 5.
(d) [3 points] For price p = 5, determine how much money is left with buyer 3 after buying the
good.
(e) [3 points] For price p-5, determine how much money is left with buyer 8 after buying the
good.