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.

Fig: 1