Consider the market for a good that has 7 buyers. Each buyer has the same income $I. Let q denote the amount of the good and m the money left after buying the good. Buyers 1,2 have the same utility function u1 = 8q − q 2 + m. Buyers 3,4,5 have the same utility function u3 = 10q − q 2 + m. Buyers 6,7 have the same utility function u6 = 16q − q 2 + m. Denote the price of the good by p. 

(a) Note that each buyer has the same income $I. Determine I should be at least how large to ensure that for every buyer, the income $I is adequate to purchase its desired amount of the good at any price p. 

For (b)-(c), assume income $I is such that for every buyer, the income is adequate to purchase its desired amount of the good at any price p. 

(b)  Solving utility maximization problem, for each buyer find the individual demand. 

(c) Determine the numerical values of the market demand Q for the following prices: 

(i) p = 9, 

(ii) p = 13.