Question 1 [12 points] Consider the market for a good that has 6 buyers. Each buyer has the same income $I. Let q denote

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Question 1 [12 points] Consider the market for a good that has 6buyers. Each buyer has the
same income $I. Let q denote the amount of the good and m themoney left after buying the
good. Buyers 1,2,3 have the same utility function u1 = 12q − q2+ m. Buyer 4 has the utility
function u4 = 20q − q2 + m. Buyers 5,6 have the same utilityfunction u5 = 28q – q 2 + m. Denote
the price of the good by p.
(a) [4 points] Observe 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 isadequate to purchase its desired
amount of the good at any price p.
For (b)-(c), assume income $I is such that for every buyer, theincome is adequate to purchase its
desired amount of the good at any price p.
(b) [4 points] Solving utility maximization problem, for eachbuyer find the individual demand.
(c) [4 points] Determine the numerical value of the marketdemand Q for price p = 18.