Question

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) [5 points] 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) [5 points] Solving utility maximization problem, for each buyer find the individual demand. (c) [4 points] Determine the numerical values of the market demand Q for the following prices: (i) p = 9, (ii) p = 13.

Answer 1