Q1 (30 points) Consider a single-market analysis of welfare (with production). We use the notation q; to denote consumer z's demand for good 1, and q; be firm J's supply of good 1. There are 500 consumers. Let m' be the income of a particular consumer i. The income of the 500 consumers are distributed evenly in (0, 1) The utility of all consumers are the same. For consumer z, his utility is: Vqi + $2i The price of good 1 is denoted by p and that the price of good 2 is normalized to 1. The demand of Good 2 by consumer i is denoted by 2; - Hint: MRS 1 There are 1000 firms producing Good 1 and they are identical. Firm j has a cost function: C,(q,) - 93 * Part a (8 marks) Find q; (the demand of good 1 by consumer 2) in terms of p. ** Part b (8 marks) Find the market demand function of good 1, denoted by D(p) ** Part c (8 marks) Find the supply function for Good 1 for Firm j ** Part d (4 marks) Find the market supply function S(p) ** Part e (4 marks) Find the equilibrium price p