1. Consider a competitive market for good 1 in which there are 100 con- sumers, all with the utility function over goods 1 and 2 given by: u(x1, 2) = a ln(x1) + 3In(x2) The price of good 2 is fixed at $10. 25 of the consumers have an income of $20, 50 have an income of $40, and the remaining 25 have an income of $80. Operating in this competitive market for good 1 are two kinds of firms: there are n1 efficient firms each with the cost function c(x1) = 2, and n2 inefficient firms each with the cost function c(x1) = x3 (note that the cost of the inefficient firms is higher than that of the efficient firms) (i) Derive the Marshalian demands for goods 1 and 2. (ii) Calculate the total supply and the total demand for good 1 when its price is p. (iii) Calculate the competitive equilibrium price for good 1. Also compute the equilibrium profit for each type of firm