An aggregate equilibrium market for two goods is represented by the linear model presented in table 1 below, where Q; is the equilibrium quantity obtained by equating demand and supply in the market for good i, and prices are P, i=1,2. Aggregate income, which is exogenous, is denoted Y. The letters a, b, c, d, denote numerical constants. Table 1: Equilibrium model of two markets Market for good 1 2, = 10 + aP, + bP, + Y -2 + 3 P, Market for good 2 2, = 15 + cP, + dP, + Y Demand (la) (2a) %3D Supply (2a) 2, = -1+ 2P, (2b) (a) Use equations (2a) and (2b) to eliminate Q2, giving a single equation in terms of the P, P2, and Y. (b) Express the resultant three equation system in form AX=B where A is a coefficient matrix, Xa vector of the remaining endogenous variables, Q1, P1, and P2, (in that order), and B is a vector of constants and the exogenous variable, Y. Now let a=-2, b=1, c=1, and d=-1. (c) (i) Determine if the inverse of A exists. (ii) Use Cramer's rule to obtain solutions for endogenous variables, Q1, P1, and Pz and hence also obtain a solution for Q2. (iii) Discuss the impact of an increase in income, Y, on the solution for Q, obtained in part (ii) above.