1. (50 points) The demand functions of two goods are: Qi = di + d1P1+ d12 Pz Q2 = dz + d21 P1 + dzz Pz where Of and Q are the quantities demanded of good 1 and good 2, P, and Pz are the respective prices of good 1 and good 2, and dj, dj1, d12, d2, dy and daz are exogenous parameters. Assume that dj > 0, d2 > 0, du 0, $2 > 0, $11 > 0 and $2z > 0. a) (25 points) Using linear (matrix) algebra, derive expressions that show the effects on Pi and Q2 of an increase in a per unit subsidy granted to producers of good 1. b) (25 points) Suppose ($22 - dzz)($1 - du) > d12dzi- Sign the above effects if good 1 and good 2 are: i. Substitutes in consumption ii. Complements in consumption iii. Substitutes in production iv. Complements in production V. Neither substitutes in consumption and production nor complements in consumption and production