Question

(8 points) Consider the following two market model Market 1: Q = 20 - P1+2Pz; Qi = 2P1 - 27 Market 2: Q9 = 18 – 2P, +3P; Q:= 2 + 4P, lave where Q' is the demand for good i and Q! is it's supply. Prepresents the price for good i. As you can see the the demand for a good is affected by not only its own price but also by the price of the other good. (a) (2 points) Are the goods in this question substitutes or compliments? Is there way of answering this question using partial derivatives? (HINT: A substitute is a good who's demand increases as the price of the other substitute good increases. A complimentary good is one who's demand falls as the price of the other good falls) b) (2 points) Can you use Cramer's rule to find the inverse demand functions P1 = P (Q1,Q) and P, = P(Q1,Q)? (HINT: Use only the demand functions. Treat Qi and Q as constant terms and solve for P, and P, as functions of the quantities.) -) (4 points) Using the equilibrium condition for markets (Demand=Supply), solve for the equilibrium prices using matrices. Show your all your steps.

Answer 1

a) If the demand for good 1 goes up when the price of! good a goes up them we say that good f is substitute for good 2. In terms of rates of change good 1 is a aubstitute for good 2 if - Ax >0. On the other hand, if the demand for good 1 goes down when frie of gered a goes up then good 1 is a complement to good 2 This means that - Here, l, - Price of gool 1. P₂-11 11 good a.

Market 1:8 - 20-P, + 21, 8-21, -2 Market & ad = 18-212 +3P, 9.5 = 2440 SP perfect subalit sa sod is positive then, they are Isle -=3 70, they are perfect as w P, AP, C91, ) and , = 1, (6,5, 9.) 787 P 4 -20 afy 'R = 20-92 + 3082 I 21, 48 - od A 3P, - 2 = 20-od -3P, +222 = 18-gd - The coofficient Matrix teekes the 0 1 form - S :) -3 2

1 20 The Column verton - of Contents 2 - 6 40-204+ 36 - 29 76-269 1 20- 18-92 18- 9.+3(20.9.4) 2-6 p* 18-9022 +60 -39.978-60,4+39.49) 11 -> Q0-P, +2 P2 = QP,- 2 -> 22= 3P, 9-2/₂ =) 18-2P 2+ 3P, = 27482 => 16 = 4P 2+ 2P2 - 38, 7=> 16 = 66₂-31,

1 20 The Column verton - of Contents 2 - 6 40-204+ 36 - 29 76-269 1 20- 18-92 18- 9.+3(20.9.4) 2-6 p* 18-9022 +60 -39.978-60,4+39.49) 11 -> Q0-P, +2 P2 = QP,- 2 -> 22= 3P, 9-2/₂ =) 18-2P 2+ 3P, = 27482 => 16 = 4P 2+ 2P2 - 38, 7=> 16 = 66₂-31,

82 18+6 ५४ +66_11५.57 २५ २५

Hope this helps you.