Question

7. (10%) In an economy different economic equations are found as follows: 2C+31 + G = 10 C-1+G = a 4C - 1-5G = -8 a. b. (4%) Show that this system has a unique solution without actually solving it. (6%) Suppose (C", 1", G*) is the solution of this system. When the value of a increase, will G* increase or decrease? (Hint: Use Cramer's rule)

Answer 1

236-2-207 3179=10 = (- Itaza de 42--I-5453 de siste and hous ing Lu can sees 10 Now from these three equation wl. Can See o that none of the equation is a trans formation of to any of the three equation rie none of the equation is double or tripple to on any numby multiplicd by the other 1. equation in the systur] Thes, we can inte that the systur has an - tui Unique ss solution . د لدا را از بدان را ا ر اور ز (b) Now to get et, IA, G* We will apply Crammn's rule. Thes, the system of equations can be written in the matriu form as below! 2 3 1 7 re 1 - 1 1 14 -1 -5 P 10 EN Scanned with CamScanner

3 1 d -Now, DINOU C² let - 8 3 do 10 cm - 4 -1 -5 TO(5+1)-3(-52+8) +16--) sp (571) - 31-5-4) +10 +1+4)* 60715a 60+ 150 -24 - & -glu = 12 +27+3 28 7140 (216) 42 R1A) Na 1 2 3 10 l Now Similarly on amilarly I i I a 4 - 1 -81 12,3! My 1 -1 1 1 4 -1 -5 0 2687a)-3.1-8 - Haj +104-1+4) = = 42 pe 16 20 224 + 122-10+ 40 Toi o 42 Scanned with Cam Sean

22 +148 - Git - 0.523.7 0.33 42 Now con can to get the effect of increase in a we derive dat Gamşçanner

Now, dat and -*- 0:33Yo da - This when the value of a increases a * will increase to - We Scanned with CamScanner