Question

Let the national-income model be

Y = C + I0+ G

C = a + b(Y –T0)(a > 0, 0 < b < 1)

G = gY(0 < g < 1)

a. Solve the above national-income model by Crammer’s rule.

b. In your answers in part a, what restriction on the parameters is needed for a solution to exist?

Answer 1

Y ctlota c. a + bct - Te) We first need to rearrange the equchon so that the endogoncow vorables are on the Ltd and the exgenen veriable one on the Rite Y-c- 9= la cobry = a - b To Gogy = 0 We can write this system is matrie form Ax - b Ti -1 -17 17 7 1-6 o c = Igo i La To a-bTo L alalok IAI A) 2 ((1-0) + (-6-0) -1 (0-(-3)) JA), 1 (1) + C 6D-1 (9) Play :) / AJ = 1-b-g

Salve و نهاد . . . . . الد مرد . (ن۔ م) ۔ (ہ ۔ و] - م) (+ (ی -۱) مد لA| ملاحه ل لرحيل الماد To ta-b To + Y* و - 6 -1 I Side for at ہوا۔ 4 ا ا ا ه 4 : لم 1 - -۱-۱۸ د اراده ای - (-) - | ) 8- ملی۔ |ه وآ یا۔ 4 | 3-| | 5 | ال(۲۰ نا۔ ) (3) - ه) 1- (ی - -) :- (ن - Toا - 4) A l | = a-bTu t To bo - 1 (ga-gi To). Ay (د 8- ه) و. دا مل + دا-4 = 14 رويال + (4-1) ا-ه : (ع

1+) a-bru (1-g) + Into Sohre for Gr -Llo7 1 abro 1 A = -6 1A) - 1 a-blo - (-1)-b a-blo + Toob 143), 1 (0-0) + (0-6) (4-670) + Io (0 - 1) (As) = 1 (0) + g(e- 6T) & Tog. Az/ {[=67)+723] G : 1431 G ] g [ca-bo) + 1 If . In order for a solution to exist, 611-6-9 should be positive. I LA for that (bg) should be less than one. - a parameter a should be possive,