Question

Find Y* and C*

Y= C+ I+G

C=25+6Y*1/2

I=16

G= 14

Answer 1

$$solution$$

$Y = C + I + G \\ C = 25 + 6Y ^\frac{1}{2} \\ I = 16 \\ G = 14$

$Substituting\ C, I, G\ values :\\Y = 25 + 6Y^\frac{1}{2} + 16 + 14\\Y = 6Y^\frac{1}{2} + 55\\ Y - 55 = 6Y^\frac{1}{2 }\\$

$But\ we \ know\ that :\\Y = (Y ^\frac{1}{2} ) 2 .\\ Let \ Y ^\frac{1}{2} = a, \ and \ we\ can\ rewrite\ above \ in \ the\ following \ way:\\ a ^2 = 55 + 6a \\ a^ 2 − 6a =55$

$using \ the\ quadratic\ formula\ ,we \ should\ be\ able\ to\ find \ that:\\a \ is\ either \ a= 11 \ or\ a= −5. \\This\ allows\ us\ to \ find\ that:\\ Y = 121. \\Note\ that\ a = −5 \ doesn’t \ make\ economic\ sense.\\ Given \ that\ Y = 121, we\ can\ go\ back , \ and\ find \ that\\ C =25+66\\C= 91$