Question

I NEED ANSWER FOR 5-6-7-8-9

Question Kayla's utility depends on her consumption of good 1(Q1) and good 2 (Q2), and it is described by the following utility function: U(Q), Q2 ) = 27 Q7'3 Q3 Deriving Demand functions 1. What are her uncompensated demand functions (Marshallian demand function) for Q1 and Q2? 2. What are her compensated demand functions (Hicksian demand function) for Q1 and Q2? Effects of a price increase (substitution, income, and total effects) Her income is currently $360. Consider that the price of good 1, P, is $10, and the price of good 2, P2, is $40. 3. What is Kayla's optimal bundle of good l and good 2 4. What is her utility level at this optimal bundle found in question 3.8 Consider that the price of good l increases to $16. 5. What is Kayla's optimal bundle of good 1 and good 2 6. What is the level of her utility at this optimal bundle found in question 5.2 7. What is Kayla's substitution effect resulting from the increase in the price of good 1? 8. What is Kayla's income effect resulting from the increase in the price of good 1? 9. What is the Kayla's total effect resulting from the increase in the price of good 1?

Answer 1

Question 1 Ulilily fiction is ! ula, , Q2) = 278,23 224 Now, Marginal Whiliff of gode mu, = Qu(Q1,92% 27 (5) Q 3Q23 sar. 18 Q1-13 QuYS and marginal Whility of good 2 2 Q2 Muz = 20 (Q1, Q) = 27 (13) Q 2/Q2 ² 399,2/322- 33 Now, when Price of good A in mass to $16 ie pi= $16, P2 = $40 and in core M=9360 Huce budget constraint ist m = P Q1 + P2 Q2 . 2) 360 = 16 217 40Q2 Now atlity Manimesing condition will be MUI - Pil 100-120.43 . qq, 2/02/5 40 MUZ 21 16Q1 = 8092 Q = 5Q2 . ) 1. Q 1=502 in the budgit Now contuairt substituting qet! at Scanned with CamScanner:

OQ - 360=160, + 4002: = 360 = 16 x S Q2 + 4002 :52 360 = 80Q2t 4.0Q2 = 360 - 80 120Q2 =360 Q2 = 3 . =) and as Q1 = 502 = 5x3 =15 those op final bundle of good 1 and 2 will be - Q1 = 15 and Q2 = 3 . 62 lence of utility at Q, = 15 and Q2 =3 will be U= 27 Q1 2/Q24 = US 87.(15) 43 13)/3 = 236.95 utils 7 when P, = $ 10 and R = $40, initially Wility manimising condition will be : 21807²Q -) qQ, 2/3 Q2 = 2² 3) 2 Q2- ) Q1 = 8 Q2 Qi Now & budg it construint m= P, Q, TP2Q2 : -) 360= 1001 +40 02 Now, substituting Qi=802 is the budget construint 1 360= 10 (8Q2) + 40Q2. ... =) 360= 10 Q2 =) Q2 =3 ! هه و دما CS Ased Q1 = 892 = (8X3) - 24

Huice, initial consumption bo bundle is (Q1, Q2) - (24,3) Whu Po increases to $16, final consumption bulle is (0,,Qz) = (15,3). Now, we have to find the decomposition bulle which is ! D on the iritial in dit tunce cure 2) Tangent to a budget line with its slope equal to the final budget line. Now to find the utility on the original i distance cmuc, we substitute the initial consumption budle (Q1, Q2) = ( 24,3) in the chility fuction. Ance U = 270,20 432 27 (24) (3)3 ) . 27 Q 2/3 Q2 = 324 :-) Q, 2/3 Q2/3 = 12 -17 Now the tangency condition requires; 1 . slope of in distance cauc= slope of new budg it live 180 / Q2" 1 9 Q, 2/3 Q₂ 2½ 40 : 2Q2 = 16 1.80 Q2 = 16Q1 CS Scanned with the Q1 = 5Q2 ** Qz3 = 16 s2 40 ) CamScanner

Now Substituting Q1 = 502 is the equation i) weat Q , 2/3 Q2 /3 =12 = 12 =) (562) 3/3 Q2/ 212:9292 = 12 =) Q22 .1 and as, Q1 = 502 = ($ 4,1) = 20.5. Huice the decon position bulle is (Q,,Q2) = (2015, 4.1) Hace we can write the f. initial budle, the final budle and the decomposition budle as follows: Initial buelle final bundle Decomposition Bulle Q,= 24 ....- Q, = 15 ६, २015 Q2 = 3 Q2 = 3 Q2 = 4,1 I now the substitution effect for good is is the decomposition budle mines the initial buelle. = 120.5-24) = -3,5 Hnce as price of good 1 in reass, eo Kayla buys 7 3,5 lits less mit of good l due to the 1 Substitution effect. 8 . Now the incore effect is for good 1 is final bulle mines the decomposition bulle i = (15 - 2015) - - 5.5 f Hrice as price of good 1 în creans, Kayla will 1 ful poores and will buy 5.5 be less nits of Csgis dred a due to the in cone effect. y CamScanner

1 9 Hence totul effect for good 1 resulting from the increase in pice of good 1 is = ( final bundle Initial budle) = (15-24) = q mits Hince due to lineant in PA, kay la buys a less units of good 1. This is a Bes thats substitution effect for Kayla bys 3.5 less mits of good 1 and due to the in cone effect for which Kayla bugs 5is less hits of good 1. to due This is ood 1. as Scanned with CamScanner