Question

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

1) uca1, 027 = 270213 02 Do = mui = 2713.) 0,3 023 Dot pode - MO2= 270,312023 = 99,123 - 213 MRS = moi - 218 6 3 0 3 90,213 0 2/3 9 Q1 Q2 muz At optimal choice MRS = Pi 02 = (01) ( ) Q2 = (as) ( . ) in budget constraint put post Pz O2 = m hos + 2 or (b) = m 280, + PIQI =m 2 - 3P, Q = am

2m 38 22 = (22) () = 622 (39) La 02 = (2) and O2= m in put or = am utility for 213 213 213 m' v= 29 (39% (+) * m lucu (DP28,013) * (P) I am Elur, M) - (?** 09* Thur, Expenditure fu

using shephard Lemma ) (3) (Mo"cles en een (3) (03 cm 5(87 ON oba (34) (3) ) ne () () 307*13) () (223" - (0)| 3) $ (81) "* 12773 (1272/3 - (0)38 139 (2)

(3) 2 m= 360 - Pi= 10, P2=uo 0i = 2m = 2x360 2m 2x360 3Pi 3x10 OI = 24 Q2 = m 282 = 360 3xvo = 3 Q2 213 Yz (u) = - u= 270 02² 213 27 (3) (24) 27 (3) 213 (0x37'3 = 27 (3223 18993 133'3 = 27(3) (23)3 = 27(32 (27 = 27x6 = 162