Question

The utility function of the consumer is ?(?1,?2)=√?1+?2.a) Let ?1=2,?2=20????=24. Calculate the optimal quantity demanded of good 1 and 2. (7 points)b) Let ?1=1,?2=4????=100. Calculate the optimal quantity demanded of good 1 and 2. (6 points)c) Let ?1=1,?2=4and ?=4. Compared to point b), by how much would the consumer decrease the quantity demanded of good 1 and good 2? (7 points).

Answer 1

Given; U= 1 + x (a) P2 = 2, P2 = 20 & m= 24. Budget en 2x+ 20%, = 24. At eam condition, MRS= P. 2X 20 sale 20 - 9-25 24-2010 - 2020 - 26 < 0 20 :. Optimal quaudity 5 (41", 2") = (12,0). (b) -- Pi =1, P2= ?4 & m m=100 Budget aan H, + 4% = 100. At egon condition; MRS= Pi P2 1 25x, 4 2. =0-4 86 24 Optimal quandity (20 , x ) = (4,24) 100 - 49 24

(c) P = P2 = 4 &m=4. Budget eg: X, +422=4. At egon condition: MRS= - 4 1 2 4. (2) = my =4. & x = 4-xi 4-4 o ĉo. 4 Optional quality = (x,x)= (4,0) When compared to point (b). Quaudity demaded in goods decreased by o. 2 "n by 24