Question

1. Consider a case where utility of Ali from two goods I, and 2, is given by (21,22) = x1*29. Good 1 has price Pa, good 2's price is P2 and Ali has money m. (6 points) a) What is Ali's marginal utility from consuming good 1, what about good 2? Hint: Take the natural logarithm of Ali's utility function first. (1 point) b) What is Ali's demand function for good 1, what about good 2? (1 point) c) Consider when P = 4, P = 2 and m = 100. How much of each good does Ali consume? (1 point) d) Imagine the price of good 1 decreased from 4 to 2. How much of each good does Ali consume? (1 point) e) What is the compensated income of Ali when the price of good 1 decreased from 4 to 2. (1 point) f) The Slutsky equation states that the change in quantity demanded after a price change can be split into income and substitution effects. What are the values of substitution and income effects when the price of good 1 falls to 2? (1 points)

Answer 1

Ans-1 0.4 0.6 u(x1, x2 ) = xi x2 (a) marginal utility from good-1 mua du = 0.4x ar -0.6 0o6 muxl = 0.4/X2 , Oof merginal Utility from gool-2 muxa = do = ooo o 2004 MUX2 = 0.6 (24)004 dar (b) equlibrium condition. for demand function MRS = b MUXI Y) 0202 munca pe 04 (22/06 ay ( ) 04 - 0.4 x 20.6 0.6 0.6 x 0.4 x 20.4

of ooh X2 4 X2 6 2,004,0.6 2 6 4Х2. 6X1 = 4X2 = 6 piaci = X2 = 6 pisci pr = x2 = 3 Pixi 2 p2 From Budget constraint http. z = m kiai + b ( 2 box) = bixir 3 bixi =m M 2 pixi + 3 bix = m. 2 -) 4 5 bixi = 2m 2m 5p

3 bi xi Z p2 - () x2 = 3m b = 4, P2= 2 m =100 X₂ = 3 592 = 3 (100) 5(2) = 300 = 30 To (dj. when price of good. I decreased from h To 2. Then x 2m = 2(100) = 200 = 20 New 5 P 5(2) 10 X₂ = 3m = 30 Bundle (20, 30) 5b2 I e in order to consume brevious Bundle (10,30) at new Prices (6,= 2, k2=2)

The income needed is 10 (20) + 30 (2) = fo Compensated income of Ali (100-80) = 20 Substitution effect. where m=80 p =2 x = 80 2m' skil 2180) 5(2) = 160 = 16 10 Substitutio effect xi- x = (6-10 = 6 units, Income effect x New x = 20-16= 4 units PE = SETIE 10 = 6 tu
if you like the work please appreciate thank you !