Question

EXERCISE 2 Consider a consumer who consumes two goods and has utility function u(x1, x2) = x, + 1x1 The price of good 2 is 1, the price of good 1 is p, and income is m. Derive the ordinary demand functions of good l and good 2. For what values of p and m is: a. good l normal? b. good 2 normal? c. good 1 an ordinary good? d. good 2 a gross substitute for good 1?

Answer 1

Enercise 2 1012 2 xl -/ considning a consmen who consmens two goods and has Ubility function ů CX, X) = Xz+Vixi uflity of x1, Mula ou axl 4 = 2 and marginal utility of Hz, mu2 = 2004 = 1 NON Price of god 1 ... and price of quod 2 = P2 - and in come = m . hance the budget constaunt will ber M = Pixit P2k2 Hince the utility to maimisation condition will be 2 mu z = 0 / 2 = ²x1-% I =) P2 x 1-1/2 =P =) pa =) 2x, ² pl = P2 = x1½ - P2? 1 2 282 u the budg it constraint 222 - Now substituting ni = P2 2 We gets m. PX1+P2 22 m = PX1+P2 H2 Pi P22+ P2K2 =) m = 2012 222 Scanned with CamScann 122 2P 7

[mment = x2 | 33 mzale med et par Now when Pi= p and P2 = 1 twis ordinay de und for good a and ordinary demand for gode X3 let 3, Xo = cm- ) = 2 - 2P huce ordinay demand for clon' for goods Kiche 1 and 2 = (2pm-1) a Now, in general demand for good Ar =) du har =0 As increase is incore has no effect on demand for good 1, hence god Xi is a sticky good, CS This ned it is not a normal good.

Now in general denard for groda x2 = P2 [m- Paz or xe = (m / - P Now, den in 1270 tuce as, P2=1 I fuce dentar = 1 0 as, da greath other Zuo, hence Xz is a normal good. e) Now demand for good a, x1 = P22 1 20 Now he a Paz (-22,-3) za Part P 3 her ca as Pienneasu dinand for ai falls. The Mi is a normal good. d Now, demand for good a P2 (= 2P12 Scanned with Canowane cross price elsticity betwon good 1 and 2:

xxx2 = 2x te pa Now Xis pare Now do y = 200 m = p m 2 Now substitueting 20 1 l = le 2 jX1 = P2 2 2 2 2 w at, in nX1 X2 wc gut! bodies a lot more than all2 - P22 1 = P2 _ * P2 * 29/12 . = 2 Yo Huce as vade of Ra Ra is positive lie 2 hence in nease in Price of good 2 lúcreases the demand for good 1. Huce, good aa gross substitute for good ai Su CamScanner