Question

Exercises ferences. Consider two of her indifference Assume a consumer has quasilinear preferences. Consi curves, corresponding to u . distance between the two indifference in might be onding to u( 12) = 5 and ( 12) = 10. Show that the ve two indifference curves remains constant, no matter what maneatind variation Animalanti

Answer 1

where v is an quasi- dinear Preferences can be reforesented by quasi- Linear Utility Function U (2, A2) = V(21)+22 Truphis For Example arbitrary function U (21, 22 ) = 5x + X2 and can be any i function It is In this case Utility function is Linear in good X2 and non Linear in good-xc, since it is partly Linear and Partly non-dincar So, it is known as quasi linear Btility function. Son abestiny For Ufor 32Y=8 . Indifference carve for you: Uomo r(81) + X2 = 5 Explicit function of s ] or no Now I Translated x2 = 40-V (au) / 6 Explicit function of a For u=5 x2 = 5- V(21) or da = 5- Pai For u=10 x2 = 10-v(21) or X2 = 10 - Ja

X2 = 5-100 0 I2 = 10-Jan - where CŮ is the indifference equation for utility at equal to 5 and is the indifference equation you uning cquals to lo. So the graph of (ii) is an 5 units above of graph of (?) [easily seen the diffcrcne blo These Two's are 5 ] lo 5 units, 5 units --- - L So, indifference Curves are verticel Toaslate to each Other.no mater what Vaue of a might be I one more thing To Notice is that MRS = 1 is independent of x2. imflies That slope of Ic's will not change it we move from ufword (also True for down wood)