ECO204Y5 Lecture Notes - Lecture 6: Utility, Giffen Good, Lagrange Multiplier
Document Summary
Bundle a: utility-max: budget constraint: 9x + 1y = 72. Y = 72 9x: tangency: mrs = (cid:3273)(cid:3274) = (cid:3273)(cid:3274, 72 9x = 9x (y/x) = (9/1) ---> y=9x ---> y = 9(4) = 36. 4 = x: therefore, a: 4x, 36y. Bundle c: utility-max: budget constraint: 4x + 1y = 72. Y = 72 4x: tangency: mrs = (cid:3273)(cid:3274) = (cid:3273)(cid:3274, 72 4x = 4x (y/x) = (4/1) ---> y=4x ---> y = 4(9) = 36. 9 = x: therefore, c: 9x, 36y. X from 4x to 6x, and y fro(cid:373) (cid:1007)6y to (cid:1006)(cid:1008)y. Conclude x is a normal good; if x<4 then it would have been a giffen good. Lagrange multiplier: also calculates utility-max bundles for an individual. Mu: small additional gain when we increase x by one unit in utility: do this by calculating partial deri(cid:448)ati(cid:448)e of a utilit(cid:455) fu(cid:374)(cid:272)tio(cid:374): (cid:454) ---> u? assu(cid:373)i(cid:374)g all other variable constant (py, y, i)
