Question

Suppose a person has a utility function U(x1,x2)= xa1+xa2, which she maximizes subject to her budget constraint, px1 + qx2 = m, where p, q, m are all positive. Use the Lagrangian method to solve the maximization problem, and find the demand functions for the consumer. Show that the demand functions are homogeneous of degree zero in prices (p, q) and income (m)

(2.5 marks) Suppose a person has a utility function U(x1, x2) = xq +xm, which she maximizes subject to her budget constraint, px1 + qx2 = m, where p, q, m are all positive. Use the Lagrangian method to solve the maximization problem, and find the demand functions for the consumer. Show that the demand functions are homogeneous of degree zero in prices (p, q) and income (m).

Answer 1

pri-qX2) 2= OL x,x+ x2 + dlm- x xd-1 + d(-p) = PL = 23247 + d(-2) 8x2 OL - m - pri- 2x2 put males aos o cos zo xxx-1= xp a neza-1 = 12 m= pritque i7 8 lii (ii2 (iv) from AP & Kidul & Radar da x2 x = X2 x)

put x:= x2(2) in equ cil2 prit qu2 = m P .X2 + q x2 = m P looks .x2 + 2x2 =m x2 + 2(2) x2= X2 + q x2 = m (2) - dit x-1 q = mau 12 =

2 ) = 2 x2= (P) in q (2) T-a tq 1 mp to IP tq X P , a, m ) = 1- x (tp, tq, tm) = tm (AP) It mo ti ta photo T-4 tq

= t' xi (Pr q, m) " x o is in homogeneous of degree prices (P. 92 and income (m) K2 (p, q, m = m qe X2ltp, te, m) = . tml - tmete tº x2(1, 2, m) X2 is homogeneous of degree Prices (1, 2) and income (m). o in