Question

Consider a consumer in a two good economy domy whose preferences are rep- resented by the following utility function U(z,y) = x + y a) Find her Marshallian demand functions for good X and good Y , 1.e., x* (Pæ, Py, I) and y* (Pz, Py, 1)? b) Find her Hicksian demand functions for good X and good Y, i.e., x" (Pc, Py, U) and yº(Px; Py, U)? c) Find her indirect utility function, V(Pa, Py, I). d) Find her expenditure function, E(pr. Pu, U).- e) Solve her utility maximization problem for when pz = 1TL, Py = 4TL, and, I = 16TL. f) Solve her expenditure minimization problem for when pr = 1TL, P = 4TL, and, U = 2. g How much do we have to compensate her (in terms of money to keep her at this utility level (2 utils) if py increases to 6T L? h) Compare and contrast her welfare for a 4 TL unit tax on good Y versus a 4 TL tax on income out of 16 TL). Which one is better for the consumer?

Answer 1

As per the HOMEWORKLIB POLICY, answering the first four parts. Please find the answers below:

Page 1 u(x,y) = vor ty a) Budget constraint: xlx + y Py = 1–0 Slope = Px lPy MR Sa, y = MU x = aulax July MR Say Muy = ac at equilibrium, Mrsa, y = Px / Py » Ole Jo = Py = 40 Marshallian DD for a Put a in ean. xPx + yly z I - ( 4 ) 2 Px + y Py = I yPy = (1 - 14h > y = (1-4 ve este Marshallion DD for y. b) Minimizing x Petty Py = I st. ū = te ty at equilibrium, MRSx, y = Belly o valore delle Hicksion DD for x. from constraint, x= (het) Hicksion DD for a u = 5x + y siya ü -*) Hickson DD fry

c) Indirect utility function, UCPxrly, I): Pye 2 So, v (Px, Py, I) = 5x + y* 1 = Yy + I - I Py - Ž x y Pe et e Amy d) Expenditure function, E (perly, o): So, e (Px, Py, I) = Px x* + Pg y* i la (42) + Po da-ei + Pola na Ayo