Question

2. Major Barbara Undershaft is a member of the Salvation Army and believes that in order to be in solidarity with poor people, she should subsist on only food and water. Her preferences over food () and water (w) are given by the following utility function: Ulf, w) = min {f, w/2} Let Y denote Major Barbara's total income; let P, denote the price of food; and let Pw denote the price of water. a. In what ratio does Major Barbara like to consume food and water? b. Derive Major Barbara's Marshallian demand functions for food and for water. C. Do her demand functions satisfy the law of demand? d. What is the cross-price elasticity of Major Barbara's demand for water with respect to the price of food?

Answer 1

I major bar bara's atlity function is : u(f, W) = min e fj W/23 here Y= major Barbqa's to stal income Pr = pace of Good Фw: Ru - wwn Now budget constraint will be 1 Y= F PF + WPW as now in general at-lity for thion function for pufect complement will be'r - 0(FW) = min qaf, bw} here a=1 and b= 2 hence major Barbra like to consue bood and wath in 1:2 or i 2: 1 ratio .. condition will be: Now utility manimising fall - 2f - w Scanned with CamScanner

w=2f in the budget Now substituting constraint we gets Y=F Pf t W PW 2) Y=fPpt 2F Pw =) Y = (pf + 2 Pw) F =) Y F (Pfthew . . - 2Y (PF +2°c)? Now as w= 2F = 24 [PF +2Pw] Now Major Boa bra's Masstallian demand for itons for food and watu will be f= Y +2pu) - 2Y (Prt 2pw) and wz de 1. apr - 27 (C) Now. Ficht 2m = Y (84 +20) -- - - Y (PF +2Pw)-220 - Pf+2Pw] = 2y (PF +2Pw)-1 . a pw = - 2y (Prt 2 Pw) 220 and aw Scanned with CamScanner

As of or Lo md gw to hence her apw satisfy law of demand. demand functions y major Bubna's demand for water w= ay CPF + 2Pw)-1 aw - Qy (pp +2 pu) -2 Now, a PE of demand betwan Now, food Gross price- clasacity and wath will be? ӘРЕ substituting aw - - 2y (PF +2PU) 2 and p w=ay (Pf + 2Pw) - we get! Ec= -2y (Pf 72Pw)-2} - Pf 2 y(Pet2Pull . (PF +2PW) LO As Ec Lo, hence Food and wath are Scaputect complements of each other. [cs CamScanner