Question

Karla treats Coke (good 1) and Pepsi (good 2) as perfect substitutes, with MRS =-1

1. Write down an utility function that will represent her preferences

2. Derive her demand functions for the following two cases (show your argument graphically):

A. when price of Coke (p1) is greater than price of Pepsi (p2)

B. when price of Pepsi (p2) is greater than price of Coke (p1)

Answer 1

Perfect Substitutes hoods are said to be perfect substitutes if consumer is willing to sacrifice units of one commodity for other commodity at a constant rate &. e M.R.S is constant Now there are two substitute Coke (good I) and Pepsi (good 2). let coke be "x" and Pepsi be da". New Utility Function of lerfect Substitute 0(36,76)) - axi + bx2: Now M.R.S=)-2 Case 1 slope of Indifferrie howe < Slofe of Budget Line ( h > h2 1) 2) M.R.S 2 fi This means that x2 is cheaper than i frefer x2 Over Xo - So consumer will x=0 , x2 * = M where is income hr where - is income

10 Ilz AB.L Cose 2 slope of I (> Sloke of B.L. (R22 R.) M.R.S3 h Consumer will prefer So in this case x, is cheaper than R2 Xa overxz- X, *= M, x2 * = 0 Il ghal ICH