Cindy consumes goods x and y. Her demand for x is given by x(Px, m) = 0.05m - 5.

Question

Cindy consumes goods x and y. Her demand for x is given by x(Px, m) = 0.05m - 5.15Px. Now her income is 419, the price of x is 3, and the price of y is 1. If the price of x rises to 4 and if we denote the income effect on her demand for x by DI and the substitution effect on her demand for x by DS, then: (please show work or explain. i already have the answer, just don't know how to get it)

(a) DI = -0.28 and DS = -0.52.

(b) DI = -0.28 and DS = -4.88.

(c) DI = -0.52 and DS = -0.52.

(d) DI = 0 and DS = -2.00.

(e) None of the above.

Explanation / Answer

DS = -5.15* Q average/P average

P average = (3+4)/2 =$3.5

and Q at Px =3 = 0.05*419-5.15*3 =5.5

and Q at Px =4 = 0.05*419-5.15*4 =0.35

so Q average = (5.5+0.35)/2 =2.925

=> DS =-5.15*2.925/3.5

= -4.88

and DI = -0.05* I/Q average

=-0.28

ans : (b) DI = -0.28 and DS = -4.88.

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