Question

Bundes preferences are given by the utility function u(x1+x2)=x1+x2. Suppose p2=3 and m=24. Show all working and plot this consumers PCC when p1 drops continuously from 6 to 2.

Answer 1

u = x1 + x2

For a linear utility function, x1 and x2 are perfect substitutes and indifference curves are linear touching both axes. Utility is maximized at one of the corner points.

(a) When p1 = 6,

Budget line: 24 = 6x1 + 3x2

When x1 = 0, x2 = 24/3 = 8 and Utility = 0 + 8 = 8

When x2 = 0, x1 = 24/6 = 4 and Utility = 4 + 0 = 4

Since utility is higher when x1 = 0 and x2 = 8, this is the optimal bundle.

(b) When p1 = 2,

Budget line: 24 = 2x1 + 3x2

When x1 = 0, x2 = 24/3 = 8 and Utility = 0 + 8 = 8

When x2 = 0, x1 = 24/2 = 12 and Utility = 12 + 0 = 12

Since utility is higher when x1 = 12 and x2 = 0, this is the optimal bundle.

(c) Therefore, when p1 = 6, x1 = 0 and when p1 = 2, x1 = 12. The PCC for good x1 is drawn as follows. For perfect substitutes, PCC for good x1 is identical to the indifference curve.