Question

Consider an economy with two goods only. For each part below draw a carefully labeled diagram showing the income and substitution effects for both goods.

(a) The price of good 1 increases and both goods are normal.

(b) The price of good 2 decreases and good 1 is normal while good 2 is inferior.

Answer 1

Solution:

For both the diagrams below, good 1 and good 2 are taken on horizontal and vertical axis, respectively. Further, I denote initial optimal bundle by A, corresponding values by (x1°, x2°), and corresponding indifference curve (IC) by IC°. Similarly, for compensated bundle is denoted by C, values marked as (x1^c, x2^c), and IC denoted by IC^c. Lastly, the final bundles are denoted by B, with values (x1^F, x2^F) and IC marked as IC^F.

Initial budget line and final budget line are marked; the line which appears slightly pink is the compensated income based budget line.

(a) Since price of good 1 increases, new budget line is steeper than before, changing only the horizontal intercept (moving in), with vertical intercept same as old/initial budget line. Since good 1 is normal, price effect would be such that both substitution and income effect move in same direction.

(b) Since price of good 2 falls, new budget line is again steeper, changing only the vertical intercept (moving out), with horizontal intercept same as initial budget line. Since, good 2 is an inferior good, income effect moves in opposite direction to the substitution effect. Also, for this case I have still taken income effect to be less powerful than substitution effect (keeping still a negative relation between price of good 2 and it's consumption) as no such specification of good 2 being a giffen good (that is too inferior) is given.

Following are the required graphs: