In: Economics
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.
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 (x1c, x2c), and IC denoted by ICc. Lastly, the final bundles are denoted by B, with values (x1F, x2F) and IC marked as ICF.
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: