He substitution effect and income effect of a price increase for an inferior good



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The substitution effect and income effect of a price increase for an inferior good.



C


A



sub


U1

B


inc

B1


B3

total

U2

B2


x3 x3 x1

The price of x increases causing the budget line to shift from B1 to B2. The consumer changes his consumption from the bundle of x and y represented by point A to the bundle represented by point B. The movement from A to B represents the total effect of the price change. Consumption of x goes down from x1 to x2 for two reasons. The substitution effect occurs because x is now more expensive relative to y (B2 is steeper than B1). The income effect of the price change occurs because real income (I/Px) has decreased. B is on a lower indifference curve than A. The total effect is the substitution effect plus the income effect.



To separate the substitution effect from the total effect, first draw a new budget line, B3. B3 is parallel to B2 because it represents the higher price for x. It must be tangent to the original indifference curve U1. In the graph above this is point C. Point C shows us how much x the consumer would buy if the price of x were increased and at the same time he was given more income so that he was no worse off than he was before the price went up. The movement from A to C is the substitution effect. The income effect is what is left when the substitution effect (A to C) is subtracted from the total effect (A to B), which is B to C in the graph above. X is an inferior good because when then the budget line shifts from B3 to B2 (income decreases), consumption of X increases from x3 to x2. The demand for x is downward sloping because when price increases consumption of x goes down from x1 to x2.


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