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The substitution effect tells how Quentin would have altered his consumption because the lower rate of return makes future consumption relatively more expensive and present consumption relatively cheaper. The movement from the original choice A to point C shows how Quentin substitutes toward more present consumption and less future consumption in response to the lower interest rate, with no change in utility. The substitution arrows on the horizontal and vertical axes of [link] show the direction of the substitution effect motivation. The substitution effect suggests that, because of the lower interest rate, Quentin should consume more in the present and less in the future.

Quentin also has an income effect motivation. The lower rate of return shifts the budget constraint to the left, which means that Quentin’s utility or “buying power” is reduced. The income effect (assuming normal goods) encourages less of both present and future consumption. The impact of the income effect on reducing present and future consumption in this example is shown with “i” arrows on the horizontal and vertical axis of [link] .

Indifference curve and an intertemporal budget constraint

The graph shows the indifference curve and an intertemporal budget constraint. The x-axis is labeled “present consumption.” The y-axis is labeled “future consumption.” The original choice is A ($6,000, $7,200), at the tangency between the original budget constraint and the original indifference curve Uh. A dashed line is drawn parallel to the new budget set, so that its slope reflects the lower rate of return, but is tangent to the original indifference curve. The movement from A to C which is approximately point ($7,900, $5,000) is the substitution effect. The income effect is the shift from C to B ($7,000, $3,900). The following points are also marked: F ($4,000, $6,500), and D ($6,000, $5,200).
The original choice is A, at the tangency between the original budget constraint and the original indifference curve Uh. The dashed line is drawn parallel to the new budget set, so that its slope reflects the lower rate of return, but is tangent to the original indifference curve. The movement from A to C is the substitution effect: in this case, future consumption has become relatively more expensive, and present consumption has become relatively cheaper. The income effect is the shift from C to B; that is, the reduction in utility or “buying power” that causes a move to a lower indifference curve Ul, but with the relative price the same. It means less present and less future consumption. In the move from A to B, the substitution effect on present consumption is greater than the income effect, so the overall result is more present consumption. Notice that the lower indifference curve could have been drawn tangent to the lower budget constraint point D or point F, depending on personal preferences.

Taking both effects together, the substitution effect is encouraging Quentin toward more present and less future consumption, because present consumption is relatively cheaper, while the income effect is encouraging him to less present and less future consumption, because the lower interest rate is pushing him to a lower level of utility. For Quentin’s personal preferences, the substitution effect is stronger so that, overall, he reacts to the lower rate of return with more present consumption and less savings at choice B. However, other people might have different preferences. They might react to a lower rate of return by choosing the same level of present consumption and savings at choice D, or by choosing less present consumption and more savings at a point like F. For these other sets of preferences, the income effect of a lower rate of return on present consumption would be relatively stronger, while the substitution effect would be relatively weaker.

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Source:  OpenStax, Openstax microeconomics in ten weeks. OpenStax CNX. Sep 03, 2014 Download for free at http://legacy.cnx.org/content/col11703/1.2
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