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An Intertemporal Choice Example

Quentin has saved up $10,000. He is thinking about spending some or all of it on a vacation in the present, and then will save the rest for another big vacation five years from now. Over those five years, he expects to earn a total 80% rate of return. [link] shows Quentin’s budget constraint and his indifference curves between present consumption and future consumption. The highest level of utility that Quentin can achieve at his original intertemporal budget constraint occurs at point A, where he is consuming $6,000, saving $4,000 for the future, and expecting with the accumulated interest to have $7,200 for future consumption (that is, $4,000 in current financial savings plus the 80% rate of return).

However, Quentin has just realized that his expected rate of return was unrealistically high. A more realistic expectation is that over five years he can earn a total return of 30%. In effect, his intertemporal budget constraint has pivoted to the left, so that his original utility-maximizing choice is no longer available. Will Quentin react to the lower rate of return by saving more, or less, or the same amount? Again, the language of substitution and income effects provides a framework for thinking about the motivations behind various choices. The dashed line, which is a graphical tool to separate the substitution and income effect, is carefully inserted with the same slope as the new opportunity set, so that it reflects the changed rate of return, but it is tangent to the original indifference curve, so that it shows no change in utility or “buying power.”

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.

Questions & Answers

what's economic
kamal Reply
Management of money such as saving.
babu
study of how society manage it's scare resources
Maulik
Please help me how to compute national income. what are those included on national income like for an example in W= WAGE what included in wage ?
love Reply
what is competitive market?
Shantal Reply
a compataive market is when there are many producers competating to provide consumers with a goods and services needed
Tanveer
in a compitative market no single producer or consumer can dictate the market
Tanveer
where many buyer and many seller interact for particular good or service, all buyers and sellers have negligible affect on market price.
Maulik
types of demand elasticity
Farouq Reply
What is price elasticity of demand and its degrees. also explain factors determing price elasticity of demand?
Yutansh Reply
Price elasticity of demand (PED) is use to measure the degree of responsiveness of Quantity demanded for a given change on price of the good itself, certis paribus. The formula for PED = percentage change in quantity demanded/ percentage change in price of good A
GOH
its is necessarily negative due to the inverse relationship between price and Quantity demanded. since PED carries a negative sign most of the time, we will usually the absolute value of PED by dropping the negative sign.
GOH
PED > 1 means that the demand of the good is price elasticity and for a given increase in price there will be a more then proportionate decrease in quantity demanded.
GOH
PED < 1 means that the demand of the good is price inelasticity and for a given increase in price there will be a less then proportionate decrease in quantity demanded.
GOH
The factors that affects PES are: Avaliablilty of close substitutes, proportion of income spent on the good, Degree of necessity, Addiction and Time.
GOH
Calculate price elasticity of demand and comment on the shape of the demand curve of a good ,when its price rises by 20 percentage, quantity demanded falls from 150 units to 120 units.
Helen Reply
5 %fall in price of good x leads to a 10 % rise in its quantity demanded. A 20 % rise in price of good y leads to do a 10 % fall in its quantity demanded. calculate price elasticity of demand of good x and good y. Out of the two goods which one is more elastic.
Helen
what is labor
Grace Reply
labor is any physical or mental effort that helps in the production of goods and services
Kwabena
what is profit maximizing level of out put for above hypothetical firm TC = Q3 - 21Q2 + 600 + 1800 P = 600 MC = 3Q2 - 42Q + 600
Sosna Reply
consider two goods X and Y. When the price of Y changes from 10 to 20. The quantity demanded of X changes from 40 to 35. Calculate cross elasticity of demand for X.
Sosna
sorry it the mistake answer it is question
Sosna
consider two goods X and Y. When the price of Y changes from 10 to 20. The quantity demanded of X changes from 40 to 35. Calculate cross elasticity of demand for X.
Sosna
The formula for calculation income elasticity of demand is the percent change in quantity demanded divided by the percent change in income.
Sosna
what is labor productivity
Lizzy Reply
if the demand function is q=25-4p+p² 1.find elasticity of demand at the point p=5?
Puja Reply
what are some of the difference between monopoly and perfect competition market
Obeng Reply
n a perfectly competitive market, price equals marginal cost and firms earn an economic profit of zero. In a monopoly, the price is set above marginal cost and the firm earns a positive economic profit. Perfect competition produces an equilibrium in which the price and quantity of a good is economic
Naima
what are some characteristics of monopoly market
Obeng Reply
explicit cost is seen as a total experiences in the business or the salary (wages) that a firm pay to employee.
Idagu Reply
what is price elasticity
Fosua
...
krishna
it is the degree of responsiveness to a percentage change in the price of the commodity
Obeng
economics is known to be the field
John Reply
what is monopoly
Peter Reply
what is taxation
Peter
is the compulsory transfer of wealth from the private sector to the public sector
Jonna
Equilibrium price is a stable price and it must stay.discuss
Elvis Reply
Card 14 / 21: What are the similarities between a consumer’s budget constraint and society’s production possibilities frontier, not just graphically but analytically?
Ali Reply

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Source:  OpenStax, Principles of macroeconomics for ap® courses. OpenStax CNX. Aug 24, 2015 Download for free at http://legacy.cnx.org/content/col11864/1.2
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