Unit 6 - Consumption and Savings


The typical measure of economic health and growth is Gross Domestic Product or GDP. GDP is comprised of the current expenditures of four different sectors of the economy:

Of these four sectors, the majority of spending is undertaken by consumers - roughly 70% of total U.S. GDP is comprised of consumption. Understanding consumer behavior is a very important part of economics and business. In this section we will look at the basics of consumer spending and saving. This information will give a foundation for further studies in economics, business or any field that includes rational consumer behavior as part of its curriculum. For example, understanding individual preferences is a fundamental part of public policy decisions in areas such as political science, environmental economics and other areas.

The Consumer Budget Constraint

We begin with a look at a simple model of the behavior of a typical consumer, starting with some basic assumptions that will be modified later.

Our first assumption is that there is only one relevant time period for the consumer: t1. This implies that there is no future and our consumer lives for today.

The importance of this assumption is that there is no need for saving. We save so that we can increase our future consumption. In our model, the consumer spends all the money he or she earns in the current time period

Our consumer never considers leaving an inheritance.

Our second assumption is that the only money available to the consumer is what he or she earns in wages.

There are no other non-wages sources of income such as dividends and interest earned on savings or trust funds.

Let's give our consumer a name - Boomer is a good choice for her. Boomer's budget constraint (also known as a budget line) shows how much that she can consume given:

For an example, assume that we have two goods and two prices: roses have a price = pr and pizza has a price = pp. A rose costs $1 each and a slice of pizza $2. Next we have to give Boomer an income to spend on roses and pizza. Let's assume that she make $200 during the time period under consideration. Using Figure 6-1 as a reference we can derive Boomer's budget constraint. A budget constraint shows the limits of consumption given the consumer's income and the prices of goods.

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To find the limits or end points graphically for Boomer's budget constraint, we take her total income and divide it by the price of each good. Consumed with romance, Point A in the graph shows how many roses Boomer can buy if she spends all of her money on   roses. At Point A, Boomer purchases 200 roses and no pizza. In contrast, Point B located along the horizontal axis shows a point where Boomer spends all of her money on pizza and shows no interest in the delicate roses. Not to worry, Boomer lives in Boulder, Colorado and has tofu and bean sprouts as toppings on her pizza. At Point B, Boomer loads up on 100 slices of pizza and passes on the roses entirely.

If Boomer earns $200 (I) during t1 she can buy a maximum of 200 roses ($200/$1; (I/pr) or 100 slices of pizza ($200/$2; (I/pp). This information gives us the end points along the x and y axis for Boomer's budget constraint.

Connecting the two endpoints gives us Boomer's budget line. The budget line shows the different combinations of roses and pizza that can be consumed for a given level of income.

Boomer likes to combine her pizza and roses and picks some point along her budget constraint; Point U for example. At Point U, Boomer consumes 50 slices of her favorite pizza (spending $100) and uses the other half of her $200 income to balance her life with 100 roses.

Given a budget constraint, there are several points to note. First, consumption amounts that are represented by a point outside the budget constraint are not obtainable given the consumer's present income or the current prices of the goods.

Secondly, consumption amounts that are represented by a point inside Boomer's budget constraint are not rational since they imply that she has not spent all of the money available to her. Boomer will spend all of her income since there is no reason to save given our assumption of only one time period.

Variations in the Consumer's Budget Constraint: price changes

Over time, Boomer's budget constraint will change for two reasons:

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In Figure 6-2 we show the effect on the budget line when we change the price of Pizza, holding the price of Roses constant. If the price of a good decreases then the budget constraint rotates outward along the axis of the good whose price has fallen.

Begin with the original budget line that connects a point along the vertical roses axis with Point B along the horizontal pizza axis. If the price of pizza falls, from $2.00 a slice to $1.00 per slice, and holding income constant at $200, then if all income is devoted to the purchase of pizza, 200 slices of pizza can be purchased at the lower price for pizza. A decrease in the price of pizza is shown graphically by a rotation outward of the budget constraint from Point B to Point B'.

Note the consumption effect of a decrease in the price of pizza, holding rose prices constant: Boomer can buy more of both roses and pizza as shown by a movement from Point U to Point U'. Since the price of pizza has fallen, she can buy more pizza and still have additional money remaining to purchase even more roses.

As previously noted, assume that at the original price of pizza, Boomer buys 50 slices of pizza and 100 roses during period t1. When the price of pizza decreases from $2 a slice to a $1, assume that Boomer increases her pizza consumption to 80 slices. She still has $120 left to buy roses and that she does, increasing her purchases of roses to 120 since rose prices have remained at a $1 each.

Conversely, if we return to our original price for pizza of $2 a slice and then increase the price per slice to $4, the budget line rotates inward. At $4 per slice and holding income constant at $200, only 50 slices of pizza can now be purchased. Under these circumstances, the budget line rotates inward along the horizontal axis from Point B to Point B''.

In both examples of a change in the price of pizza, the price of roses remains constant; the budget line remains anchored along the vertical axis. Roses still go for a $1 each and thus $200 can still buy 200 roses regardless of the price of pizza.

In general, if the price of a good changes, holding the price of the other good constant, then the budget constraint rotates along the axis of the good whose price has changed. However, there can be a time when the prices of both goods change simultaneously for a fixed income. If the prices of both goods change, then the intercepts of the budget constraint change on both axis. For example, if the price of both roses and pizza drop, the budget constraint will shift outward since the consumer can afford more of both goods.

Variations in the Consumer's Budget Constraint: changes in income

Let us examine the case where the prices of both goods remain constant but now income is allowed to vary. Consider two possibilities. The energetic Boomer is rewarded for her fine contributions at the office with a raise. Or perhaps the shiftless and lazy Boomer finds her salary slashed.

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Figure 6-3 shows both possible outcomes. We start with the stable case where Boomer's income is $200 and consumption is at Point U. If her income increases to $300 and the prices of pizza and roses remain constant, there is a parallel outward shift in her budget line. Consumption can rise to a point like U' where our consumer is buying more of both goods. Or if income decreases, the budget line shifts inward and consumption also falls to a point such as U''.

In summary (holding prices constant):

Income Elasticity of Demand

Earlier is the course we looked at the price and income elasticity's of demand. The price elasticity of demand gave us an measure of the responsiveness of the quantity demanded for a good to a change in its price. Holding prices constant, we can use income elasticity to measure how demand for a good responds to a change in income.

Income Elasticity = % change in the demand for a good / % change in income

Income elasticity can have a positive or negative value.

A normal good is a good that we increase our consumption of when income rises and has a positive income elasticity.

If income increases (a (+) change) and consumption also increases (a (+) change), then the income elasticity for a normal good is positive.

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Figure 6-4 illustrates a normal good. When income increases from $200 to $300, the consumer budget constraint shifts outward and the consumer moves from consumption of pizza and roses at Point U to Point U'. Notice that pizza is a normal good. As income increases, pizza purchases increase from P to P'. Roses are also a normal good as rose purchases increase from R to R' when there is an increase in income.

Normal goods are split into two groups:

0 < value of income elasticity < 1.0

value of income elasticity > 1.0

A necessity has a positive income elasticity with a value less than or equal to one. Assume that Earl's income elasticity for books is 0.70. Since this is a positive income elasticity we know that books are a normal good for Earl. If Earl's income rises, he buys more books. The interpretation of the coefficient is as follows:

For every 10% increase in our consumer's income, he will increase his spending on books by 7%. Assume that Earl's income is $10,000 and book spending is $100. If income increases by 10% or $1,000 to $11,000, he will spend an additional $7 on books or $107 in total.

Since Earl increases his spending on books when his income increases, books are a normal good. However, since his income elasticity for books is less than one, books are an income inelastic good for him.

Earl loves to fish. As soon as spring arrives in the mountains, Earl will pack up his station wagon in Glenwood Springs and make the 25 mile drive to the Frying Pan River located just outside Basalt, Colorado. Earl claims that the Frying Pan River Valley is the closest place to heaven that you can find on earth, and it is hard to disagree.

Not surprisingly, Earl's income elasticity of demand for fishing equipment has been estimated to be 1.50 although his wife would argue that number is simply too low. Income elasticity's with a value greater than one indicate that the good is an income elastic good.

In contrast to the normal goods described above, an inferior good is a good that we decrease our consumption of when income rises and has a negative income elasticity.

If income increases (a (+) change) and consumption decreases (a (-) change), then the income elasticity for a normal good is negative.

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Figure 6-5 illustrates the concept of an inferior good, pizza in this example. As the consumer's income increases and the budget line shifts outward, the consumer moves from Point U to a preferred Point U' on the higher budget line. Notice that the level of pizza consumption at Point U is higher than at Point U'. As income increases, pizza consumption falls from P to P'. By definition, less of an inferior good is purchased with an increase in income. You may notice that in the two good model shown here, both goods can not be inferior.

Some common examples of inferior goods that we buy less of when our income rises are:

Deriving a Good's Demand Curve

We can use the information from the consumer's budget constraint to derive the demand curve for a good.

Remember the demand curve shows the relationship between the quantity demanded of a good and the price of the same good. As the price of the good varies the quantity demanded will respond.

fig76.gif (13716 bytes)Using Figure 6-6, we can use the consumer budget constraint to derive her demand for pizza. We return to the case where pizza is a normal good.

In the top part of Figure 6-6, start by holding the price of roses constant and allowing the price of pizza to decrease. Starting with the budget line furthest to the left, pizza consumption is at Point P0.

As the price of pizza falls, the budget constraint rotates outward. The first price decrease leads to an increase in pizza consumption to Point P1. With a further decline in the price of pizza the outward rotation of the budget line takes our consumer to Point P2.

Turning our attention to the lower part of Figure 6-6, we have a graph with the usual labels for a demand curve. The vertical axis represents the price of a good, pizza in this case, and the horizontal axis represents the quantity of pizza purchased.
A demand curve shows the relationship between the price of a good and the quantity demanded for the same good. In the top part and at the initial price of pizza, consumption was at Point P0. Point P0 shows the relationship between a price for pizza and the corresponding consumption of pizza. This gives us a point on the bottom part of the graph labeled Pd0. At Point Pd0, The price of pizza is Pp0. and the amount of pizza consumed is P0.

With the first decrease in the price of pizza, Point P1 is obtained in the top part of the graph and Point Pd1 in the bottom part of the graph. At Point Pd1 in the lower part, consumption is at a level P1 and price is Pp1.

As the price of pizza continues to fall, Point P2 is now attainable in the top part of the graph and Point Pd2 in the bottom part of the graph. At Point Pd2 in the lower part, consumption is at a level P2 and price is Pp2.

As we change the price of pizza (holding the price of roses constant) in the top part of Figure 6-6, we can derive a relationship between the price of pizza and the quantity demanded of pizza in the lower part of Figure 6-6. Connecting the various points derived in the lower part gives us the consumer's demand curve for pizza. As the price of pizza falls, the quantity demanded of pizza increases.

Income and Substitution Effects

When the price of a good changes, the quantity demanded responds for two reasons:

Please note that we are now describing the income effect. Earlier in this unit we covered income elasticity. Income elasticity describes changes in demand when income changes, holding prices constant. The income effect is the result of change in the price of a good, holding income constant.

Assume that the price of a good, gasoline for example, has risen.

Since we will still purchase gas at a higher cost per gallon, we will have less disposable income left after our gas purchase than at the lower price per gallon. This is know as the income effect - the drop in disposable income due to paying a higher price for a good than before the price increase.

For example, start with $100 in your wallet. You buy 10 gallons of gasoline at $1.20 a gallon,spending $12. This leaves $88 to purchase other goods or even more gasoline if needed. However, if to your dismay gas prices had risen to $1.40 per gallon, you would only have $84 left after purchasing 10 gallons.

The income effect describes variations in purchasing power and leads to a change in the consumption of all goods, including the one we are measuring directly, gasoline in this case.

Or if the price of the good falls, the income effect leads to higher amounts of consumption.

With an increase in the price of a good, we seek out substitutes in consumption. If the price of gasoline rises, we may drive less and make more commutes on the bus, rail or bicycle. The substitution effect leads to a decrease in the quantity demanded of a good when its price rises as consumers increase their purchases of substitute goods. We assume that the price of substitutes remains constant.

Of course, if the price of the good we are examining falls, holding other prices constant, the substitution effect leads to greater amounts of consumption of the good that is now relatively cheaper.

As the price of a gasoline rises, our quantity demanded falls because each gallon costs more to purchase, leaving less disposable income to buy the next gallon - the income effect. We also decrease our quantity demanded of gasoline as we seek relatively cheaper substitutes - the substitution effect.

As we have seen, a change in the price of a good results in a change in the slope of the budget line (refer to Figure 6-2). When the price of a good changes, the quantity consumed of the good will respond. The change in consumption of a good can be broken into two parts:

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We can illustrate what we mean by using Figure 6-7. Here is a demand curve for gasoline. Holding income, prices of other goods and everything else constant, we increase the price of gasoline. On the demand curve, the quantity demanded decreases from Q0 to Q1 as the price of gasoline rises. The decrease in quantity demanded, shown by the movement from Point X to Point Y is the sum of the income and substitution effects described here.

Savings

Thus far we have assumed there is only one time period (T1) in our consumer's life. Boomer literally lived for the moment. Now let us expand our analysis to include a future for our adventurous consumer. After a lively upbringing, assume that Boomer has two relevant parts to her life, T1, and T2.

T1 represents Boomer's working years, where she smartly navigates the business world. By the time she reaches time period T2, Boomer has retired completely. Thus T2 represents the post-working years of Boomers life where she lives of her savings from her working days during T1. For simplicity, we assume that the only source of money for Boomer during period T2 is her savings, or the income that she did not spend during T1. In time period T2, Boomer has no other sources of money. There is no Social Security system, no gifts from her fine children nor help from her dubious husband. Furthermore, we assume that the rate of return on her savings is fixed. We could assume that all of Boomer's 401k and other savings has been converted into fixed yield, long-term government bonds.

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Figure 6-8 shows the two time period model graphically in the form of a budget constraint. On the horizontal axis is time period T1, and on the vertical axis, T2. Income not spent during time period T1 is available for spending during T2.

Point A found along the horizontal axis show the limit of Boomer's potential consumption during time period T1. If she wanted or had to, Boomer could spend all of her wages when she earned them. In this case, she would maximize her consumption during period T1 and save nothing. Point A represents the total potential consumption when Boomer spends all of her wages earning during time period T1 of her life. The problem with this outcome is that she has no savings and thus no money for time period T2, and she would have no money to spend on necessities during T2.

Point B in the graph shows the other extreme. If there were some way for Boomer to save all the income that she earning during T1, all of the money would be available for consumption during T2. This point is needed to define the other intercept of the budget constraint.

As noted, Boomer is able to achieve comfortable financial success during her working years and she was never one to take the route of pure hedonism. Boomer wisely chooses Point E along her hypothetical budget constraint. At Point E, consumption during period T1 is shown along the horizontal axis from the origin (Point O) to Point A'. The distance A' to A is savings during time period T1 and Point O to Point A is total wage income during T1.

As we will describe in more detail shortly, the slope of the budget line is determined by the rate of return on savings. At Point E, consumption in time period T2 equals total saving plus the return on savings. Total consumption during T2 equals the vertical distance from Point O to Point B'. Boomer enjoys a comfortable retirement in Silt, Colorado.

Increasing the Rate of Return on Savings

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Figure 6-9 shows what happens if Boomer's wise choice in where she places her savings pays of in an increased rate of return on savings. As the rate of return on savings increases, the budget constraint rotates outward. Assume that the original two-period constraint shown in Figure 6-8 represents the return earned on a conservative investment in government bonds. However, Boomer was fortunate to put some of her savings in the stock market during a bull market. The result for her is a higher rate of return and the rightward rotation of her budget constraint. With the increase in the rate of return on her savings, Boomer certainly felt wealthier. Yet she also had the discipline to maintain her total consumption during time period T1 at the level shown by the distance on the horizontal axis from Point O to Point A.

On the higher budget constraint representing the greater return on savings, Boomer now can reach Point E'. At E', consumption during T1 remains constant at OA', but increases to the distance OB'' during T2. In this case, an increase in the rate of return on savings generates additional money to spend during T2. Alternatively, if a point slightly to the right of E' was chosen it is certainly possible to increase consumption during both periods.

In our one-period model, we used the substitution and income effects to show the total change in quantity demanded along a demand curve when the price of the good changed. For a normal good, the income effect is positive - a decrease in the price of a good results in greater disposable income and an increase in consumption of the same good. As the price of a good decreases, the substitution effect leads to an increase in consumption of the same good. The consumer favors goods that are falling in price relative to fixed price substitutes.

The income and substitution effects can also be used to describe consumer choice between spending and savings when the rate of return on savings rises. As the return on savings increases, the substitution effect leads the consumer to substitute away from current consumption in favor of an increase in savings. The "price" of current consumption has risen and demand for the substitute, savings, increases.

In the two time period model, current consumption is considered to be a "normal" type of good. As a result, with an increase in the rate of return on savings, the consumer will demand more of the normal good, current consumption in this case.

Overall, when there is an increase in the rate of return on savings, the total change in current consumption is the sum of the substitution and income effects. The substitution effect leads to less current consumption and the income effect, more. In reference to Figure 6-9, just where the consumer moves from Point E on her original budget line to a new point on the new budget line depends on the relative strengths of the substitution and income effects.

In summary, most of us hope to live to an age where we no longer need to work. To ensure that we can live with a degree of comfort during our retirement, we attempt to save some of our income during our working years. The need and desire to spend today vs. save for tomorrow is further complicated when the return on investment increases. Our innate substitution effect tugs us in the direction of increased savings and less present consumption since savings is so rewarding - we can see our balances rising and there is a great deal of comfort in knowing that money is available in case it is needed. However, there is also the strong urge to look at faster pace of accumulated savings and give in to the income effect: spend more today as a reward for our savvy at saving.