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6.E: Consumer Choices (Exercises)

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    4083
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    6.1: Consumption Choices

    Self-Check Questions

    Q1

    Jeremy is deeply in love with Jasmine. Jasmine lives where cell phone coverage is poor, so he can either call her on the land-line phone for five cents per minute or he can drive to see her, at a round-trip cost of \(\$2\) in gasoline money. He has a total of \(\$10\) per week to spend on staying in touch. To make his preferred choice, Jeremy uses a handy utilimometer that measures his total utility from personal visits and from phone minutes. Using the values given in Table below, figure out the points on Jeremy’s consumption choice budget constraint (it may be helpful to do a sketch) and identify his utility-maximizing point.

    Round Trips Total Utility Phone Minutes Total Utility
    0    0    0      0
    1  80   20   200
    2 150   40   380
    3 210   60   540
    4 260   80   680
    5 300 100   800
    6 330 120   900
    7 200 140   980
    8 180 160 1040
    9 160 180 1080
    10 140 200 1100

    Q2

    Take Jeremy’s total utility information in Q1, and use the marginal utility approach to confirm the choice of phone minutes and round trips that maximize Jeremy’s utility.

    Review Questions

    Q3

    Who determines how much utility an individual will receive from consuming a good?

    Q4

    Would you expect total utility to rise or fall with additional consumption of a good? Why?

    Q5

    Would you expect marginal utility to rise or fall with additional consumption of a good? Why?

    Q6

    Is it possible for total utility to increase while marginal utility diminishes? Explain.

    Q7

    If people do not have a complete mental picture of total utility for every level of consumption, how can they find their utility-maximizing consumption choice?

    Q8

    What is the rule relating the ratio of marginal utility to prices of two goods at the optimal choice? Explain why, if this rule does not hold, the choice cannot be utility-maximizing.

    Critical Thinking Questions

    Q9

    Think back to a purchase that you made recently. How would you describe your thinking before you made that purchase?

    Q10

    The rules of politics are not always the same as the rules of economics. In discussions of setting budgets for government agencies, there is a strategy called “closing the Washington monument.” When an agency faces the unwelcome prospect of a budget cut, it may decide to close a high-visibility attraction enjoyed by many people (like the Washington monument). Explain in terms of diminishing marginal utility why the Washington monument strategy is so misleading. Hint: If you are really trying to make the best of a budget cut, should you cut the items in your budget with the highest marginal utility or the lowest marginal utility? Does the Washington monument strategy cut the items with the highest marginal utility or the lowest marginal utility?

    Problems

    Q11

    Praxilla, who lived in ancient Greece, derives utility from reading poems and from eating cucumbers. Praxilla gets \(30\) units of marginal utility from her first poem, \(27\) units of marginal utility from her second poem, \(24\) units of marginal utility from her third poem, and so on, with marginal utility declining by three units for each additional poem. Praxilla gets six units of marginal utility for each of her first three cucumbers consumed, five units of marginal utility for each of her next three cucumbers consumed, four units of marginal utility for each of the following three cucumbers consumed, and so on, with marginal utility declining by one for every three cucumbers consumed. A poem costs three bronze coins but a cucumber costs only one bronze coin. Praxilla has \(18\) bronze coins. Sketch Praxilla’s budget set between poems and cucumbers, placing poems on the vertical axis and cucumbers on the horizontal axis. Start off with the choice of zero poems and \(18\) cucumbers, and calculate the changes in marginal utility of moving along the budget line to the next choice of one poem and \(15\) cucumbers. Using this step-by-step process based on marginal utility, create a table and identify Praxilla’s utility-maximizing choice. Compare the marginal utility of the two goods and the relative prices at the optimal choice to see if the expected relationship holds.

    Hint:

    Label the table columns:

    1. Choice
    2. Marginal Gain from More Poems
    3. Marginal Loss from Fewer Cucumbers
    4. Overall Gain or Loss
    5. Is the previous choice optimal?

    Label the table rows:

    1. \(0\) Poems and \(18\) Cucumbers
    2. \(1\) Poem and \(15\) Cucumbers
    3. \(2\) Poems and \(12\) Cucumbers
    4. \(3\) Poems and \(9\) Cucumbers
    5. \(4\) Poems and \(6\) Cucumbers
    6. \(5\) Poems and \(3\) Cucumbers
    7. \(6\) Poems and \(0 \)Cucumbers.

    Solution

    S1

    The rows of the table in the problem do not represent the actual choices available on the budget set; that is, the combinations of round trips and phone minutes that Jeremy can afford with his budget. One of the choices listed in the problem, the six round trips, is not even available on the budget set. If Jeremy has only \(\$10\) to spend and a round trip costs \(\$2\) and phone calls cost \(\$0.05\) per minute, he could spend his entire budget on five round trips but no phone calls or \(200\) minutes of phone calls, but no round trips or any combination of the two in between. It is easy to see all of his budget options with a little algebra. The equation for a budget line is:

    \[Budget = P_{RT}\times Q_{RT} + P_{PC}\times Q_{PC}\]

    where \(P\) and \(Q\) are price and quantity of round trips (\(RT\)) and phone calls (\(PC\)) (per minute). In Jeremy’s case the equation for the budget line is:

    \[\$10 = \$2\times Q_{RT} + \$0.05\times Q_{PC}\\ \frac{\$10}{\$0.05} = \frac{\$2Q_{RT} + \$0.05Q_{PC}}{\$0.05}\\ 200 = 40Q_{RT} + Q_{PC}\\ Q_{PC} = 200 - 40Q_{RT}\]

    If we choose zero through five round trips (column 1), the table below shows how many phone minutes can be afforded with the budget (column 3). The total utility figures are given in the table below.

    Round Trips Total Utility for Trips Phone Minutes Total Utility for Minutes Total Utility
    0     0 200 1100 1100
    1   80 160 1040 1120
    2 150 120   900 1050
    3 210   80   680   890
    4 260   40   380   640
    5 300     0       0   300

    Adding up total utility for round trips and phone minutes at different points on the budget line gives total utility at each point on the budget line. The highest possible utility is at the combination of one trip and \(160\) minutes of phone time, with a total utility of \(1120\).

    S2

    The first step is to use the total utility figures, shown in the table below, to calculate marginal utility, remembering that marginal utility is equal to the change in total utility divided by the change in trips or minutes.

    Round Trips Total Utility Marginal Utility (per trip) Phone Minutes Total Utility Marginal Utility (per minute)
    0     0 - 200 1100 -
    1   80 80 160 1040   60/40 = 1.5
    2 150 70 120 900 140/40 = 3.5
    3 210 60   80 680 220/40 = 5.5
    4 260 50   40 380 300/40 = 7.5
    5 300 40     0     0 380/40 = 9.5

    Note that we cannot directly compare marginal utilities, since the units are trips versus phone minutes. We need a common denominator for comparison, which is price. Dividing \(MU\) by the price, yields columns 4 and 8 in the table below.

    Round Trips Total Utility Marginal Utility (per trip) MU/P Phone Minutes Total Utility Marginal utility (per minute) MU/P
    0 0 - - 200 1100 60/40 = 1.5 1.5/$0.05 = 30
    1   80 80 80/$2 = 40 160 1040 140/40 = 3.5 3.5/$0.05 = 70
    2 150 70 70/$2 = 35 120   900 220/40 = 5.5 5.5/$0.05 = 110
    3 210 60 60/$2 = 30   80   680 300/40 =7.5 7.5/$0.05 = 150
    4 260 50 50/$2 = 25   40   380 380/40 = 9.5 9.5/$0.05 = 190
    5 300 40 40/$2 = 20    0      0 - -

    Start at the bottom of the table where the combination of round trips and phone minutes is (\(5, 0\)). This starting point is arbitrary, but the numbers in this example work best starting from the bottom. Suppose we consider moving to the next point up. At (\(4, 40\)), the marginal utility per dollar spent on a round trip is \(25\). The marginal utility per dollar spent on phone minutes is \(190\).

    Since \(25 < 190\), we are getting much more utility per dollar spent on phone minutes, so let’s choose more of those. At (\(3, 80\)), \(MU/P_{RT}\) is \(30 < 150\) (the \(MU/_{PM}\)), but notice that the difference is narrowing. We keep trading round trips for phone minutes until we get to (\(1, 160\)), which is the best we can do. The \(MU/P\) comparison is as close as it is going to get (\(40\; vs.\; 70\)). Often in the real world, it is not possible to get MU/P exactly equal for both products, so you get as close as you can.

    6.2: How Changes in Income and Prices Affect Consumption Choices

    Self-Check Questions

    Q1

    Explain all the reasons why a decrease in the price of a product would lead to an increase in purchases of the product.

    Q2

    As a college student you work at a part-time job, but your parents also send you a monthly “allowance.” Suppose one month your parents forgot to send the check. Show graphically how your budget constraint is affected. Assuming you only buy normal goods, what would happen to your purchases of goods? 

    Review Questions

    Q3

    As a general rule, is it safe to assume that a change in the price of a good will always have its most significant impact on the quantity demanded of that good, rather than on the quantity demanded of other goods? Explain.

    Q4

    Why does a change in income cause a parallel shift in the budget constraint?

    Critical Thinking Questions

    Q5

    Income effects depend on the income elasticity of demand for each good that you buy. If one of the goods you buy has a negative income elasticity, that is, it is an inferior good, what must be true of the income elasticity of the other good you buy?

    Problems

    Q6

    If a \(10\%\) decrease in the price of one product that you buy causes an \(8\%\) increase in quantity demanded of that product, will another \(10\%\) decrease in the price cause another \(8\%\) increase (no more and no less) in quantity demanded? 

    Solution

    S1

    This is the opposite of the example explained in the text. A decrease in price has a substitution effect and an income effect. The substitution effect says that because the product is cheaper relative to other things the consumer purchases, he or she will tend to buy more of the product (and less of the other things). The income effect says that after the price decline, the consumer could purchase the same goods as before, and still have money left over to purchase more. For both reasons, a decrease in price causes an increase in quantity demanded.

    S2

    This is a negative income effect. Because your parents’ check failed to arrive, your monthly income is less than normal and your budget constraint shifts in toward the origin. If you only buy normal goods, the decrease in your income means you will buy less of every product. 

    6.3: Labor-Leisure Choices

    Self-Check Questions

    Q1

    Siddhartha has \(50\) hours per week to devote to work or leisure. He has been working for \(\$8\) per hour. Based on the information in Table below, calculate his utility-maximizing choice of labor and leisure time.

    Leisure Hours Total Utility from Leisure Work Hours Income Total Utility from Income
    0 0 0 0 0
    10 200 10 80 500
    20 350 20 160 800
    30 450 30 240 1,040
    40 500 40 320 1,240
    50 530 50 400 1,400

    Q2

    In Siddhartha’s problem, calculate marginal utility for income and for leisure. Now, start off at the choice with \(50\) hours of leisure and zero income, and a wage of \(\$8\) per hour, and explain, in terms of marginal utility how Siddhartha could reason his way to the optimal choice, using marginal thinking only. 

    Review Questions

    Q3

    How will a utility-maximizer find the choice of leisure and income that provides the greatest utility?

    Q4

    As a general rule, is it safe to assume that a higher wage will encourage significantly more hours worked for all individuals? Explain.

    Critical Thinking Questions

    Q5

    In the labor-leisure choice model, what is the price of leisure?

    Q6

    Think about the backward-bending part of the labor supply curve. Why would someone work less as a result of a higher wage rate?

    Q7

    What would be the substitution effect and the income effect of a wage increase?

    Q8

    Visit the BLS website and determine if education level, race/ethnicity, or gender appear to impact labor versus leisure choices.

    Solution

    S1

    This problem is straightforward if you remember leisure hours plus work hours are limited to \(50\) hours total. If you reverse the order of the last three columns so that more leisure corresponds to less work and income, you can add up columns two and five to find utility is maximized at \(10\) leisure hours and \(40\) work hours:

    Leisure Hours Total Utility from Leisure Work Hours Income Total Utility from Income Total Utility from Both
    0 0 50 400 1,400 1,400
    10 200 40 320 1,240 1,440
    20 350 30 240 1,040 1,390
    30 450 20 160 800 1,250
    40 500 10 80 500 1,000
    50 530 0 0 0 530

    S2

    Begin from the last table and compute marginal utility from leisure and work:

    Leisure Hours Total Utility from Leisure MU from Leisure Work Hours Income Total Utility from Income MU from Income
    0 0 - 50 400 1,400 160
    10 200 200 40 320 1,240 200
    20 350 150 30 240 1,040 240
    30 450 100 20 160 800 300
    40 500 50 10 80 500 500
    50 530 30 0 0 0 -

    Suppose Sid starts with \(50\) hours of leisure and \(0\) hours of work. As Sid moves up the table, he trades \(10\) hours of leisure for \(10\) hours of work at each step. At (\(40, 10\)), his \(MU_{Leisure} = 50\), which is substantially less than his \(MU_{Income}\) of \(500\). This shortfall signals Sid to keep trading leisure for work/income until at (\(10, 40\)) the marginal utility of both is equal at \(200\). This is the sign that he should stop here, confirming the answer in question 1. 

    6.4: Intertemporal Choices in Financial Capital Markets

    Self-Check Questions

    Q1

    How would an increase in expected income over one’s lifetime affect one’s intertemporal budget constraint? How would it affect one’s consumption/saving decision?

    Q2

    How would a decrease in expected interest rates over one’s working life affect one’s intertemporal budget constraint? How would it affect one’s consumption/saving decision?

    Review Questions

    Q3

    According to the model of intertemporal choice, what are the major factors which determine how much saving an individual will do? What factors might a behavioral economist use to explain savings decisions?

    Q4

    As a general rule, is it safe to assume that a lower interest rate will encourage significantly lower financial savings for all individuals? Explain.

    Critical Thinking Questions

    Q5

    What do you think accounts for the wide range of savings rates in different countries?

    Q6

    What assumptions does the model of intertemporal choice make that are not likely true in the real world and would make the model harder to use in practice?

    Solution

    S1

    An increase in expected income would cause an outward shift in the intertemporal budget constraint. This would likely increase both current consumption and saving, but the answer would depend on one’s time preference, that is, how much one is willing to wait to forgo current consumption. Children are notoriously bad at this, which is to say they might simply consume more, and not save any. Adults, because they think about the future, are generally better at time preference—that is, they are more willing to wait to receive a reward.

    S2

    Lower interest rates would make lending cheaper and saving less rewarding. This would be reflected in a flatter intertemporal budget line, a rotation around the amount of current income. This would likely cause a decrease in saving and an increase in current consumption, though the results for any individual would depend on time preference.