Lesson Topics - Pepperdine Universityseaver-faculty.pepperdine.edu/jburke2/ba445/PowerP1/ReviewA_6.pdf · combine substitution and income effects of a price ... increased purchasing

A.6 Manipulating Others Review Questions

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Lesson Topics

Consumer Optimum is when a consumer maximizes happiness over his budget constraint on time and money. — So, customers optimize purchases and workers optimize leisure and work. Gross Substitutes and Complements (1) combine substitution and income effects of a price increase for one good on demand for another good. — So, they explain the affect of higher-priced housing on cars. Buy 1 Get 1 Free (2) indirectly affect consumer optimum choices by manipulating their budget sets. — So, firms can manipulate customers to buy more. Quantity Discounts (5) manipulate customers’ budget sets. — So, firms can manipulate customers to spend more while receiving less quantity.

Overtime Wages (6) manipulate workers’ budget sets. — So, firms can manipulate workers to receive less income while working more hours.


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Gross Substitutes and Complements Question. Suppose Alfred and Bart are originally paid $10 per hour at In N Out, and they originally choose to each work 8 hours per day. Explain how a wage increase to $11per hour could make Alfred choose to increase work hours per day, but could make Bart choose to decrease work hours per day. Your explanation should include substitution and income effects.


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Answer to Question: Any wage increase causes both a substitution effect and an income effect. The substitution effect will decrease the amount of leisure consumed by each worker (increase the amount of labor supplied). The income effect of higher wages is, first, increased purchasing power, which will increase the amount of leisure consumed by each worker (decrease the amount of labor supplied), assuming leisure is a normal good. Therefore, Alfred will choose to increase work hours per day if his substitution effect is larger than his income effect. But Bart will choose to decrease work hours per day if his substitution effect is smaller than his income effect.


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Buy 1 Get 1 Free Question: Citgo Petroleum Corporation’s frequent filler program awards 2 free gallons of gasoline after the purchase of 10 gallons. A gallon costs $3.00.

Given that information, evaluate the following statement: Citgo would have the same effect on demand by eliminating their frequent filler programs and simply lowering the gas prices to $2.50. Tip: Be sure to draw the appropriate budget lines and indifference curves as part of your answer.


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Answer to Question: The statement is false. The frequent filler program is a "buy 10 gallons, get 2 free" deal. In the graph below, the buy X = 10 units and get 2 free is the black budget line; the price reduction is the red budget line. The two budget lines intersect at 12 units of good X because

the cost of 12 units of good X is $30 under either budget line .

Specifically, under buy X = 10 units and get 2 free, the consumer gets 12 units of good X by buying 10 units at $3.00 each, and under the price reduction, the consumer gets 12 units by buying 12 units at $2.50 each. Finally, the statement in question assets that the two alternative deals result in the same optimal consumption for each individual in the economy, regardless of their indifference curves. In particular, given the indifference curves drawn in the graph below, the optimal consumption of good X is 12

under the buy 10 get 2 free budget line, which is more than the optimal

consumption of good X under the price reduction


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Optimal consumption under price reduction

Optimal consumption under buy 10 get 2 free

10 12

30 drop


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Buy 1 Get 1 Free Question. Use indifference curve and constraint analysis to show how American Airlines can get customers to fly more often (consume more flights) through a Buy X Get Y free deal than if American charged a uniform price for all flights. To begin analysis, divide all consumption into two categories: flights and “all other goods”. Suppose “all other goods” cost $1 per unit. Consider a typical customer and a typical 2,000-mile round-trip flight. Consider two alternative potential deals offered by American:

• $240 for each round-trip flight. • $270 for each round-trip flight, but after buying 8 round-trip flights,

you get one free round-trip flight. Given that information, graph the budget constraints for each potential deal. Then, draw indifference curves so that under the second deal ($270 for each round-trip flight, but after buying 8 round-trip flights, you get one free round-trip flight) the consumer chooses more flights. Tip: Draw budget sets as part of your answer, and label essential points.


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Answer to Question: In the graph below, the buy X = 8 units and get 1 free is the black budget line; the price reduction is the red budget line. The

two budget lines intersect at 9 units of good X because the cost of 9 units

of good X is $2160 under either budget line . Specifically, under buy X =

8 units and get 1 free, the consumer gets 9 units of good X by buying 8 units at $270 each, and under the price reduction, the consumer gets 9 units by buying 9 units at $240 each. Finally, given the indifference curves drawn, the optimal consumption of good X is 9 under the buy 8 get 1 free

budget line, which is more than the optimal consumption of good X under

the price reduction .

Optimal consumption under price reduction

Optimal consumption under buy 8 get 1 free

8 9

2160 drop


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Quantity Discounts Question. To encourage energy conservation, many public utility companies charge consumers a higher rate on units of electricity consumed in excess of some threshold amount. In contrast, a common marketing ploy by other firms is to offer "quantity discounts" to consumers who purchase large quantities of a good. To illustrate how these pricing schemes affect consumers, suppose income = $12, the price of the one good is PX = $3, and the price of the other good is PY = $4. Draw the budget constraint.

Keeping the same income and PY, now suppose PX = $3 for each unit of X up to 2 units, but PX = $6 for each unit of Good X beyond 2 units. Draw the new budget constraint. Use indifference curves to show how the consumer might decrease consumption of Good X because of that change in the budget constraint.

Keeping the same income and PY, now suppose PX = $3 for each unit of X up to 2 units, but PX = $1 for each unit of X beyond 2 units. Draw the new budget constraint. Use indifference curves to show how the consumer might increase consumption of Good X because of that change in the budget constraint.

Tip: Label the points where the budget constraints intersect the horizontal and the vertical axes.


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Answer to Question: Budget line with price increase. Select indifference curves I and II so that consumption of X decreases as price increases.

Budget line with price decrease. Select indifference curves I and II so that consumption of X increases as price increases.

II

I

X

Y

2 0

1.5

3

4 3

II I

X

Y

2 0

1.5

3

4 8


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Quantity Discounts Question. Not far from Hollywood is a legendary entertainment mecca — Medieval Times’ California Castle. Guests at the Buena Park Castle are treated like nobility and served a royal feast, as the action begins. The show’s stunning battle sequences and authentic medieval jousting tournament offer one thing Hollywood doesn’t: the thrill of live action. To increase repeat business, Medieval Times has a loyalty club. Each of the first two visits in a year cost $50, but any visits after those two cost only $20. Suppose a typical customer has $600 to spend per year on all goods. Draw and label the budget set if there were no loyalty club. Now consider the loyalty club. Draw and label the budget set. Then, determine whether any customer would ever visit Medieval Times exactly two times during the year. Explain your answer.

Tip: Label the points where the budget sets intersect the horizontal and the vertical axes.


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Answer to Question: To simplify, set the price of all other goods to one. Graphically, the budget line without the quantity discount is the red budget line; the quantity discount is the black budget line. The two budget lines intersect at 2 Medieval Times visits and 500 units of all other goods. Under the quantity discount, a consumer will never purchase exactly 2 visits, since at this kink in the budget set the consumer would always be better off by buying more or less visits. In other words, it is impossible to draw a typical indifference curve that is tangent to the budget line at the point (2,500). The indifference curve in the graph would result in the purchase of exactly 2 visits, but it has a kink and so is not typical. (Note: The graph below uses continuous variables.)

Indifference Curve

Medieval times visits per year

All other goods

2 0

500

600

27 12


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Quantity Discounts Question. To encourage energy conservation, many public utility companies charge consumers a higher rate on units of electricity consumed in excess of some threshold amount. In contrast, a common marketing ploy by other firms is to offer "quantity discounts" to consumers who purchase large quantities of a good. To illustrate how these pricing schemes affect consumers, suppose income = $100, PX = $2, and PY = $5. Draw the budget constraint.

Keeping the same income and PY, now suppose PX = $2 for each unit of X up to 40 units, but PX = $3 for each unit of X beyond 40 units. Draw the new budget constraint. Use indifference curves to show how the consumer might decrease consumption because of that change in the budget constraint.

Keeping the same income and PY, now suppose PX = $2 for each unit of X up to 40 units, but PX = $1 for each unit of X beyond 40 units. Draw the new budget constraint. Use indifference curves to show how the consumer might increase consumption because of that change in the budget constraint.



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Answer to Question: Budget line with price increase. Select indifference curves so that consumption of X decreases as price increases.

Budget line with price decrease. Select indifference curves so that consumption of X increases as price decreases.

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20


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Quantity Discounts Question. To encourage energy conservation, many public utility companies charge consumers a higher rate on units of electricity consumed in excess of some threshold amount. In contrast, Medieval Times Dinner Theater offer a discount to consumers who purchase large quantities of a good. Consider how one of those pricing schemes affect Mr. T, who is a typical consumer:

A) First, consider Good X = Electricity, Good Y = All Other Goods, income = $20, PX = $4, and PY = $2. Draw the budget set. Draw an indifference curve for Mr. T. so that he would choose to consume exactly 2 units of Electricity.

B) Next, keep the indifference curves the same as above and keep income = $20 and PY = $2, but change the price of Good X so that PX = $4 for each unit of X up to 2 units, but PX = $6 for each unit of X beyond 2 units. Draw the new budget set. What can you conclude about the amount of Good X Mr. T. would now choose to consume if he faced that new budget set? Does the consumption of Good X increase? Decrease? Stay the same?



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Answer to Question: A) First, consider Good X = Electricity, Good Y = All Other Goods,

income = $20, PX = $4, and PY = $2. Draw the budget set. Draw an indifference curve for Mr. T. so that he would choose to consume exactly 2 units of Electricity.

In that graph, the intercepts X2 = 5 and Y2 = 10, and consumption X1 = 2 and Y1 = 6.

B) Next, keep the indifference curves the same as above and keep income = $20 and PY = $2, but change the price of Good X so that PX = $4 for each unit of X up to 2 units, but PX = $6 for each unit of X beyond 2 units. Draw the new budget set. What can you conclude about the amount of Good X Mr. T. would now choose to consume if he faced that new budget set? Does the consumption of Good X increase? Decrease? Stay the same?


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In that graph, the intercepts X2 = 4 and Y2 = 10, and consumption X1 = 2 and Y1 = 6. Given the same indifference curve from A), Mr. T. does not change his consumption.


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Quantity Discounts Question: The Great Harvest Bread Company offers their customers quantity (or volume) discounts. Specifically, if a customer consumes 8 or fewer loaves of bread per month, then the price is $4 per loaf. But if a customer consumes more than 8 loaves of bread, then the price is $3 per loaf for each loaf after 8. Graph how that plan affects a consumer’s budget set. Under that plan, will a customer ever consume exactly 8 loaves? Prove your answer.


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Answer to Question: The graph below illustrates a consumer’s budget line when a firm offers a “quantity discount.” A consumer will never purchase exactly 8 loaves of bread, since at this kink in the opportunity set the consumer would always be better off by buying more or less bread. The only way to buy exactly 8 loaves is to have your indifference curves kinked.

The Graph

Budget Line with Quantity Discount

0102030405060708090

100110

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Quantity of Wine

Quantity of Other Goods

of Bread


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Overtime Wages Question. Use indifference curve and constraint analysis to analyze the behavior of employees who are paid an hourly wage rate of $8 per hour, and they choose to work 8 hours per day. Which of the following deals results in more hours worked?

A. An overtime bonus of $4 for every hour worked in excess of eight hours.

B. A bonus of $4 for every hour worked. Explain your answer.

Tip: Clearly state any assumptions about typical employees needed for your conclusions.



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Answer to Question: Overtime induces less leisure, and so more labor. The reason is shown on the graph below: the difference between overtime and a bonus for every hour worked is an income effect (the line through D is paralell to the line through C), which increases leisure (assuming leisure is a normal good).


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Overtime Wages Question. Use indifference curve and constraint analysis to analyze the behavior of typical employees who are paid

A. An hourly wage rate of $4 per hour. B. An hourly wage of $4 per hour, plus an additional overtime bonus of

$4 for every hour worked in excess of eight hours. C. A fixed payment of $40 per day, plus $4 for each hour worked.

Which of the above schemes would you choose to yield the largest number of hours worked? Explain.



Tip: The “fixed payment” is made regardless of the number of hours worked during the day. One example is the employer’s portion of an employee’s medical insurance, or other benefits. To keep this problem simple, do not consider how that payment might change in the future if the employee chooses zero work.


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Answer to Question: Scheme A: An hourly wage rate of $4 per hour. The opportunity set is the triangle in the graph below through $96 on the vertical axis, consumption point A, and 24 on the horizontal axis. Scheme B: A fixed hourly wage of $4 per hour; plus an overtime bonus of $4 for every hour worked in excess of eight hours. The opportunity set in the graph below goes through $160 on the vertical axis, point A, and 24 on the horizontal axis. Scheme C: A fixed payment of $40 per day, plus $4 for each hour worked. The opportunity set in the graph below goes through $136, point C, and 24 on the horizontal axis. Which of the three schemes would yield the largest number of hours worked? Assuming leisure is a normal good, Scheme C yields fewer hours worked than Scheme A since the only difference in the schemes is that C adds income. Between Schemes A and B, if you draw indifference curves as in the graph below, then Scheme A yields more hours worked (less leisure). Alternatively, you can also draw indifference curves so both Schemes A and B yield the same hours worked (the same leisure). And you can draw indifference curves so that Scheme B yields more hours worked. Therefore, choose Scheme A or B but not C for more hours worked. Why can Schemes A and B yield either more or less leisure when the person is in the overtime region? Because in the overtime region (with less than 16 hours of leisure, moving from Scheme A to B (overtime) causes a substitution effect of less leisure because wages are higher, but also causes an income effect of more leisure because purchasing power is higher, assuming leisure is a normal good..


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Comment: If you only consider the case where Scheme A yields 8 hours worked, as in the graph above, you conclude Scheme B yields more hours worked than Scheme A.


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$4 for every hour worked in excess of eight hours. C. A fixed payment of $40 per day, plus $8 for each hour worked.

Label the points that define the budget constraints (that includes, for each budget constraint, labeling where the constraint intersects the vertical axis). Which of the above schemes would you choose to yield the largest number of hours worked? Explain.





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Answer to Question: Scheme A: An hourly wage rate of $8 per hour. The opportunity set is the

triangle in the graph below through $192 on the vertical axis,

consumption point A, and 24 on the horizontal axis .

Scheme B: An hourly wage of $8 per hour, plus an additional overtime bonus of $4 for every hour worked in excess of eight hours. The

opportunity set in the graph goes through $256 on the vertical axis, point

A, and 24 on the horizontal axis .

Scheme C: A fixed payment of $40 per day, plus $8 for each hour worked.

The opportunity set in the graph goes through $232, point C, and 24 on

the horizontal axis .

Which of the three schemes would yield the largest number of hours

worked? Assuming leisure is a normal good, Scheme C yields fewer

hours worked than Scheme A since the only difference in the schemes is

that C adds income. Between Schemes A and B, if you draw indifference curves as in the graph below, then Scheme A yields more hours worked (less leisure). Alternatively, you can also draw indifference curves so both Schemes A and B yield the same hours worked (the same leisure). And you can draw indifference curves so that Scheme B yields more hours

worked. Therefore, choose Scheme A or B but not C for more hours

worked .

Why can Schemes A and B yield either more or less leisure when the person is in the overtime region? Because in the overtime region (with less


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than 16 hours of leisure, moving from Scheme A to B (overtime) causes a substitution effect of less leisure because wages are higher, but also causes an income effect of more leisure because purchasing power is higher, assuming leisure is a normal good.


$256 $232 $192 $96 $76 $64

15 16 17


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$5 for every hour worked in excess of 40 hours per week. C. A fixed payment of $300 per week, plus $10 for each hour worked.

Label the points that define the budget constraints (for example, for each budget constraint, label where the constraint intersects the vertical axis). Which of the above schemes would you choose to yield the largest number of hours worked? Explain.



Tip: The “fixed payment” is made regardless of the number of hours worked during the week. One example is the employer’s portion of an employee’s medical insurance, or other benefits. To keep this problem simple, do not consider how that payment might change in the future if the employee chooses zero work.


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Answer to Question: Scheme A: An hourly wage rate of $10 per hour. The opportunity set is the triangle in the graph below through $10x24x7 = $1680 on the vertical axis, consumption point A, and 24x7 = 168 hrs. (per week) on the horizontal axis. Scheme B: An hourly wage of $10 per hour, plus an additional overtime bonus of $5 for every hour worked in excess of 40 hours per week. The opportunity set in the graph below goes through $256 on the vertical axis, point A, and 24x7 = 168 hrs. (per week) on the horizontal axis. Scheme C: A fixed payment of $300 per week, plus $10 for each hour worked. The opportunity set in the graph below goes through $1980 on the vertical axis, consumption point C, and 24x7 = 168 hrs. (per week) on the horizontal axis. Which of the three schemes would yield the largest number of hours worked? Assuming leisure is a normal good, Scheme C yields fewer hours worked than Scheme A since the only difference in the schemes is that C adds income. Between Schemes A and B, if you draw indifference curves as in the graph below, then Scheme A yields more hours worked (less leisure). Alternatively, you can also draw indifference curves so both Schemes A and B yield the same hours worked (the same leisure). And you can draw indifference curves so that Scheme B yields more hours worked. Therefore, for more hours worked, choose Scheme A or B but not C. Why can Schemes A and B yield either more or less leisure when the person is in the overtime region? Because in the overtime region (with less than 16 hours of leisure, moving from Scheme A to B (overtime) causes a substitution effect of less leisure because wages are higher, but also causes an income effect of more leisure because purchasing power is higher, assuming leisure is a normal good.


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$2320 $1980 $1680 $600 $550 $400

118 128 138 168


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Overtime Wages Question. Use indifference curve and constraint analysis to analyze the behavior of employees who are paid a. An hourly wage rate of $4 per hour. b. A fixed hour wage of $4 per hour, plus an overtime bonus of $4 for every hour worked in excess of eight hours. c. A fixed payment of $40 per day, plus $4 for each hour worked. Which of the above schemes would you choose to yield the largest number of hours worked? Explain.

Tip: Draw opportunity sets and sample indifference curves with leisure on the horizontal axis and income (or All Other Goods) on the vertical axis.



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Answer to Question:

Scheme A: An hourly wage rate of $4 per hour. The opportunity set is the triangle in the graph below through $96 on the vertical axis, consumption point A, and 24 on the horizontal axis. Scheme B: A fixed hour wage of $4 per hour; plus an overtime bonus of $4 for every hour worked in excess of eight hours. The opportunity set in the graph below goes through $160 on the virtical axis, point A, and 24 on the horizontal axis. Scheme C: A fixed salary of $40 per day, plus $4 for each hour worked. The opportunity set in the graph below goes through $136, point C, and 24 on the horizontal axis. Which of the three schemes would yield the largest number of hours worked? Assuming leisure is a normal good, Scheme C yields fewer hours worked than Scheme A since the only difference in the schemes is that C adds income. Between Schemes A and B, if you draw indifference curves as in the graph below, then Scheme A yields more hours worked (less leisure). Alternatively, you can also draw indifference curves so both Schemes A and B yield the same hours worked (the same leisure) . And you can draw indifference curves so that Scheme B yields more hours worked. Therefore, choose Scheme A or B but not C for more hours worked. Why can Schemes A and B yield either more or less leisure when the person is in the overtime region? Because in the overtime region (with less than 16 hours of leisure, moving from Scheme A to B (overtime) causes a substitution effect of less leisure because wages are higher, but also causes an income effect of more leisure because purchasing power is higher.


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Overtime Wages Question. Use indifference curve and constraint analysis to show how Pizza Hut can get employees to work more hours and receive less income than if they offered a uniform wage for all hours worked. To begin analysis, divide all consumption into two categories: leisure and “all other goods”. Suppose “all other goods” cost $1 per unit. (If it makes analysis simpler for you, divide consumption into leisure and food, with the price of food $1 per unit.) Consider a typical customer with 24 hours available each day. Consider two alternative potential employment deals offered by pizza hut:

• Work for $10 for each hour. • Work for $5 for each of the first 8 hours, then $10 for each additional

hour beyond 8. Given that information, graph the budget constraints for each potential deal. (Be sure to label the points where the budget constraints intersect the horizontal and the vertical axes.) Then, draw indifference curves so that under the second deal (work for $5 for each of the first 8 hours, then $10 for each additional hour beyond 8) the employee chooses less leisure and less of “all other goods” than he chooses under the first deal (work for $10 for each hour). What can you conclude about the total hours worked and total income received under the second deal?



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Answer to Question: Graphically, the first deal is the red budget line. That red line intersects the vertical axis at 240 and the horizontal axis at 24. The second deal is the black line segments. Those segments intersect the vertical axis at 200, the horizontal axis at 24 and pass through the bundle (16,40) of 16 hours of leisure and 40 units of all other goods. Finally, given the indifference curves drawn, the optimal consumption of both goods is less under the second deal than they are under the first deal. (Going beyond the original question: That conclusion is true for any indifference curves for which both goods are normal goods and the consumption of leisure is less than 16.) In particular, the total hours worked is greater under the second deal because the consumption of leisure is less, and total income received under the second deal is less because the consumption of all other goods is less.


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Optimal consumption under overtime

All other goods

24

240

200

16

Optimal consumption under uniform wage

40

Leisure hours per day

Documents

Lesson Topics - Pepperdine Universityseaver-faculty.pepperdine.edu/jburke2/ba445/PowerP1/ReviewA_6.pdf · combine substitution and income effects of a price ... increased purchasing