# Chapter 5 Problem 2 by dffhrtcv3

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```									         Chapter 5
Demand: The Benefit Side of the
Market
Even-number Questions
After prices of beans have been reduced, consumption of
beans falls. Why?

A)   The Sub Effect caused people to substitute noodles
and rice for beans.
B)   The Income Effect caused people’s real income to fall,
so they could no longer afford as much food.
C)   The Income Effect caused people’s real income to rise
so they purchased less of what they considered to be
inferior goods.
D)   Demand for beans is price inelastic.
E)   The only possible explanation is that people chose
irrationally.
• (A) is logically wrong.
• Holding real income constant…
• Substitution effect is always driving Qd up when P drops.
Beans have become cheaper, and hence, people will have
more of beans and giving up some of the other goods.

• (B) says Real Income ↓ so Qd ↓.
• Wrong! Price of a good drops, even though the money
income of people has not changed, their Real Income has
increased because of the increase in purchasing power.
• (D) is obviously wrong because even if demand is price
inelastic, Qd would still ↑ when P ↓ -- law of demand!! At
the extreme situation that demand is perfectly price inelastic,
Qd will be unchanged when P ↓.

• (E) In economics, it is a very basic assumption that all people
choose rationally. Hence, (E) is also not the correct answer.
• (C)Now, we know that Sub Effect must have raised Qd for
beans.

• Nevertheless, the final outcome of the price cut is a reduction
in consumption of beans. That must mean Income Effect has
driven down Qd by much.

• Plus, we know that Real Income increases. As a result, we can
conclude that beans are inferior goods (negative Income
Effect)

• Ans: c
Given Jessy’s MU of watching movies and eating out each
month, find the optimal combination of the two if she
spends \$100 every month on these, PM=\$10, PD=\$20.

Movies   MUM   Dinners   MUD
A)   4 movies, 3 dinners      1      60      1       150
B)   2 movies, 4 dinners      2      50      2       140

C)   6 movies, 2 dinners      3      20      3       120
4       5      4       100
D)   4 movies, 0 dinners
E)   0 movies, 8 dinners
• A bundle is optimal when the Rational Spending Rule is
followed. MU per dollar is the same for each good
MUM MUD

PM      PD

• Calculate MU/P for each unit of Movie and Dinner, then find
the optimal bundle by matching the ratios.
Movies   MUM     MUM/PM     Dinners    MUD     MUD/PD
1       60        6          1        150      7.5
2       50        5          2        140       7
3       20        2          3        120       6
4        5       0.5         4        100       5

• Total spending for each month is \$100

• The MUM/PM for 1 movie is the same as the MUD/PD for 3 dinners
• In total, it costs \$10 + 3(\$20) = \$70
• This is not efficient in the sense that she is not using all of her
available resources

•The MUM/PM for 2 movie is the same as the MUD/PD for 4 dinners
• In total, it costs 2(\$10) + 4(\$20) = \$100

•Now, the MU/\$ is the same for each activities.

Ans:     b
According to the Law of Diminishing Marginal Utility,

A)    If you consume less of something, your total utility from
that consumption increases.
B)    If you consume more of something, the next unit you
consume will deliver more utility than did the last unit
you consumed.
C)    You should never consume any more of something after
marginal utility has begun to diminish.
D)    If total utility is increasing as you consume more, then
marginal utility must be increasing as well.
E)    Marginal utility tends to decrease when you consume
more of the same item.

Ans: e (by definition)
If MU is positive as consumption increases,
A)   The consumer will not experience diminishing MU.
B)   Total utility will remain high and constant as consumption
increases.
C)   Total utility will increase as consumption increases.
D)   The demand curve will necessarily have a positive slope.
E)   The demand curve will be a horizontal line.
• According to the Law of Diminishing MU, MU of the last unit
will decrease as more units are consumed, holding other
factors constant.

• However, that does not mean Total Utility will drop.

• MU can still be positive as it diminishes.

• As long as MU is positive, ↑ Q will ↑ TU.
• (A) is not true. No special assumptions on MU mentioned, so
the usual Law of Dim MU assumption still holds.

• (B) is wrong as well. TU will not remain constant as we know
that consumption of additional units brings positive MU
(hence raising TU).

• (D) is incorrect. We certainly are not assuming increasing MU.

• (E) is implicitly assuming MU staying constant. As there is any
• (C) is the correct answer.

• The satisfaction from each additional unit may come in a
lower lever as consumption continues, nevertheless, more
utility is generated.

• Total utility will always increase when MU is positive.

• Ans: C
Chapter 5 Problem 2
2) You are having lunch at an all-you-can-eat buffet. If you are rational, what
should be your marginal utility from the last morsel of food you swallow?

• Rational decision makers make their decisions/choices that maximizes their
total benefit. (maximizes their total satisfactions)
Therefore, we can always predict people’s behavior as the consequences of
choices that maximize total utility.

• Thus, Marginal benefit means Marginal utility
Marginal Utility: the additional utility (satisfaction) gained from
consuming an additional unit of good.

So, what is the marginal benefit (marginal utility) for this person to
have an additional morsel of food in the buffet?

In the all-you-can-eat buffet, the marginal cost of an additional
morsel of food is Zero (free).

Therefore, a rational person will continue to eat until the marginal
benefit (marginal utility) of the last morsel falls to Zero.
Chapter 5 Problem 4
4) Toby’s current marginal utility from consuming peanuts is 100utils
per ounce and his marginal utility from consuming cashews is
200utils per ounce. If peanuts cost 10 cents per ounce and
cashews cost 25 cents per ounce, is Toby maximizing his total
utility from the kinds of nuts? If so, explain how you know. If not,
how should he rearrange his spending?
Rational Spending Rule:

Spending should be allocated across goods so that the marginal
utility per dollar (the ratio) is same for each good

MU X/PX = MUY/PY

If Rational Spending Rule is not satisfied, we can always reallocated
the goods
Rational Spending Rule:

Increase (decrease) the consumption of one good, will decrease
(increase) the MU per dollar of that good.
(Marginal Utility is a decreasing function with consumption)

Spending a dollar                                       Spending a dollar
MUX / PX > MUY / PY            less on good Y, the
more on good X, the
MU per dollar from                                      MU per dollar from
consuming X falls                                       consuming Y rises

The adjustment process continues until there is no way to increase
the utility by moving the last dollar from one good to the other, i.e.,
when Rational Spending Rule is satisfied.

MUX / PX = MUY / PY
Check the marginal utility per dollar spent on the two goods.

• The MU per dollar from consuming peanuts is:
100utils per ounce/\$0.10 per ounce
= 1000utils per dollar from his last dollar spent on peanuts

• The MU per dollar from consuming cashews is:
200utils per ounce/\$0.25 per ounce
= 800utils per dollar from his last dollar spent on cashews
MU/\$ on Peanuts: 1000utils per dollar
MU/\$ on Cashews: 800utils per dollar

Toby is not maximizing his total utility from the kinds of nuts.

In order to maximizes his total utility, he should rearrange his
consumption.

He should increase total utility by spending one dollar more on
peanuts and one dollar less on cashews.
Chapter 5 Problem 6
6)   Ann lives in Princeton and commutes by train each day to her job
in New York City (20 round trips per month). When the price of a
round trip goes up from \$10 to \$20, she responds by consuming
exactly the same number of trips as before, while spending \$200
per month less on restaurant meals.
a)   Does the fact that her quantity of train travel is completely
unresponsive to the price increase imply that Ann is not a rational
consumer?
b)   Explain why an increase in train travel might affect the amount she
spends on restaurant meals.
Facts:
Ann is facing a rise in price of train ticket. Her total monthly spending
on train ticket has not changed and spending \$200 less on meals.

Her preferences determine her utility/benefit.
- She values more on work than meals. She doesn’t want to miss 1
day trip, meaning that she doesn’t want to miss 1 day work.
- She has no choice on other transportation to commute to work. So,
she has to take the train.
Therefore, her choice of preferences is to decrease her spending on
meals in order to compensate the increase in price of train ticket.
Then, this will not violate her preferences.

Therefore, she is rational.

To explain her preferences in terms of marginal utility per dollar:

More generally, even at twice the original price, the marginal utility
per dollar of the last train trip may be higher than the corresponding
ratio for any other good that Ann might consume, in which case she
would be perfectly rational not to change the number of trips she
takes.
Construct a numerical example so that the observed
phenomenon can be reconciled

- For simplicity, let’s assume:
- Originally, Ann takes 5 train trips per month at P=\$5; takes 10
meals per month at P=\$1. Total budget to spend on trips and
meals per month is \$35. Given her total utility on the two activities,
what is the optimal combination that maximizes her total utility?

- Compare the MU/\$ of the two activities
-   allocate each unit of the resource to the activity where its marginal utility per
dollar is highest.

- According to her preferences, we would expect that the MU/\$ of
train is higher than the MU/\$ of meal.
- According to her preferences, her marginal utility per dollar for the two
activities will be as follow:

Meal (per        MU        MU / \$
Train          MU         MU / \$        month)     (utils/meal)
(per month)   (utils/trip)
1            20          20      6
1            500          100     1
2           19.5        19.5     7
2            450           90     2
3            19          19      8
3            400           80     3
4           18.5        18.5     9
4            300           60     4      5            18          18      10
5            200           40     5      6           17.5        17.5     11
7            17          17      12
The optimal combination that
8           16.5        16.5     13
costs \$35 is, 5 train trips and
10 meals per month.                  9            16          16      14
10          15.5        15.5     15
The price of train tickets increases from \$5 to \$6.
Price of meals and total budgets stay the same.
What is the optimal combination after the price increases?
Train          MU         MU / \$         Meal (per        MU        MU / \$
(per month)   (utils/trip)                   month)     (utils/meal)
1            500         83.33    1        1            20          20      6
2            450          75      2        2           19.5        19.5     7
3            400         66.67    3        3            19          19      8
4            300          50      4        4           18.5        18.5     9
5            200         33.33    5        5            18          18      10
6           17.5        17.5
•The optimal combination that costs          7            17          17
\$35 is 5 trains, 5 meals. (consumption
8           16.5        16.5
of meals falls)
•The MU/\$ of the last train trip is          9            16          16
higher than the corresponding ratio for      10          15.5        15.5
any other good that Ann might
consume.
•She is rational not to change the
number of trips.
b) Explain why an increase in train travel might affect
the amount she spends on restaurant meals.
Income Effect
- is observed through changes in purchasing power
- when price of a good increases, purchasing power of individual
decreases

• Her total monthly spending is the same.
• The increase in price of ticket actually makes her poorer than
• The income effect of the price increase is what leads to the
reduction in the number of restaurant meals she eats.
Chapter 5 Problem 8
8) Tom has a weekly allowance of \$24, all of which he spends on pizza
and movie rentals, whose prices are \$6 per slice and \$3 per rental,
respectively. If slices of pizza and movie rentals are available only in
whole-number amounts, list all possible combinations of the two
goods that Tom can purchase each week with his allowance.
All combinations must be within Tom’s budget

Possible combinations of pizza   Tom’s total weekly allowance
and rentals                        (\$24)
(\$6/slice, \$3/rental)
0 pizzas, 8 movie rentals                 \$24

1 pizza, 6 movie rentals                  \$24

2 pizzas, 4 movie rentals                 \$24

3 pizzas, 2 movie rentals                 \$24

4 pizzas, 0 movie rentals                 \$24
Chapter 5 Problem 10
10) The buyers’ side of the market for amusement park tickets consists
of two consumers whose demand are as shown in the diagram
below.
a) Graph the market demand curve for this market.

36

24
Price (\$/ticket)

Price (\$/ticket)

0                                         0
96                                        48
Tickets/yr                                Tickets/yr
The market demand curve is the horizontal summation of the two
individual demand curves.

First, we need to derive the demand curve for consumer A and B.
P = a - bQ
Demand curve for Consumer A:                                  Demand curve for Consumer B:
P = 24 – 24/96 Q1                                             P = 36 – 36/48 Q2
P = 24 – 0.25 Q1                                              P = 36 – 0.75 Q2

36

24
Price (\$/ticket)

Price (\$/ticket)

0                 96                      0                  48
Tickets/yr                                 Tickets/yr
The market demand curve is the horizontal summation of the two
individual demand curves.

Price      Consumer A     Consumer B      Total
(\$/ticket)    (Ticket/yr)    (Ticket/yr)   Quantity
\$36            0              0            0
\$24            0             16           16
\$0            96             48           144
\$12           48             32           80
Horizontal
Summation
b)   Calculate the total consumer surplus in the amusement park
market if tickets sell for \$12 each.

Total Consumer surplus is the cumulative difference between the
most the buyers are willing to pay for each unit (reservation price)
and the price they actually pay (market price).
Total Consumer surplus is the cumulative sum of difference
between their reservation prices and the market price.

That is, the sum of the three shaded areas:

Price                                 Price                      Price
(\$/ticket)                          (\$/ticket)                 (\$/ticket)
36                         36

24                                  24                           24

12                                  12                           12

tickets/yr                       tickets/yr                     tickets/yr
48   96                     16        48                 16    80   144
32
• Area of the small triangle:
• (\$12/ticket x 16 tickets/yr) / 2 = \$96/yr

• Area of rectangle:
• (\$12/ticket x 16 tickets/yr)                    = \$192/yr

• Area of large triangle:
• (\$12/ticket x 64 tickets/yr) / 2 = \$384/yr
Price                                 Price                      Price
(\$/ticket)                          (\$/ticket)                 (\$/ticket)
36                         36

24                                  24                           24

12                                  12                           12

tickets/yr                       tickets/yr                     tickets/yr
48   96                     16        48                 16    80   144
32
• Total consumer surplus:
\$96/yr + \$192/yr + \$384/yr
= \$672/yr

Price                               Price                    Price
(\$/ticket)                        (\$/ticket)               (\$/ticket)
36                       36

24                                24                         24

12                                12                         12

tickets/yr                     tickets/yr                     tickets/yr
96                     16      48                 16    80   144
End of Chapter 5

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