Download Economics 101 L

Economics 101 L
Homework No. 5 (due in respective labs on Oct. 13 and Oct. 15, 2008)
WORTH 100 POINTS TOTAL
1. A consumer’s budget can be written as: Y = P f F + Px X
WORTH 40 POINTS
where Y is income, Pf is the price of food, Px is the price of all other goods besides food, F is the
quantity of food consumed, and X is the quantity of all other goods consumed besides food.
a.
Suppose a consumer's income is $3,600 per month, P x is equal to $4/unit, and Pf is
$3/unit. Using Excel, draw the consumer's budget constraint in a graph with food on the
horizontal axis and other goods on the vertical axis, and call it Figure A. 5 POINTS
Figure A
Original Budget
New Budget
1000
900
Other Goods
800
700
600
500
400
300
200
100
0
0
200
400
600
800 1000 1200 1400 1600 1800 2000 2200 2400 2600
Food
b.
Suppose the price of food falls from $3/unit to $1.50/unit.
3 POINTS EACH
1. Draw the new budget constraint in Figure A.
2. Draw a hypothetical indifference curve tangent to the original budget constraint at a
consumption level of 800 units of food. What is the consumption level of other
goods at this point? ~300 units
3. Draw a second indifference curve tangent to the new budget constraint at a
consumption level of 1200 units of food. What is the consumption level of other
goods at this point? ~450 units
4. Has the demand for food increased or decreased? By how much? Increased by
400 units
5. Draw a line parallel to the new budget constraint tangent to the original budget
constraint. (This can be done by tracing a new line over the new budget constraint
and dragging it to where it is tangent on the original budget constraint.)
See
above graph.
6. Are there substitution effects? If yes, by approximately how much did food
consumption increase (or decrease) due to the substitution effect? Yes, sub. effects
increased food consumption by about 150 units.
7.
Redraw the original budget constraint from (a) in a new figure, and call it Figure B. In this
figure, draw also another budget constraint assuming the original prices (i.e., Px = $4/unit and
Pf = $3/unit), but a monthly income of $2,400. 2 POINTS
Figure A
1000
900
800
Other Goods
c.
Are there income effects? If yes, by approximately how much did food consumption
increase (or decrease) due to the income effect? Yes, income effects increased
food consumption by about 250 units.
700
600
500
400
300
200
100
0
0
100
200
300
400
500
600
700
800
900 1000 1100 1200 1300
Food
1.
2.
3.
4.
1-4 WORTH 3 POINTS EACH
Again, draw a hypothetical indifference curve tangent to the original budget constraint at
a consumption level of 800 units of food.
See graph
Has the demand for food increased or decreased? By how much?
Decreased by
200 units.
Are there substitution effects on the quantity food consumed? If yes, how much did food
consumption increase (or decrease) due to the substitution effect?
No sub. effects.
Are there income effects? If yes, by approximately how much did food consumption
increase (or decrease) due to the income effect?
Yes, decreased food consumption
by 200 units.
Lisa’s total utility from Movies is given in the table
2.
Quantity per
month
Marginal
Utility
Total utility
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
WORTH 20 POINTS
0
50
88
121
150
175
196
214
229
241
250
256
259
261
262
50
38
33
29
25
21
18
15
12
9
6
3
2
1
Draw a computer-generated graph illustrating Lisa’s total utility from Movies with quantity on the
horizontal axis. 5 POINTS
a.
Total utility
Total utility
300
250
Utility
200
150
100
50
0
0
5
10
15
Quantity
b.
Describe in simple words what is meant by “marginal utility”.
5 POINTS
Marginal utility is the change in total utility an individual obtains from consuming an
additional unit of a good or service.
c.
Calculate Lisa’s marginal utility and draw a new computer-generated graph illustrating this
marginal utility. 5 POINTS. See table above and graph below.
Marginal Utility
60
Marginal Utility
50
40
30
20
10
0
0
2
4
6
8
10
12
14
16
Quantity
d. Explain, in one or two sentences, the principle of diminishing marginal utility. 5 POINTS
Diminishing marginal utility refers to the notion that marginal utility continually decreases as
more and more of a particular good is consumed.
3.
You have a fixed budget of $30 per month to spend on two types of candy bars: chocks and
minties. Your marginal utility (MU) schedules for the two are shown below. WORTH 40
POINTS – 5 POINTS EACH
Chocks
1
2
3
4
5
6
7
8
9
10
a.
b.
c.
d.
e.
f.
g.
h.
MU of Chocks
20
18
16
14
12
10
8
6
4
2
Minties
1
2
3
4
5
6
7
8
9
10
MU of Minties
40
36
32
28
24
20
19
18
17
16
Suppose the price of chocks (Pch) and price of minties (Pmi) are equal at $3 per bar. You are
consuming two chocks and eight minties per month. What is your utility from the second chock?
From eighth minty?
18 from second chock. 18 from eighth minty.
If you transfer $3 of spending from minties to chocks, what is your reduction in utility from losing
the eighth minty? What is your increase in utility from gaining the third chock? Will you make
this transfer? Why/why not?
Loss of 18 from eighth minty. Gain of 16 from 3rd chock.
You would not make this transfer because you are decreasing your overall utility level.
If you transfer $3 of spending from chocks to minties, what is your reduction in utility from losing
the second chock? What is your increase in utility from gaining the ninth minty? Will you make
this transfer? Why/why not?
Loss of 18 from 2 nd chock. Gain of 17 from 9th minty. No
you would not make this transfer because your overall utility level would decrease.
Given your answers to a, b, and c, which combinations of chocks and minties will you choose?
For that option, how does the ratio of marginal utilities MU ch /MUmi for the last chock and the last
minty compare with the ratio of their prices, P ch / Pmi 2 chocks and 8 minties. MUc/MUm = 1/1 =
$3/$3…. Ratio of marginal utilities equals price ratio.
Now the price of chocks falls to $2 and the price of minties rises to $4. What has happened to the
opportunity cost of the chock bar? Suppose you now buy three chocks and six minties. What is
your utility from the 3rd chock? From the sixth minty?
The opportunity cost of the chock
bar has decreased from 1 to 0.5. Utility from the 3 rd chock is 16. Utility from the 6th minty is
20.
If you now transfer $4 of spending from minties to chocks, how much utility do you lose from
minties? How much utility do you gain from chocks? What happened to your total utility
compared to (e)? will you make this transfer? Why? Loss of 20 from minties. Gain of 26 from
chocks. Utility increased by 6. Yes you would make this transfer because your overall utility
level has increased.
If you transfer another $4 from minties to chocks, what happens to your total utility from minties
and chocks combined? Will you make this transfer? Why?
There is a reduction in overall
utility by 6. You would not make this transfer because your overall utility level decreases.
Given your answers to e, f, and g which combinations of chocks and minties will you choose? For
that option, how does the ratios of marginal utilities MU ch /MUmi for the last chock and the last
minty compare to the ratio of their prices, P ch / Pmi ? Do you see any similarity between this
comparison and the comparison you found in (d)? What do you conclude in the conditions for
utility maximization?
You would choose 5 chocks and 6 minties. Pc/Pm = 0.5 = MUc/MUm
= 12/24. Yes there is a connection. Consumption takes place at a level where the ratio of
prices is equal to the ratio of marginal utilities.