ECO202 Microeconomics Equation of The Budget Line Problems Assignment

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ECO-202-online
Online Assignment 2
Spring 2019
Microeconomics
DUE DATE:
11:00 PM on Sunday, May 19, 2017
DIRECTIONS:
1. Answer each of the questions below and submit them before the due date. Late submissions and submitting by email will
not be accepted.
2. The nal draft of your answers should be composed on a word processor. (See Creating your Problem Set Answers videos for help on composing equations and graphs in
Microsoft Word.)
3. Your answers should be presented in numerical order and saved as a single le in a pdf
format (or at least a Word.docx).
(The video, Creating your Problem Set Answers,
shows you how to convert your Word.doc les into pdf documents.)
4. As noted in the Syllabus, copying the answers of a classmate or from an online source
(or simply sharing answers with classmates) is grounds for receiving zero credit for the
problem set and an automatic nal grade of F in the class. If you work with a classmate,
make sure that your answers are dierent and not exact copies.
5. Credit will be reduced for the following:
(a) Incorrect answers
(b) Illegible or disorganized answers
(c) Failure to show the derivation and calculation of your nal answers
(d) Failure to compile your answers together into a single le or presenting them in order
6. A Discussion Board (Questions about Online Assignment 2) has been provided on
Blackboard for questions about the assignment. Oce hours are available for questions
about the assignment, as well (and if you are unable to meet during regular oce hours,
then contact me via email to set up an appointment).
Question 1:
(worth 25%)
I II, and III ) over two products (X and Y ) as described
A, B, C, and D ) in Table 1. Each
pair of numbers is ordered (QX , QY ); for example, point B on indierence curve I is where
Consider three indierence curves ( ,
by quantities of the two products at four dierent points (
QX = 4
and
QY = 12.
1
Table 1: Indierence Curves I, II, and III
I
II
III
A
(1, 16)
(1.5, 18)
(2, 20)
B
(4, 12)
(4, 13)
(4, 15)
C
(7, 9)
(7.5, 10)
(6, 13)
D
(10, 7)
(11, 8)
(9, 11)
1(a):
Which indierence curve represents the highest utility? Explain why.
1(b):
What is the MRS between points A and B on indierence curve I? What is the MRS
between points C and D on the same indierence curve?
1(c):
Why does the MRS change between the two dierent sets of points in Question 1(b)
(or all the points on every indierence curve, for that matter)? What is the explanation
for this?
1(d):
If the budget of a consumer was
and
PY = $9.00,
Question 2:
B = $195, and the prices of X and Y were PX = $15.00
then what would the consumer’s optimal consumption bundle be?
(worth 25%)
$20.00 on two products, Apples and Bananas. The
$2.50 per quantity and the price of bananas (PB ) is $2.00 per quantity.
Assume that you can spend a budget of
price of apples (PA ) is
The marginal utilities of successive quantities of each is provided in Table 2.
M UA
QA
M UB
QB
20
18
1
16
1
2
14.8
2
16
3
13.6
3
14
4
12.4
4
12
5
11.2
5
10
6
10
6
8
7
8.8
7
6
8
7.6
8
4
9
6.4
9
2
10
5.2
10
Table 2: Marginal Utilities for Apples and Bananas
∗
2(a).
What is the optimal consumption bundle (QA ,
2(b).
What is the
MRS
Q∗B )
of apples and bananas?
at the optimal consumption bundle?
(Hint: the
MRS
should be
close to a ratio of the prices.)
2(c).
Graph the budget constraint and indicate the location of the optimal consumption
bundle. (Be sure to put
QA
on the horiztonal axis.)
2
Question 3:
(worth 25%)
A monopolist has its total costs (
TC ) of production given in Table 3.
curve it faces in the market is described by this equation:
The (inverse) demand
P = a − bQ = 3, 000 − (31.15)Q.
Table 3: Total Costs for a Monopolist
Q
3(a).
3(b).
TC
Q
TC
0
800
21
6243.2
1
1131.2
22
6977.6
2
1409.6
23
7810.4
3
1642.4
24
8748.8
4
1836.8
25
9800
5
2000
26
10971.2
6
2139.2
27
12269.6
7
2261.6
28
13702.4
8
2374.4
29
15276.8
9
2484.8
30
17000
10
2600
31
18879.2
11
2727.2
32
20921.6
12
2873.6
33
23134.4
13
3046.4
34
25524.8
14
3252.8
35
28100
15
3500
36
30867.2
16
3795.2
37
33833.6
17
4145.6
38
37006.4
18
4558.4
39
40392.8
19
5040.8
40
44000
20
5600
MC and ATC
Draw the MC and ATC
Derive the
values using the equation
curves using the values derived for 3(a).
demand curve and its corresponding
the equation learned in class,
3(c).
M C = ∆T C/∆Q
and
AT C = T C/Q.
Draw the inverse
MR curve. Note: for the MR curve, be sure to use
M R = a − 2bQ.
What is the price (PM ) and quantity (QM ) that the monopolist will choose in order to
maximize prot?
3(d).
What is their total prot from the price and quantity combination in 3(c)?
3(e).
What is the consumer surplus when they charge the price
3
PM
from 3(c)?
Question 4:
(worth 25%)
Two rms (RowGen and ColCom) are considering either releasing their new product line this
month or next month (thus, they have two strategies Now and Later). Both rms benet
from releasing their product sooner than their competitor, but if they release at the same
time, then they compete directly with each other and harm each others prominence on the
market.
This strategic interaction is presented in normal-form in Table 4. The lower-left number in
each cell represents the payo to RowGen from its strategy, while the upper-right numbers
represent the payo to ColCom from its strategy. For example, if ColCom chooses Later
and RowGen chooses Now, then ColCom receives 0 and RowGen receives 8.
Table 4: Normal-Form Game for Two Firms, RowGen and ColCom
ColCom→
Now
RowGen↓
2
Now
2
0
8
8
Later
4(a).
Later
0
Does either of the rms have a dominant strategy?
4
4
If so, what is it?
Provide your
reasoning.
4(b).
What is the Nash Equilibrium of this game? Explain why it is the equilibrium of the
game.
4(c).
Is there an outcome that would be better (for both rms) than the Nash Equilibrium?
Explain your answer.
4
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