Homework 1

```Homework 4
Part I
Economics 503
Foundations of Economic Analysis
Assigned: Saturday, September 24th, 2005
Due: Saturday, October 8th, 2005
I.
Quantitative Problem
1.
You are the brand manager of a new lemon flavored toothpaste. You make
the toothpaste in batches of 1000 boxes. You face the following demand and cost
schedule.
a. Calculate the profit maximizing price and output level. Calculate the
marginal revenue from moving to the next batch size. Calculate the
marginal cost of increasing to the next largest batch size. Calculate the
( P  MCt )
Lerner Markup Index t
for this market using the profit
Pt
maximizing price and this marginal cost. Calculate the elasticity of
demand for this market by calculating the % effect on raising the price by
\$2 from the profit maximizing price.
b. Considering that your company is the only one that produces exactly this
flavor of toothpaste but anyone can enter the toothpaste market, how
would you expect to see the Lerner index evolve over time. What will
happen to profits?
Table 1. Quantity, Price and Cost
(measured in thousands of boxes and thousands of dollars).
Quantity
1
2
3
4
5
6
7
8
9
10
Price
Cost
58
56
54
52
50
48
46
44
42
40
13
12
17
28
45
68
97
132
173
220
There are profits available in this industry. Other toothpaste producers are likely to
introduce a lemon flavored toothpaste. This will be a good substitute for the new
toothpaste brand-managed by you. Better substitutes imply more elastic demand
which means lower markups. Eventually the profit maximizing markup will drop to a
level such that the implied price is equal to average cost. Profits will disappear.
2.
You observe a monopoly electric company operating in a market with price
schedule given by the equation
P  150  2  Q
where P is the price per Megawatt Hour and Q is the quantity of megawatt hours.
You know the electricity company must pay a fixed cost of 1050 to operate plus
50 per unit of output produced. Create a table like the one in Table 1 for quantities
in the range of 10 to 60 inclusive with increments of 5 MWH. Calculate revenue,
profits, and average cost of production at all levels. Calculate the profit
maximizing level of production. Calculate levels of production where profits are
zero (i.e. where average total cost of production is equal to the price level). Is it
possible for an average cost pricing scheme to be less efficient than a monopoly?
Calculate the marginal cost of increasing production by another by MWH at a
zero profit level of production. Would the firm operate if it had to price at
marginal cost?
Quantity Price
10
15
20
Monopoly
25
30
AC Price
35
40
45
MC Price
50
55
60
Cost
130
120
110
100
90
80
70
60
50
40
30
Revenue Profit
MC
1550
1300
-250
1800
1800
0
2050
2200
150
2300
2500
200
2550
2700
150
2800
2800
0
3050
2800
-250
3300
2700
-600
3550
2500
-1050
3800
2200
-1600
4050
1800
-2250
MR
50
50
50
50
50
50
50
50
50
50
50
100
80
60
40
20
0
-20
-40
-60
-80
-360
The profit maximizing output is 25 and the price where profits are 0 is 35. It is
possible that average costs could be higher than monopoly price. In that case, in
the short-run, a monopoly might be more efficient. The marginal cost of
increasing production is 50, though the price that could be charged at zero profts
Unit 4
3.
You are analyzing the profitability of Hong Kong’s movie industry. You hear that
Steven Chao’s Kung Fu Hustle is the top grossing Hong Kong film of all time.
You are given a list of local gross box office receipts for a number of Hong Kong
movies.
1. Kung Fu Hustle
2. Shaolin Soccer
3. First Strike
4. Rumble In The Bronx
5. Infernal Affairs
6. God of Gamblers Return
7. Justice My Foot
8. All's Well, End's Well
9. Thunderbolt
10. Mr. Nice Guy
11. Fight Back to School
12. All for the Winner
13. Drunken Master II
14. God of Cookery
15. God of Gambers II
16. Flirting Scholar
17. All's Well, End's Well 1997
Box Office Revenues
HK\$60,830,000
HK\$60,770,000
HK\$57,519,000
HK\$56,911,000
HK\$55,030,000
HK\$52,540,000
HK\$49,880,000
HK\$48,990,000
HK\$45,650,000
HK\$45,420,000
HK\$43,830,000
HK\$41,330,000
HK\$40,970,000
HK\$40,860,000
HK\$40,340,000
HK\$40,170,000
HK\$40,160,000
Year
2004
2001
1996
1995
2003
1993
1992
1992
1995
1997
1991
1990
1994
1997
1990
1993
1997
(Source: www.Asianboxoffice.com)
Adjust these for inflation using the yearly Hong Kong GDP deflator which is
available at :
Hong Kong Department of Census and Statistics
http://www.info.gov.hk/censtatd/eng/hkstat/fas/nat_account/gdp/gdp1_index.html
Convert all of these numbers into 2004 dollars using 2004 as the reference year.
Box Office
Year
1. Kung Fu Hustle
\$60,830,000.00
5. Infernal Affairs
\$55,030,000.00
2. Shaolin Soccer
\$60,770,000.00
7. Justice My\$49,880,000.00
Foot
12. All for the\$41,330,000.00
Winner
8. All's Well,\$48,990,000.00
End's Well
6. God of Gamblers
\$52,540,000.00
Return
15. God of Gambers
\$40,340,000.00
II
11. Fight Back
\$43,830,000.00
to School
4. Rumble In\$56,911,000.00
The Bronx
3. First Strike\$57,519,000.00
9. Thunderbolt
\$45,650,000.00
16. Flirting Scholar
\$40,170,000.00
13. Drunken\$40,970,000.00
Master II
10. Mr. Nice \$45,420,000.00
Guy
14. God of Cookery
\$40,860,000.00
17. All's Well,
\$40,160,000.00
End's Well 1997
P_Year
2004
2003
2001
1992
1990
1992
1993
1990
1991
1995
1996
1995
1993
1994
1997
1997
1997
85.8
88.7
98.2
84.6
70.8
84.6
91.7
70.8
77.2
100.5
106.3
100.5
91.7
98.1
112.2
112.2
112.2
P_2004
85.8
85.8
85.8
85.8
85.8
85.8
85.8
85.8
85.8
85.8
85.8
85.8
85.8
85.8
85.8
85.8
85.8
Iin 2004 dollars
\$60,830,000.00
\$53,230,823.00
\$53,096,395.11
\$50,587,517.73
\$50,086,355.93
\$49,684,893.62
\$49,159,563.79
\$48,886,610.17
\$48,712,616.58
\$48,586,704.48
\$46,426,436.50
\$38,972,835.82
\$37,585,452.56
\$35,833,088.69
\$34,732,941.18
\$31,245,882.35
\$30,710,588.24
```