Homework 6
Economics 503
Foundations of Economic Analysis
Assigned: Week 6
Due: Week 7
1.
Below is a table showing a nominal interest rate on long-term bonds that was
prevailing in the December of each year from 1991-2005. Also shown is the level,
P, of the CPI index for 1991-2006. Assume that there is a fixed equilibrium real
interest rate in each period of 2.5% (r = .025). Use that estimate to derive the
forecast of inflation for the subsequent year. Use this to calculate, the actual
inflation rate in Hong Kong in the years 1992-2006. Calculate the ex post real
interest rate for HK for each year the period 1991-2005? In which years, was the
ex post interest rate greater than the ex ante real interest rate? In which years was
the ex post real interest rate negative?
P
Dec, 1991
Dec, 1992
Dec, 1993
Dec, 1994
Dec, 1995
Dec, 1996
Dec, 1997
Dec, 1998
Dec, 1999
Dec, 2000
Dec, 2001
Dec, 2002
Dec, 2003
Dec, 2004
Dec, 2005
Dec, 2006
i
73.1
79.9
86.8
94.6
100.8
107.6
112.7
111.1
108
105.9
99.4
100.3
99.1
99.7
101
102.9
5.18
5.47
4.26
7.74
5.54
5.58
9.6
5.96
6.37
5.42
3.41
1.763
1.125
0.993
3.983
3.519
2. Costs of Running a Factory You examine the production of an auto-parts
factory which uses labor, materials and capital machinery referred to as a die
press to produce goods. To start producing any goods, the factory has sunk set-up
costs of $25,000 per year. Up to 300 die presses can be installed in the factory in
increments of 50. The costs of owning and using a die press (including
depreciation and financing costs) in a given year are $5,000 per press. Therefore,
fixed costs are $25,000 plus $5000 times the number of die presses used. Die
presses are varied in increments of 50. In addition, producing goods requires some
variable inputs including materials, energy, and labor. Producing each good
requires material and energy costs of $20 per unit. For various reasons, production
can only be done in batches of 10,000 units. The following Table 1 reports the
variable labor costs of producing different levels of output at different levels of
die-press usage.
Table 1. Variable Labor Costs at the Auto Parts Factory
Production
Level
10000
20000
30000
40000
50000
60000
70000
80000
90000
100000
A.
50
$121,904.74
$501,327.80
$1,146,431.10
$2,061,688.19
$3,250,269.77
$4,714,646.67
$6,456,848.58
$8,478,600.52
$10,781,403.97
$13,366,589.17
# of Die Presses
100
150
$60,113.22
$39,751.81
$247,212.94
$163,477.55
$565,323.92
$373,838.72
$1,016,652.16
$672,294.10
$1,602,761.17 $1,059,877.64
$2,324,869.37 $1,537,395.02
$3,183,977.62 $2,105,508.13
$4,180,936.56 $2,764,779.45
$5,316,486.60 $3,515,698.63
$6,591,283.69 $4,358,699.41
200
$29,642.81
$121,904.74
$278,770.47
$501,327.80
$790,347.74
$1,146,431.10
$1,570,071.43
$2,061,688.19
$2,621,646.48
$3,250,269.77
250
$23,608.65
$97,089.53
$222,023.30
$399,276.34
$629,462.71
$913,060.90
$1,250,464.01
$1,642,006.11
$2,087,977.98
$2,588,637.25
Short-run The factory has set up 100 die presses. Fill in the Table 2 cost
chart for the firm in the short term. Calculate the marginal cost for each
level of production as the cost of producing one more batch (i.e. the cost
of producing another 10,000).
Table 2: Cost Chart: 100 Die Presses
Output
TFC
TVC
TC
10000
20000
30000
40000
50000
60000
70000
80000
90000
100000
AFC
AVC
ATC
MC
300
$19,602.27
$80,613.45
$184,345.99
$331,519.22
$522,642.99
$758,114.63
$1,038,260.49
$1,363,357.96
$1,733,648.48
$2,149,345.96
B.
Long-run Now assume that the factory managers can vary the number of
die presses. Calculate the average total cost function for each level of
production for each # of die presses. For each quantity of die-presses,
calculate the minimum average cost. For each level of production,
calculate the minimum average cost and the number of die presses that
would generate the lowest average total cost. Draw a diagram of those
minimum points. Over what range is the firm operating according to
increasing returns to scale? Over what range is the firm operating over
decreasing returns to scale? What is the minimum efficient scale (i.e. what
scale of production will result in the lowest overall level average total cost
when we can vary energy, workers, and # of die presses)? At what number
of die-presses is that minimum achieved?
Table 3. Average Total Costs at the Auto Parts Factory
50
Production
Level
10000
20000
30000
40000
50000
60000
70000
80000
90000
100000
# of Die Presses
100
150
200
250
300
Optional Problem
3. Construct a real exchange rate for HK for the years 2002-2007. In 2002, the
relative price of a market basket of goods in HK in HK$ relative to the price of
goods in the US in US$ is HK$6.9 per 1 US$ while the exchange rate is 7.8.
Below is the CPI for HK and the US with base years of 2000.
Price: P
HK
2002
2003
2004
2005
2006
2007
100.3
99.1
99.7
101
102.9
103.2
US
180.9
184.3
190.3
196.8
201.8
207.92
In which years is the HK undervalued and which is it overvalued?
.