Homework 3
Paving
A. The City of Albany paves its own streets
using labor, trucks (although several different types of equipment are employed,
in our example let’s generically think of them as trucks), and storage
facilities. In the short run the number
and size of storage sites is fixed.
However, the City does vary the amount of labor and the number of trucks
it employs. The following table
indicates the linear length of streets that can be paved (in yards) with
various combinations of the two inputs.
For example, 50 hours of labor and 2 trucks yield 32 yards of road.
|
|
Number of Trucks |
|||
|
Hours
of Labor |
1 |
2 |
3 |
4 |
|
|
|
|
|
|
|
50 |
12 |
32 |
47 |
57 |
|
100 |
26 |
46 |
61 |
71 |
|
150 |
38 |
58 |
73 |
83 |
|
200 |
48 |
68 |
83 |
92 |
|
250 |
57 |
77 |
92 |
102 |
|
300 |
65 |
85 |
100 |
110 |
|
350 |
72 |
92 |
107 |
117 |
|
400 |
78 |
98 |
113 |
123 |
|
450 |
83 |
103 |
118 |
128 |
|
500 |
87 |
107 |
122 |
132 |
|
550 |
90 |
110 |
125 |
135 |
|
600 |
92 |
112 |
127 |
137 |
1. Calculate the marginal product for labor (use
50 hours of labor as one unit) when the number of trucks is fixed at 1.
2. If the rental rate of trucks is $1500 per day
and the wage rate of workers is $20 per hour, what is the
cheapest way to pave 92 yards of street in a day?
3. Would it ever be the case
that the City would find it cheaper to rent a different number of trucks (give
an example)?
B. The following
total cost data is calculated assuming that Albany has two storage sites that
cost $400 each to rent per day . Answer
the questions following the table.
Output Total Average Average Marginal Total Marginal Profit
(yards) Cost Total Variable Cost
Revenue Revenue
Cost
Cost
0 800
20 4000
40 6000
60 8200
80
10,600
100 13,200
120 16,000
140 19,000
160 22,200
180 25,600
200 29,200
1. Calculate the
average total cost, average variable cost, and marginal cost for street paving
per day.
2. The going
rate for paving by private sector firms is $155 per yard. If the above cost data were for a private
sector firm calculate total revenue, marginal revenue, and profit (per yard of
paving).
3. Graph (at
least in a rough way) average total cost, average variable cost, marginal cost,
and marginal revenue (all on the same graph).