ECN 101
Fall 2007
PROBLEM SET 5
1.
2.
Gomez runs a small pottery firm. He hires one helper at $12,000 per year, pays annual rent of $5,000
for his shop, and materials cost $20,000 per year. Gomez has $40,000 of his own funds invested in
equipment (pottery wheels, kilns, etc) which could earn him $4,000 per year if alternatively invested.
Gomez has been offered $15,000 per year to work as a potter for a competitor. He estimates his
enterepreneurial talents are worth $3,000 per year. Total annual revenue from pottery sales is $72,000.
Calculate accounting and economic profits forGomez’s pottery.
(a) Construct the marginal product and average product schedule for the following production
function:
LABOR
TOTAL PRODUCT
1
15
2
34
3
51
4
65
5
74
6
80
7
83
8
82
(b) Graph the total product, marginal product and average product curves. Explain in detail the
relationsip between each pair of curves.
(c) When does the firm first experiences diminishing returns to labor?
3.
The number of repairs produced by a computer repair shop depends on the number of workers as
follows:
NUMBER OF WORKES
NUMBER OF REPAIRS (per week)
0
0
1
8
2
20
3
35
4
45
5
52
6
57
7
60
Assume that all inputs (office space, telephone, utilities) other than labor are fixed in the short run.
(a) Add two additional columns to the table, and enter the marginal product and average product for each
number of workers?
(b) Over what range of labor input are there increasing returns to labor? Diminishing returns to labor?
Negative returns to labor?
(c) Over what range of labor input is marginal product greater than average product? What is happening to
average product as employment increases over this range?
(d) Over what range of labor input is marginal product smaller than average product? What is happening to
average product as employment increases over this range?
4. A firm can use three different production technologies, wtih capital and labor requirements at each
level of output as follows:
Daily
Output
100
150
200
250
K
3
3
4
5
Technology 1
L
7
10
11
13
K
4
4
5
6
Technology 2
L
5
7
8
10
K
5
5
6
7
Technology 3
L
4
5
6
8
(a)
Suppose the firm is operating in a high-wage county, where capital cost is $100 per unit per
day and labor cost is $80 per worker per day. For each level of output, which technology is
cheapest?
Now suppose the firm is operating in a low-wage country, where capital cost is $100 per unit
per day but labor cost is only $40 per unit per day. For each level of output, which
technology is the cheapest?
Suppose the firm moves from a high wage to a low wage county but that its level of output
remains cosntant at 200 units per day. How will its total employment change?
(b)
(c)
5.
The Little Red Wagon Company has the following cost schedule:
WAGONS PRODUCED
0
1
2
3
4
5
(a)
(b)
6.
TVC
TFC
TC
ATC
MC
Complete the following table.
Q
1
2
3
4
5
8.
Construct the schedules for total fixed cost, total variable cost, average fixed cost, average
variable cost, average total cost, and marginal cost.
Graph the average variable cost, average total cost, and marginal cost curves.
Assume that you are in the business of producing a product for which the short-run cost function is
TC=30+3Q+Q2 where Q is output and TC represents total cost.
(a) What are total fixed costs equal to?
(b) What is the equation that represents total variable costs?
(c) Derive the equation for average variable costs.
(d) Fill in the blanks in the following table:
Q
0
1
2
3
4
5
6
7.
TOTAL COST
$ 30
60
80
90
110
150
TFC
240
240
TVC
50
TC
290
330
110
MC
50
AFC
240
AVC
50
45
ATC
290
20
60
100
480
Complete the following table.
Q
1
2
3
4
TFC
300
TVC
70
TC
370
MC
70
60
AFC
AVC
70
315
ATC