Economics 172
Fall 2007
Due Friday October 12
Chapter 6: Questions: 2, 10, 12
2. In the
first graph, total output increases with the addition of L, so the total
product curve is upward sloping wth a slope of 45
degrees. When 6 workers are hired, 6 units of output are produced.
But then each additional worker produces 0 output so
the TP line is horizontal. In the second graph, the AP and MP
curves are drawn. AP and MP are both equal to 1
as each additional unit of labor is hired. But the seventh worker
has an MPL of 0. That brings the APL down to something less than 1.
The 8th worker and everyone after that also has
an MPL of 0, so the APL continues to fall and is asymptotic to the x axis.
10.
Diminishing marginal returns is a short run phenomenon caused by the existence
of a fixed factor of production. Constant returns to scale is a long run
issue where all inputs are variable. Figure 6.5 in the text shows the
returns to scale in the long run. Since isoquants
are convex, this means that in the short run,
there are diminishing marginal returns to each factor.
12. If US
firms lay off workers, the remaining workers have a higher APL. Since the
Japanese firms always have the same number of workers, when their output falls
their APL falls as well.
Think of it this
way. Here are 10 years worth of production for the
|
Year |
Output |
|
Japanese L |
|
J APL |
|
|
|
|
|
|
|
|
1 |
100 |
10 |
10 |
10.0 |
10.0 |
|
2 |
90 |
9 |
10 |
10.0 |
9.0 |
|
3 |
90 |
9 |
10 |
10.0 |
9.0 |
|
4 |
100 |
10 |
10 |
10.0 |
10.0 |
|
5 |
90 |
9 |
10 |
10.0 |
9.0 |
|
6 |
90 |
9 |
10 |
10.0 |
9.0 |
|
7 |
90 |
9 |
10 |
10.0 |
9.0 |
|
8 |
100 |
10 |
10 |
10.0 |
10.0 |
|
9 |
100 |
10 |
10 |
10.0 |
10.0 |
|
10 |
90 |
9 |
10 |
10.0 |
9.0 |
|
|
|
|
|
|
|
|
|
|
|
Avg 10 Years |
10.0 |
9.4 |
|
|
|
|
|
|
|
Note that the
answer given in the textbook solution area is different because Perloff says it depends on what happens during
expansions. My assumption is that the increase in labor inputs is
proportional to the increase in output.
1. You are given the following information about a
company that uses a fixed amount of trucks and a variable number of workers to
deliver refrigerators in
|
Number of Trucks |
Amount of Labor |
Total Output |
APL |
MPL |
|
2 |
0 |
0 |
-- |
-- |
|
2 |
1 |
75 |
75 |
75 |
|
2 |
2 |
200 |
100 |
125 |
|
2 |
3 |
300 |
100 |
100 |
|
2 |
4 |
380 |
95 |
80 |
|
2 |
5 |
430 |
86 |
50 |
|
2 |
6 |
450 |
75 |
20 |
When does diminishing marginal productivity set in? At an output level of 200 (after the 2nd
worker is hired). After that MPL begins to decline.
2. In 1965 Gordon Morre, the
cofounder of Intel, predicted that the number of transistors per square inch on
integrated circuits, and thus the computing speed of a given size microprocessing chip, would continue to double every year
for the foreseeable future. In subsequent years the pace has slowed down
a bit, but data density has approximately doubled every 18 months. This
is the current definition of
a. Does
No it does not. The law of diminishing marginal returns says that, in this case, computing speed would eventually decrease if there was a fixed input and more variable inputs were applied to it. But if all inputs are variable, which they have been in this case, you can get more and more output (speed) from the computing chip.
b. Using the internet to find the answer, tell me how many transistors can be placed on an integrated circuit today.
Wikipedia (you should be careful about Wikipedia, but I trust it here) says up to 1 million transistors can be placed per square millimeter. and a chip has up to 350 square millimeters. That implies 350 million. This source says 410 million (but it's from 2003). In the early 1970s, chips had less than 4,000 transistors on them.
3. Suppose LeBron James makes half of his two point shots in professional basketball games in his career and forty percent of his three point shots. James should shoot only two point shots. True, false, or uncertain and explain.
Uncertain. We don't know how many points he
makes on his marginal shot. These are just average numbers.
4. Suppose a firm
uses three inputs to produce its output. When we draw an isoquant showing the relationship between two of the inputs
and a given level of output, we make no assumptions as to the quantity of the
third input which is used to produce the good; there can be any amounts of it
used. True, false, or uncertain and explain.
False. We assume that the third input is held constant. We are looking at how the pair of inputs must change in order to keep output constant. If a third input is changing as well, output will be changing also.
5. Draw isoquants for the following pairs of inputs for the following sandwiches:
a. Big Macs: hamburger patties and slices of cheese.
This isoquant shows that in order to make one Big Mac you need a
certain fixed number of beef patties and a certain number of slices of cheese.
Having more of either (without more of both) does not allow you to make any
more Big Macs. This is a fixed
proportion production function.
b. Subway foot long subs: Swiss cheese and provolone cheese.
This shows that
you can substitute Swiss and provolone in the production function. They are
perfect substitutes in production.