Economics 172

Spring 2006

Due Friday March 3

 

Chapter 6:  Questions:  2, 5, 8, 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.

 

 

5.  This fixed proportion production function has L shaped isoquants.  No matter how many more workers we use, if capital is fixed, there is no more outpu possible.  The graph of the production function looks like a. 

For the total product curve, start with 2 units of capital and 1 unit of labor.  That makes total output equal to 1.  If we hold K constant at 2 and increase L to 2, total output is still 2.  So the total product curve is a horizontal line at the level of output chosen and it starts at L=1.  If we increase K, the total product curve is also horizontal, but it is at a higher level of output and it begins at L=2. 

 

 

 

The marginal product curve looks like the following.  The marginal product of labor for the first worker hired, for the production function where Q=1, is 1.  With any additional workers, the MPL is 0, just like the previous question.  And for the same reason, the APL slopes downward and is asymptotic to the L axis.

 

 

 

 

8.   The isoquant for Q=100 will be the quarter of the circle to the southwest, that is the convex part.  That is the only efficient part of the circle.

 

 

 

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 shows the returns to scale in the long run.  Since isoquants are convex, this means that in  the short run, there is 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 US and Japan. 

 

Year

Output

US L

Japanese L

US APL

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 in the text 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 Chittenden County, Vermont.  Fill in the missing spaces in the table with the correct values.  (They are in blue.)

 

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

 

 

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 ocntinue to double every year for the forseeable 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 Moore’s Law. 

 

a.  Does Moore’s Law contradict the law of diminishing marginal returns?

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.

 

According to an article in wikipedia (http://en.wikipedia.org/wiki/Computer_chip) today you can put 1 million transistors on a chip of 1 square millimeter.  Computer chips can be up to 100 square millimeters, which means about 100 million transistors on a chip.

 

Courtesy of http://www.kurzweilai.net/meme/frame.html?main=/articles/art0277.html (thanks to Gwen Pokalo for bringing this website to me).

 

Year      Transistors in Intel's Latest Computer Chip

1972           3,500

197           46,000

197         829,000

1982       134,000

1985       275,000

1989    1,200,000

1993    3,100,000

1995    5,500,000

1997    7,500,000

 

 

 

*****************************************

 

Here’s an old exam question from the consumer theory section of the course that is a good application to public policy issues.  It’s a good review for the final…..I won’t give you the answer. 

 

This problem is based on a real incident, although the numbers have been changed slightly.  The Town of Perkasie, Pennsylvania faced a garbage crisis in the late 1980s.  The town originally charged a fee of $120 per household per year to dispose of as much garbage as each household wanted.  That is, for $120 in taxes, residents could put as many garbage cans or bags as they wanted out on the curb and the trash hauler would take them to a landfill.  Perkasie households generated an average of 2,000 pounds of trash per year and with 1,000 households in town the town generated 2.0 million pounds (2,000 x 1,000) of trash per year.

 

a. Draw the initial budget line and indifference curve and equilibrium situation for a representative Perkasian with trash disposal as one good and the compositive good as the other. 

 

 

In an attempt to reduce the volume of trash, the town decided to require people to buy trash bags; the only trash that haulers would pick up would be trash placed in these bags.  The bags cost $1.50 each and the price was set such that the average household would use 80 bags per year and generate the same amount of trash for the same costs as before the new program.  The town eliminated its $120 annual trash collection fee, so the only cost of trash disposal was $1.50 per bag.  (Assume that a bag of trash holds exactly 25 pounds of trash; 25 pounds x 80 bags = 2,000 pounds of trash per household.)

 

b.  Draw the new budget line, indifference curve, and equilibrium situation for a representative Perkasian household after the new policy was put into effect and show how it is possible that one Perkasian household could generate the same volume of trash as before.

 

 

c. In reality, the total volume of trash generated by Perkasians was reduced as a result of the new program.  Show how an average Perkasian household could reduce its volume of trash and be made better off as a result of the new policy.  Redraw your graph from part a and draw the new budget line, indifference curve, and equilibrium situation for this representative Perkasian household that did reduce the volume of trash that it disposed of and achieved a higher level of utility.  Briefly explain and compare this to your results from part a.

 

d.   What would happen to the annual cost of trash disposal to this representative household you described in  part c?  Explain.  (Note that the actual total trash disposal costs did decline in Perkasie after this program was implemented.)