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```									Factor Demand
Factor Demand
• Inputs are also called factors of production

• So, the demand for inputs is called factor
demand.

• To know how many inputs we want, need
to know the value of output (price) and the
cost of the input.
Some Ag Prices
http://money.cnn.com/data/commodities/
Some Ag Costs
• Average Pasture Value in Texas (\$/acre)
– 1998: \$550
– 2002: \$600
– 2005: \$869
– 2007: \$1,370

-USDA NASS, August 2007
Simple Example
• The value of output is just the price.
– Assume price is constant: can sell as much as
you want at P.
–P=5
• The price of labor is just the wage.
– Assume the wage is constant: can hire a
many workers (or as many hours) as you
want at w.
– w = 10
Value of the Marginal Product
• The value of the marginal product, VMP, is
how much more revenue the firm gets
when they sell the output produced by
using an additional input (here: labor).

VMP = P*MP
VMP
L   TP    AP   MP   P   VMP
0    0     0
1    2     2    2   5    10
2    8     4    6   5    30
3   21     7   13   5    65
4   32     8   11   5    55
5   40     8    8   5    40
6   45   7.5    5   5    25
7   49     7    4   5    20
8   52   6.5    3   5    15
9   54     6    2   5    10
10   54   5.4    0   5     0
MP and VMP
Marginal Product

70
VMP        MP
60
Output/ VMP

50
40
30
20
10
0
0   2     4         6        8         10        12
Labor
Marginal Factor Cost
• The marginal factor cost, MFC, is the cost
of adding another factor of production.

• For labor, the MFC = w.

MFC = w
VMP and MFC
Value of the Marginal Product

70
VMP
60
50
40
VMP

30
20
10                                                  w
0
0   2         4          6          8     10       12
Labor
VMP and MFC
Value of the Marginal Product
VMP > w
70
60       VMP                             “What comes into your cash
register from hiring is more
50                                       than what goes out”
40
VMP

HIRE THE WORKER!
30
20
10                                                           w
0
0     2         4          6          8            10              12
Labor
VMP and MFC
Value of the Marginal Product
VMP > w
70
60       VMP                             “What comes into your cash
register from hiring is more
50                                       than what goes out”
40
VMP

KEEP HIRING!
30
20
10                                                           w
0
0     2         4          6          8            10              12
Labor
VMP and MFC
Value of the Marginal Product

70                                       VMP = w
60       VMP
What you paid for the worker
40                                       they brought in
VMP

30
20
10                                                          w
0
0     2         4          6          8           10           12
Labor
VMP and MFC
Value of the Marginal Product
VMP < w
70
60       VMP                             “What comes into your cash
register from hiring is less than
50                                       what goes out”
40
VMP

STOP HIRING!
30
20
10                                                            w
0
0     2         4          6          8             10            12
Labor
The RULE
• This leads to a simple rule for factor
demand:

VMP = MFC
2 Problems
• At a given price, how much labor does the
firm want? Factor demand.

• At a given price and wage, how much
does the firm decide to produce and how
much does it earn? Profit maximization.
Factor Demand
Value of the Marginal Product
If the wage is 10, you hire 9
70                                       workers.
60       VMP
50
40
VMP

30
20
10                                                           w
0
0     2         4          6          8            10               12
Labor
Factor Demand
Value of the Marginal Product
If the wage is 10, you hire 9
70                                       workers.
60       VMP                             If the wage is 20, you hire 7
workers.
50
40
VMP

30
20                                                           w
10
0
0     2         4          6          8            10               12
Labor
Factor Demand
Value of the Marginal Product
If the wage is 10, you hire 9
70                                       workers.
60       VMP                             If the wage is 20, you hire 7
workers.
50                                       If the wage is 40, you hire 5
workers.
40
VMP

w
30
20
10
0
0     2         4          6          8            10               12
Labor
Question?
• Why do you never hire when VMP is still
rising?
Factor Demand
Value of the Marginal Product
If the wage is 10, you hire 9
70                                       workers.
60       VMP                             If the wage is 20, you hire 7
workers.
50                                       If the wage is 40, you hire 5
workers.
40
VMP

w
30
20
10
0
0     2         4          6          8            10               12
Labor
Question?
• Why do you never hire when VMP is still
rising?

• Because, hiring an additional worker will
result in VMP > MFC and thus you would
want to hire an additional worker.
Factor Demand
Value of the Marginal Product
If the wage is 10, you hire 9
70                                       workers.
60       VMP                             If the wage is 20, you hire 7
workers.
50                                       If the wage is 40, you hire 5
workers.
40
VMP

w
30
20
10
0
0     2         4          6          8            10               12
Labor
Firm Factor Demand
Labor Demand
Factor demand for the firm is
70                            the VMP curve that is
VMP                  downward sloping.
60
50
40
w

30
20
10
0
0     2   4       6         8           10           12
Labor
Market Factor Demand
• Suppose there are only 2 identical firms in
the market.

• At w=10, one firm wants 9 workers, so two
firms want 18 workers.
Market Factor Demand
Labor Demand

70
Firm Demand            Market Demand
60
50
Market factor demand is the
40                                   horizontal sum of each firm’s
w

factor demand
30
20
10
0
0      5     10            15                20             25
Labor
REVIEW
• Firms use inputs until VMP = MFC.

• Demand for an input is decreasing in the
MFC, e.g. demand for labor is decreasing
in the wage rate.

• Market factor demand is the horizontal
sum of firm demands.
How many will you produce?
L    TP    AP   MP   P   VMP   MFC
0     0     0
1     2     2    2   5    10   10
2     8     4    6   5    30   10
3    21     7   13   5    65   10
4    32     8   11   5    55   10
5    40     8    8   5    40   10
6    45   7.5    5   5    25   10
7    49     7    4   5    20   10
8    52   6.5    3   5    15   10
9    54     6    2   5    10   10
10    54   5.4    0   5     0   10
How many will you produce?
L    TP    AP   MP   P   VMP   MFC
0     0     0
1     2     2    2   5    10   10
2     8     4    6   5    30   10
3    21     7   13   5    65   10    54
4    32     8   11   5    55   10
5    40     8    8   5    40   10
6    45   7.5    5   5    25   10
7    49     7    4   5    20   10
8    52   6.5    3   5    15   10
9    54     6    2   5    10   10
10    54   5.4    0   5     0   10
How much will you earn?
L   TP   P   VMP MFC    VTP
0    0
1    2   5    10   10     10
2    8   5    30   10     40
3   21   5    65   10    105
4   32   5    55   10    160
5   40   5    40   10    200
6   45   5    25   10    225
7   49   5    20   10    245
8   52   5    15   10    260
9   54   5    10   10    270
10   54   5     0   10    270
How much will you earn?
L   TP   P   VMP MFC    VTP
0    0
1    2   5    10   10     10
2    8   5    30   10     40
VTP: value
3   21   5    65   10    105   of the total
4   32   5    55   10    160   product
5   40   5    40   10    200
6   45   5    25   10    225
7   49   5    20   10    245   54*5=270
8   52   5    15   10    260
9   54   5    10   10    270
10   54   5     0   10    270
How much did you spend on labor?
L   TP   P   VMP MFC    VTP    TFC
0    0
1    2   5    10   10     10     10
2    8   5    30   10     40     20
3   21   5    65   10    105     30
4   32   5    55   10    160     40
5   40   5    40   10    200     50
6   45   5    25   10    225     60
7   49   5    20   10    245     70
8   52   5    15   10    260     80
9   54   5    10   10    270     90
10   54   5     0   10    270    100
How much did you spend on labor?
L   TP   P   VMP MFC    VTP    TFC
0    0
1    2   5    10   10     10     10
2    8   5    30   10     40     20
TFC: total
3   21   5    65   10    105     30   factor cost
4   32   5    55   10    160     40
5   40   5    40   10    200     50
6   45   5    25   10    225     60
9*10=90
7   49   5    20   10    245     70
8   52   5    15   10    260     80
9   54   5    10   10    270     90
10   54   5     0   10    270    100
How much did you earn net of
labor costs?
L   TP   P   VMP MFC    VTP    TFC
0    0
1    2   5    10   10     10     10     0
2    8   5    30   10     40     20    20
3   21   5    65   10    105     30    75
4   32   5    55   10    160     40   120
5   40   5    40   10    200     50   150
6   45   5    25   10    225     60   165
7   49   5    20   10    245     70   175
8   52   5    15   10    260     80   180
9   54   5    10   10    270     90   180
10   54   5     0   10    270    100   170
Profit
• If you didn’t have any other costs, then your profit would
have been 180.

• This is one way to determine what a firm does at a
particular price and wage.

• It is also very cumbersome to see the effect of a price
change and thus not the best way to build the supply
curve.

• But, it will be a useful base for using another method.
Value and Costs of Texas Ag
• USDA NASS:
http://www.agcensus.usda.gov/Publications/
2002/County_Profiles/Texas/index.asp
Change in the wage
Labor Demand
A change in the wage…
70
60       VMP
50
40
w

30
20
10
0
0     2   4       6        8          10         12
Labor
Change in quantity demanded
Labor Demand
A change in the wage…
70
VMP                  …which cause a change in
60
the quantity demanded (9 to
50                            7)
40
w

30
20
10
0
0     2   4       6        8           10              12
Labor
Change in output price
• Suppose the value of your output falls to
\$2?
Change in output price
• Suppose the value of your output falls to
\$2? L TP AP MP VMP MFC VMP`
0    0     0
1    2     2    2   10   10    4
2    8     4    6   30   10   12
3   21     7   13   65   10   26
4   32     8   11   55   10   22
5   40     8    8   40   10   16
6   45   7.5    5   25   10   10
7   49     7    4   20   10    8
8   52   6.5    3   15   10    6
9   54     6    2   10   10    4
10   54   5.4    0    0   10    0
Change in output price
Value of the Marginal Product

70
VMP
60       VMP`
50
40
VMP

30
20
10
0
0     2          4          6          8   10   12
Labor
Change in output price
D        Demand for labor
D`
70
60
50
40
wage

30
20
10
0
0        2   4         6        8   10   12
Labor
Change in output price
D        Demand for labor
D`
A change in the
70                                       value of output
60                                       changes the
demand curve for
50                                       labor
40
wage

30
20
10
0
0        2   4         6        8          10          12
Labor
Change in output price
D        Demand for labor
D`
A change in the
70                                       value of output
60                                       changes the
demand curve for
50                                       labor…
40
wage

…which changes
30
the quantity
20                                       demanded (9 to 6)
10
0
0        2   4         6        8          10           12
Labor

```
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