Transcript Input Demand

The Firm and Optimal Input Use
Overheads
Nature of the firm
A neoclassical firm is an organization that controls
the transformation of inputs (resources it controls)
into outputs (valued products that it sells),
and earns the difference between what it receives in
revenue, and what it spends on inputs.
Profit
Profit = Revenue - Cost
n
π  p yΣ wi xi
i 1
π  p yw1 x1 w2 x2
Objectives of the firm
We assume that firms exist to make money,
so they maximize profits
by choosing the optimal levels of inputs and output
Technology and the firm
The technology for a given production
process is the set of all input and output
combinations such that the output y can
be produced from the given set of inputs x
The Producible Output Set P(x)
The producible output set P(x) is the set of
all combinations of outputs
that are obtainable
from a fixed level of inputs
Production Functions
The production function is a function that gives
the maximum output attainable from a
given combination of inputs
f (x) 
max [y]
y ε P( x )
Example production function
y  f(x)
 15x 0.5 x 2
Production and factor costs in the short run
Total (physical) product - TPP
Total product (y) is the maximum quantity of
output that can be produced from a given
combination of inputs
It is the value of the production function
y = f (x1, x2 , . . . , xn )
Production Function
Output
120
100
80
Y
60
40
20
0
0
4
8
12
16
20
Input
24
Marginal (Physical) Product (MPP)
Marginal (physical) product is the increase in
output that results from a one unit increase in
a particular input
Δy
y1
y0
MPi 

1
0
Δxi
xi 
xi
Marginal Revenue Product (MRP)
The marginal revenue product of an input is the
increase in output that results from a one unit
increase in that particular input
ΔTR
MRPi 
Δxi
Marginal Revenue Product (MRP) is given by
MRPi  MR × MPPi
For a competitive firm, MRP is given by
MRPi  p × MPPi
x
0.0
1.0
y
0.00
14.50
DMPP
MRP
14.50
72.50
MFC
10.0
10.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
28.00
40.50
52.00
62.50
72.00
80.50
88.00
94.50
13.50
12.50
11.50
10.50
9.50
8.50
7.50
6.50
67.50
62.50
57.50
52.50
47.50
42.50
37.50
32.50
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
11.0
12.0
13.0
14.0
100.00
104.50
108.00
110.50
112.00
5.5
4.5
3.5
2.5
1.5
27.50
22.50
17.50
12.50
7.50
10.0
10.0
10.0
10.0
10.0
15.0
112.50
0.5
2.50
10.0
Marginal Product & Marginal Revenue Product
80
70
60
50
DMPP
MRP
40
30
20
10
0
0
2
4
6
8
10
12
14
Input
16
Marginal Factor Cost (MFC)
The additional amount that the firm has to pay for
a factor when it hires one more unit of the factor
is called marginal factor cost
For a firm that is a price taker in the input market,
marginal factor cost is equal to factor price
MFCi = wi
The Profit Maximizing Output Level
The marginal approach to profit maximization
says that the firm should take any action that
adds more to revenue than to cost
The Profit Maximizing Rule
The firm should use another unit of the ith input
as long as the marginal revenue product of the
input is larger than the marginal factor cost
of the input
MRPi MFCi  wi
MRPi  wi
Marginal Product & Marginal Factor Cost
80
70
60
50
MRP
MFC
40
30
x opt
20
10
0
0
2
4
6
8
10
12
14
Input
16
Demand for a variable input (single input)
When the firm only uses one variable input,
the downward sloping portion of the marginal
revenue product curve is the input demand curve
The input demand curve tells us how many units of
the input the firm will chose to employ at various prices
w
72.5
67.5
62.50
57.50
52.50
47.50
42.50
37.50
32.50
27.50
22.50
17.50
12.50
7.50
2.50
x
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
11.0
12.0
13.0
14.0
15.0
MRP
72.50
67.50
62.50
57.50
52.50
47.50
42.50
37.50
32.50
27.50
22.50
17.50
12.50
7.50
2.50
Input Demand
$
80
70
60
50
40
30
20
10
0
MRP
MFC
MFC 1
MFC 2
MFC 3
0
2
4
6
8 10 12 14 16 18 20 22
Input
Summary of results on the firm
Profit Maximization
p × MPPi = wi, i = 1, 2, … , n
The End