Post on 19-Jan-2016
description
The Firm and Optimal Input Use
Overheads
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.
Nature of the firm
Profit
Profit = Revenue - Cost
π p y w1x1 w2x2
π p y Σn
i 1wixi
Objectives of the firm
We assume that firms exist to make money,
by choosing the optimal levels of inputs and output
so they maximize profits
Technology and the firm
The The technologytechnology for a given production for a given production
process is the set of process is the set of all input and output all input and output
combinationscombinations such that the such that the output y can output y can
be produced frombe produced from the given set of the given set of inputs inputs
xx
The Producible Output Set P(x)The Producible Output Set P(x)
The producible output set P(x) is the set ofThe producible output set P(x) is the set of
all combinations of outputsall combinations of outputsthat are obtainablethat are obtainable
from a fixed level of inputsfrom a fixed level of inputs
Production Functions
The production function is a function that givesthe maximum output attainable from agiven combination of inputs
f(x) maxy ε P(x)
[y]
Example production function
y f(x)
15x 0.5x 2
Production and factor costs in the short run
Total (physical) product - TPP
Total product (y) is the maximum quantity ofoutput 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
0
20
40
60
80
100
120
0 4 8 12 16 20 24
Input
Out
put
Y
Marginal (Physical) Product (MPP)
Marginal (physical) product is the increase inoutput that results from a one unit increase in a particular input
MPi ΔyΔxi
y 1 y 0
x 1i x
0i
Marginal Revenue Product (MRP)
The marginal revenue product of an input is theincrease in output that results from a one unitincrease in that particular input
MRPi ΔTRΔxi
MRPi MR × MPPi
Marginal Revenue Product (MRP) is given by
MRPi p × MPPi
For a competitive firm, MRP is given by
x y DMPP MRP MFC0.0 0.00 10.01.0 14.50 14.50 72.50 10.02.0 28.00 13.50 67.50 10.03.0 40.50 12.50 62.50 10.04.0 52.00 11.50 57.50 10.05.0 62.50 10.50 52.50 10.06.0 72.00 9.50 47.50 10.07.0 80.50 8.50 42.50 10.08.0 88.00 7.50 37.50 10.09.0 94.50 6.50 32.50 10.010.0 100.00 5.5 27.50 10.011.0 104.50 4.5 22.50 10.012.0 108.00 3.5 17.50 10.013.0 110.50 2.5 12.50 10.014.0 112.00 1.5 7.50 10.015.0 112.50 0.5 2.50 10.0
Marginal Product & Marginal Revenue Product
0
10
20
30
40
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60
70
80
0 2 4 6 8 10 12 14 16
Input
DMPP
MRP
Marginal Factor Cost (MFC)
The additional amount that the firm has to pay fora factor when it hires one more unit of the factoris 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 maximizationsays that the firm should take any action thatadds 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 theinput is larger than the marginal factor costof the input
MRPi MFCi wi
MRPi wi
Marginal Product & Marginal Factor Cost
0
10
20
30
40
50
60
70
80
0 2 4 6 8 10 12 14 16
Input
MRPMFC
x opt
Demand for a variable input (single input)
When the firm only uses one variable input,the downward sloping portion of the marginalrevenue product curve is the input demand curve
The input demand curve tells us how many units ofthe input the firm will chose to employ at various prices
w x MRP72.5 1.0 72.50 67.5 2.0 67.50 62.50 3.0 62.50 57.50 4.0 57.50 52.50 5.0 52.50 47.50 6.0 47.50 42.50 7.0 42.50 37.50 8.0 37.50 32.50 9.0 32.50 27.50 10.0 27.50 22.50 11.0 22.50 17.50 12.0 17.50 12.50 13.0 12.50 7.50 14.0 7.50 2.50 15.0 2.50
MRP
MFC
Input Demand
MFC 1
MFC 2
MFC 3
0
10
20
30
40
50
60
70
80
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