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

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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

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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

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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

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Input

$

Summary of results on the firm

Profit Maximization

p × MPPi = wi, i = 1, 2, … , n

The End