3-Theory of the Firm

8/9/2019 3-Theory of the Firm

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© 2006 Daniel Kirschen 1

Concepts from the Theory of the Firm

Daniel Kirschen

University of Manchester


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Production function

• y: output

• x1 , x2: factors of production

y = f x1, x2( )

y

x1

x2 fixed

x2

x1 fixed y

Law of diminishing marginal products


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Long run and short run

• Some factors of production can be adjusted

faster than others

ß Example: fertilizer vs. planting more trees

• Long run: all factors can be changed• Short run: some factors cannot be changed

• No general rule separates long and short run


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Input-output function

Example: amount of fuel required to produce a

certain amount of power with a given plant

y = f x 1 , x 2( ) x 2 fixed

x1 = g ( y ) for x 2 = x 2

The inverse of production function is the

input-output function


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Short run cost function

• w1 , w2: unit cost of factors of production x1 , x2

c SR ( y ) = w1 ⋅ x 1 + w 2 ⋅ x 2 = w1 ⋅g( y ) +w 2 ⋅ x 2

c SR ( y )

y


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Short run marginal cost functionc SR ( y )

y

y

dcSR

( y )

dy

Convex due to lawof marginal returns

Non-decreasing function


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Optimal production

• Production that maximizes profit:

max y

π ⋅ y − c SR ( y ){ }

d π ⋅ y − cSR

( y ){ }

dy= 0

π =

dc SR ( y )

dy

Only if the price π does not depend

on y ⇔ perfect competition


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Costs: Accountant’s perspective

• In the short run, some costs arevariable and others are fixed

• Variable costs:

ß labour

ß materials

ßfuel

ß transportation

• Fixed costs (amortised):

ß equipments

ß land

ß

Overheads• Quasi-fixed costs

ß Startup cost of power plant

• Sunk costs vs. recoverable costs

Production cost [¤]

Quantity


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Average cost

Quantity

Production cost [¤]

Quantity

Average cost [¤/unit]

c( y ) = c v ( y ) + c f

AC ( y ) =c ( y )

y=

c v ( y )

y+

c f

y= AVC ( y ) + AFC ( y )


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Marginal vs. average cost

MC AC

¤/unit

Production


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When should I stop producing?

• Marginal cost = cost of producing one more unit

• If MC > next unit costs more than it returns

• If MC < next unit returns more than it costs

• Profitable only if Q4 > Q2 because of fixed costs

Marginal

cost[£/unit]

Average cost [£/unit]

π

Q1 Q3 Q4Q2


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Costs: Economist’s perspective

• Opportunity cost:

ß What would be the best use of the money spent to make the

product ?

ß Not taking the opportunity to sell at a higher price represents a

cost

• Examples:

ß Growing apples or growing kiwis?

ß Use the money to grow apples or put it in the bank where it

earns interests?

• Includes a “normal profit”

• Selling “at cost” does not mean no profit


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Perfect competition

• Perfect competition

ß The volume handled by

each market participant is

small compared to the

overall market volume

ß No market participant caninfluence the market price

by its actions

ß All market participants act

like price takers

Marginal producer

Price

Quantity

supply

demand

Extra-marginal

Infra-

marginal


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Imperfect competition

• One or more competitors can influence themarket price through their actions

• Strategic players

ß Participants with a large market share

ß Can influence the market price

• Competitive fringe

ß Participants with a small market share

ß Take the market price

• Cournot and Bertrand models of competition


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Cournot model in a duopoly

max y1

π ( y1 + y 2e

) y1 − c ( y1 )

y1 = f 1 ( y 2e)

Problem for firm 1:

Similar problem for firm 2

y 2 = f 2 ( y 1e)

y1*=

f 1( y 2

*)

y 2*= f 2 ( y 1

* )Cournot equilibrium:

Neither firm has any incentive to deviate from the equilibrium

Competition on quantity


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π (Y ) 1− si

ε (Y )

=

dc ( y i )dy i

< 1

Cournot model in an oligopoly

• Strategic player operates at a marginal cost less than the

market price

• Ability to manipulate prices is a function of:

ß Market share

ß Elasticity of demand ε

si = y i Y


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Bertrand model in a duopoly

• Competition on price

• Firm that sets the lowest price captures theentire market

• No firm will bid below its marginal cost of production because it would sell at a loss

• At equilibrium, both firms sell at the same price,which is the marginal cost of production

• Equivalent to competitive equilibrium!

• Not a realistic model!

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3-Theory of the Firm