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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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