Microéconomie, chapter 7 - CEScermsem.univ-paris1.fr/davila/teaching/SBS/Ch07_Pindyck-09.pdf · Microéconomie, chapter 7 . 2 Solvay Business School – Université Libre de Bruxelles

1 Solvay Business School – Université Libre de Bruxelles

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Production costs

Microéconomie, chapter 7


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Points to be addressed  What costs to take into account?

 Short run costs

 Long run costs

 Short and long run cost curves

 Returns to scale and economies of scale


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Introduction

 Technology and input prices determines the production costs for the firm

 Economic efficiency requires to produce at a minimum cost at each level of output


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What costs to take into account?

 Rentals of office space, machinery are obvious costs for the firm

 What if the firm owns already these inputs and needs not renting them?

 Then the unearned income from not renting them to others are costs for the firm (opportunity cost)


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 Opportunity cost  Unearned income from the most profitable

alternative uses of the firm’s assets  It is an implict cost that must be taken into

account


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Opportunity cost

 Example  The firm owns its office space  Does this firm not incur any cost for the use

of office space?  Yes, the firm could have rented the office

space it owns to receive some income


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 Sunk costs  Any past spending that cannt be recovered  They do not influence the production

decisions of the firm and need not be taken into account


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Sunk costs

 Example  The firm seeks to rent some office space  It has already made a downpayment of €500.000 for

the purchase of an office building  The sale price is €5,5 millions (€5 millions are still to

be paid)  Before the settlement, the firm finds another building

equally convenient for €4,25 millions  Which building should the firm buy?


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Sunk costs

 Example  The firm should buy the second building  The downpayment of €500.000 is a sunk

cost that has no influenec of the decision  What the firm must consider is

  to spend €4,25 millions more, or   to spend €5 millions more


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  Some costs change with the output level, others are constant

  Total cost is composed of: 1.  Fixed costs

  Independent of the output level 2.  Variable costs

  Depend on the output level


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Fixed and variable costs

 Total output depends on fixed inputs and variable inputs

 Total cost consists of fixed costs (from fixed inputs) and variable costs (from variable inputs)


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Fixed costs and variable costs

 Which costs are fixed and which variable depends on the time horizon

 In the short run, most costs are fixed  In the long run, all costs are variable


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Fixed costs and sunk costs

 Fixed and sunk costs are often confounded

 Fixed cost:  Cost independent of the level of output, to be

paid only if production takes place  Sunk cost:

 Cost independent of the level of output, paid even if production does not take place


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Average and marginal costs

 Marginal cost (MgC):  It is the additional cost from producing one

more unit of output  Fixed costs do not influence the marginal

cost:

€

MgC =ΔCΔq

=ΔVCΔq


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Average and marginal costs

 Average cost (AC)  It is the total cost per unit of output

€

AC =Cq

=VCq

+FCq


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Short run marginal cost

 If labor is the only variable input in the short run and wage is w, then

€

MgC = w ΔLΔq

€

VC = wL

€

= w 1MgPL

 The MgC increases as the MgP of labor decreases


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L

F(K,L)

Short run cost curves

q

In the short run capital is fixed


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L

f (L)


q

In the short run capital is fixed


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L,q

f –1 (q)


f (L)

q,L

The inverse of the short run production

function gives the short run cost function


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q

f –1 (q)


L




21

cost


w f –1 (q)

q




22

cost VC

FC


q

The total cost curve includes the fixed costs


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VC

MgC

AC

q


q

cost

When AC>MgC the AC decreases


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cost VC

MgC AC

q’


q

When AC<MgC the AC increases


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cost VC

MgC

AC

q*


q

When AC>MgC the AC attains its

minimum


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 When MgC < AC, then AC decreases  When MgC > AC, then AC increases  When MgC = AC, then AC attains its

minimum


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output

cost

MgC

AC


AVC

q q’ q*


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Short run and long run

 In the short run some costs are fixed, e.g. from the use of capital

 In the long run there is no fixed costs  Both capital and labor are variable inputs


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Cost minimization

  The firm chooses the combination of inputs that allows to produced any given level of output at the minimum cost

 Assume  Two inputs: labor (L) and capital (K)  Price of labor : the wage w  Price of capital

 r = depreciation rate + interest rate  r = rental cost (they coincide if capital markets are

competitive)


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Cost minimization

 The isocost line  It contains all the combinations of L and K

with the same cost C = wL + rK

 There is one for each possible level of cost C  The slope -(w/r) is the rate at which labor can

be replaced by capital without changing the cost


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Cost minimization

labor

capital

Output Q1 can be obtained through

K2,L2 or K3,L3 but at a higher cost than the minimum throuhg K1,L1 on

the isocost line C1

Q1

C0 C1 C2

A K1

L1

K3

L3

K2

L2


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Inputs substitution

 When the wage w changes, the slope -(w/r) of the isocost lines changes too

 In particular, a more expensive labor is replaced by more capital


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Inputs substitution

C2

The new combination of inputs uses less labor and

more capital K2

L2

B

C1

K1

L1

A

Q1

If labor costs increase, the slope of the

isocost line increases

labor

capital


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Cost minimization  The minimization of costs is

characterized by the tangency of the isocot line and the isoquant

€

TRMS = ΔKΔL

= - MgPL

MgPK

€

slope of the isocost lines = - wr

€

MgPL

MgPK

=wr

when the cost is minimized


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 At the combination of inputs that minimizes costs, one additional euro in capital is as productive as one additional euro in labor

€

MgPL

w=

MgPK

r

Cost minimization


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Cost minimization   Example:

let w = €10, r = €2, and MgPL= MgPK. Is the firm minimizing costs?  One less unit of labor decreases q in MgPL units, and decreases

costs in €10  One more unit of capital increases q in PMgK units and increases

costs in €2  Since MgPL= MgPK output does not change but costs decreases

in €8 = €10 - €2  The firm has incentives to replace labor with capital  Decreasing labor increases MgPL   Increasing capital decreases MgPK  The firm will replace labor with capital until:

€

MgPLw

=MgPKr


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Cost minimization

 For any given input prices w and r, for each level of output q the re is an isocost line that minimizes costs

 The expansion path draws the bundles of inputs the minimize costs at each level of output


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Expansion path

•  r= €20 and w= €10 •  the expansion path gives the bundles of inputs that produce each q at a minimum cost given the input prices

capital

25

50

75

100

150

50 labor 100 150 300 200

A

€2000

200 Units

B

€3000

300 Units

C

The expansion path


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The expansion path

 The expansion path determines the long run total cost curve:  For any given w and r, the tangency of an

isocost and an isoquant gives the minimum cost of producing the output of the isoquant

 The total cost curve graphs the combinations of output and cost thus obtained


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Long run cost curves

  Long run average cost 1.  With increasing returns to scale:

  As inputs double, output more than doubles   Average cost decreases

3.  With decreasing returns to scale:   As inputs double, output less than doubles   Average cost increases


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 If returns to scale are first increasing and then decreasing, then the average cost curve AC is “U”-shaped

 The shape in U is a consequence of the returns to scale of all factors and not of decreasing marginal returns as in the short run


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 When AC decreases, MgC < AC  When AC increases, MgC > AC  therefore, the long run MgC curve is U-

shaped too when returns to scale are first increasing and then decreasing

 MgC = AC at the minimum of AC


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output

cost

AC

MgC

A


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 When the proportions of inputs change with the level of output, the expansion path is not a straight line  We cannot rely on the returns to scale to

obtain the form of the cost curves  We have to use the notion of economies of

scale


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Economies of scale

  Average cots AC decreases first as output increases because

1.  Workers specialize 2.  Production is organized more efficiently 3.  The firm can obtain better prices for inputs


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Economies of scale

  Average cost AC eventually increases becases

1.  The organization of production can become very complex

2.  A strong demand for inputs will increase their prices


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Economies of scale

There can be  Economies of scale

 As output doubles, cost les than doubles  Diseconomies of scale

 As output doubles, cost more than doubles


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Constant economies of scale

Total cost

output 100 300 200

cost

1000

2000

3000

D

E

F


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Economies of scale

Total cost

output 100 300 200

cost

1000

2000

3000

D

E

F

Economies of scale


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Economies of scale

Proportional cost

output 100 300 200

cost

1000

2000

3000

D

E

F

Economies of scale

Diseconomies of scale


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Economies of scale

  The economies of scale are measured by the elasticity EC of cost with respect to output

 EC is the increase (in percentage terms) in the cost induced by an increase of output of 1%

€

=MgCAC


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Economies of scale

  if EC = 1, then MgC = AC  Costs are proportional to output  No economies or diseconomies of scale: constant

economies of scale

 EC < 1 when MgC < AC  Economies of scale  MgC and AC are decreasing

 EC > 1 when MgC > AC  Diseconomies of scale  MgC and AC are increasing


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 A U-shaped long run AC curve represents  Economies of scale at low levels of output

 Diseconomies of scale at high levels of output

Economies of scale


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output

cost

AC

MgC

A


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In the long run output can increase from Q1 to Q2 with

a smaller increase in the cost than in the short run

Long run expansion path

labor

capital

L2

Q2

K2

D

C

F

E

Q1

A

B L1

K1

L3

P Short run Expansion path



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output

cost

Mg1C

AC1

Long and short run cost curves

q


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output

cost

Mg1C

AC1

MgC2

AC2


q


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output

cost

MgC1 MgC2

ACLT AC1 AC2

MgC3

AC3


q* q q’


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 In the long run the firm can change K  The long run AC curve is the lower

envelope to all short run AC curves  It gives the minimum average cost of

producing each level of output


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  In the long run the firm chooses the size (K) that minimizes AC for the chosen level of output

  The long run AC curve shows  Economies of scale at low levels of output  Diseconomies of scale at high levels of output

  The long run MgC curve  satisfies MgC<AC when long run AC decreases  satisfies MgC>AC when long run AC increases  satisfies MgC=AC at the minimum long run AC



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output

cost

MgC1 MgC2

MgCLT

ACLT AC1 AC2

MgC3

AC3


q* q q’

Documents

Microéconomie, chapter 7 - CEScermsem.univ-paris1.fr/davila/teaching/SBS/Ch07_Pindyck-09.pdf · Microéconomie, chapter 7 . 2 Solvay Business School – Université Libre de Bruxelles