Chapter 9 su1
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Transcript of Chapter 9 su1
Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved.
McGraw-Hill/IrwinManagerial Economics, 9e
Managerial Economics ThomasMauriceninth edition
Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved.
McGraw-Hill/IrwinManagerial Economics, 9e
Managerial Economics ThomasMauriceninth edition
Chapter 9
Production & Cost in the Long Run
Managerial EconomicsManagerial Economics
9-2
Production Isoquants
• In the long run, all inputs are variable & isoquants are used to study production decisions• An isoquant is a curve showing all
possible input combinations capable of producing a given level of output
• Isoquants are downward sloping; if greater amounts of labor are used, less capital is required to produce a given output
Managerial EconomicsManagerial Economics
9-3
Marginal Rate of Technical Substitution• The MRTS is the slope of an isoquant
& measures the rate at which the two inputs can be substituted for one another while maintaining a constant level of output
K
MRTSL
MRTS
K LThe minus sign is added to make a positivenumber since , the slope of the isoquant, isnegative
Managerial EconomicsManagerial Economics
9-4
Marginal Rate of Technical Substitution• The MRTS can also be expressed as
the ratio of two marginal products:
L
K
MPMRTS
MP
L
K
MPMP MRTSAs labor is substituted f or capital, declines &
rises causing to diminish
L
K
MPKMRTS
L MP
Managerial EconomicsManagerial Economics
9-5
Isocost Curves
• Represents amount of capital that may be purchased if zero labor is purchased
( C ) ( w, r )
Show various combinations of inputs thatmay be purchased for given level ofexpenditure at given input prices
•
• K C r-intercept is
C w
K Lr r
•( w r )
Slope of an isocost curve is the negativeof the input price ratio
Managerial EconomicsManagerial Economics
9-6
Optimal Combination of Inputs
• Two slopes are equal in equilibrium• Implies marginal product per dollar spent on
last unit of each input is the same
Q
Q
Minimize total cost of producing bychoosing the input combination on the
isoquant for which is just tangent to anisocost curve
•
L L K
K
MP MP MPw
MP r w ror
Managerial EconomicsManagerial Economics
9-7
Optimization & Cost
• Expansion path gives the efficient (least-cost) input combinations for every level of output• Derived for a specific set of input
prices• Along expansion path, input-price
ratio is constant & equal to the marginal rate of technical substitution
Managerial EconomicsManagerial Economics
9-8
Expansion Path (Figure 9.6)
Managerial EconomicsManagerial Economics
9-9
Returns to Scale
• If all inputs are increased by a factor of c & output goes up by a factor of z then, in general, a producer experiences:• Increasing returns to scale if z > c; output goes up
proportionately more than the increase in input usage
• Decreasing returns to scale if z < c; output goes up proportionately less than the increase in input usage
• Constant returns to scale if z = c; output goes up by the same proportion as the increase in input usage
f(cL, cK) = zQ
Managerial EconomicsManagerial Economics
9-10
Long-Run Costs
• Long-run total cost (LTC) for a given level of output is given by: LTC = wL* + rK* Where w & r are prices of labor & capital,
respectively, & (L*, K*) is the input combination on the expansion path that minimizes the total cost of producing that output
Managerial EconomicsManagerial Economics
9-11
Long-Run Costs• Long-run average cost (LAC) measures the
cost per unit of output when production can be adjusted so that the optimal amount of each input is employed• LAC is U-shaped
• Falling LAC indicates economies of scale
• Rising LAC indicates diseconomies of scale
LTC
LACQ
Managerial EconomicsManagerial Economics
9-12
Long-Run Costs• Long-run marginal cost (LMC) measures
the rate of change in long-run total cost as output changes along expansion path• LMC is U-shaped
• LMC lies below LAC when LAC is falling
• LMC lies above LAC when LAC is rising
• LMC = LAC at the minimum value of LAC
LTC
LMCQ
Managerial EconomicsManagerial Economics
9-13
Derivation of a Long-Run Cost Schedule (Table 9.1)
Least-cost combination of
Output Labor (units)
Capital (units)
Total cost
(w = $5, r = $10)
LAC LMC
100
500
600
200
300
400
700
LMC
10
4052
1220
30
60
7
2230
8
10
15
42
$120
420
560
140
200
300
720
$1.20
0.840.93
0.700.67
0.75
1.03
$1.20
1.201.40
0.200.60
1.00
1.60
Managerial EconomicsManagerial Economics
9-14
Long-Run Total, Average, & Marginal Cost (Figure 9.9)
Managerial EconomicsManagerial Economics
9-15
Constant Long-Run Costs
• When constant returns to scale occur over entire range of output• Firm experiences constant costs in
the long run• LAC curve is flat & equal to LMC at
all output levels
Managerial EconomicsManagerial Economics
9-16
Long-Run Average Cost as the Planning Horizon (Figure 9.13)
Managerial EconomicsManagerial Economics
9-17
Restructuring Short-Run Costs (Figure 9.14)