Transcript EXHIBIT 6.13a Short-Run and Long

Chapter 6
Production and Costs
Steven Landsburg,
University of Rochester
Copyright ©2005 by Thomson South-Western, part of the Thomson Corporation. All rights reserved.
Introduction
•
•
•
•
Where do cost curves come from
Depends on firm’s available technology
Determines production process
Production process determines firm’s
costs
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Production and Costs in the Short
Run
• Limited options in short run (SR)
• Initial assumption
– Firm can hire more labor
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Production in the Short Run
• Total product (TP) of labor
– Quantity of output produced by firm in a given
amount of time dependent on labor hired
– Information graphically represented by
production function
• Production function slopes upward
• Production function is rule for determining how
much output can be produced with a given basket
of inputs
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Calculating MP and AP
• Marginal product of labor (MPL)
– Increase in total product based on hiring one
additional worker
– Assume capital fixed
– Slope of TP
• Average product of labor (APL)
– Total product divided by number of workers
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EXHIBIT 6.1
Total, Marginal and Average
Products
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Shape of MP and AP Curves
• AP
– If number of workers large, additional workers cause
average product of labor to decrease
– Inverted U-shape
• MP
– Inverted U-shape
• AP and MP relationship to one another
– If MP > AP, MP lies above AP
– If MP < AP, MP lies below AP
– If MP = AP, AP at maximum or peak
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EXHIBIT 6.2
The Stages of Production
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Variable Costs in the SR
• Constructing the firm’s variable cost curve
– Need total product curve
– Need wage rate
• Price of hiring labor
– Multiply number of workers by wage rate to
get variable cost
– Curve relates total product, not number of
workers, to variable cost
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EXHIBIT 6.3
Variable Cost Curve
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Fixed Costs in the SR
• Costs of capital
– Physical assets, such as machinery and
factories
– Ex. handyman’s van
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Total Cost
• Total cost equal to sum of fixed and
variable costs of production
• Additional cost considerations beside
totals
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Computing Average and Marginal
Costs
• Average variable cost (AVC): variable cost
divided by quantity of output
– Labor only variable factor of production
• Calculate AVC by taking the wage rate and dividing by APL
• Average cost (AC): total cost divided by quantity
of output
– Sometimes called average total cost
• Marginal cost (MC): additional cost attributable
to the last unit of output produced
– Labor only variable factor of production
• Calculate MC by taking the wage rate and dividing by MPL
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EXHIBIT 6.4
Deriving the Average and Marginal
Cost Curves
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Shapes of Cost Curves
• VC curve always increasing
– More output requires more labor
– Higher costs
• TC curve determined by sum of FC and
VC
– FC constant
– Has same shape as VC curve
• MC, AC, and AVC curves are U-shaped
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EXHIBIT 6.5
The
Geometry
of Product
Curves
and Cost
Curves
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Cost Curves Relations
• MC relationship to AVC and AC
– MC below AVC, AVC falling
– MC above AVC, AVC rising
– MC equals AVC, AVC at minimum
– Can replace AVC with AC, same holds true
• Shapes of cost curves related to shapes of
product curves
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Production and Costs in the Long
Run
• In long run (LR), firm can adjust
employment of capital and labor
• Attempts to achieve the least cost method
of producing a given quantity of output
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Isoquants
• Geometry of LR production
– Label vertical axis with K, stands for capital
– Label horizontal axis with L, which stands for labor
– Fixed period of time
• Want to use least costly method
– Avoid technologically inefficient points which are
outside the boundary
• General observations
–
–
–
–
Slope downward
Fill the plane
Never cross
Convex
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Marginal Rate of Technical
Substitution
• Absolute value of slope of isoquant
– MPL divided by MPK
• Amount of capital necessary to replace
one unit of labor while maintaining a
constant level of output
• If much labor and little capital employed to
produce a unit of output, MRTSLK is small
• Geometrically isoquant is convex
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EXHIBIT 6.8
The Production Function
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Choosing a Production Process
• Minimizing cost important part of maximizing
profit
• Isocost allow to keep track of costs
– Set of all baskets of inputs that can be employed at a
given cost
– Slope: -PL/PK
• Minimizing cost and maximizing output requires
firm choose tangency point between an isocost
and an isoquant
– Means that MRTS = PL/PK
– Tangencies lie along curve called the firm’s expansion
path
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EXHIBIT 6.9
Cost Minimization
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Long-Run Cost Curves
• Information needed
– Production function or isoquants
– Input prices
• Firm’s long-run total cost
– Cost of producing a given amount of output when the
firm is able to operate on its expansion path
• Long-run average cost
– Long-run total cost divided by quantity
• Long-run marginal cost
– Part of long-run total cost attributable to the last unit
produced
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EXHIBIT 6.11 Deriving Long-Run Total Cost
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EXHIBIT 6.12
Long-Run Total,
Marginal, and
Average Costs
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Returns to Scale
• When all input quantities are increased by 1%, does
output go up by
– …more than 1%
• Increasing returns to scale
• Occurs at low levels of output
• Long-run average cost curve is decreasing
– …exactly 1%
• Constant returns to scale
• “What a firm can do one, it can do twice”
• Long-run average cost curve is flat
– …less than 1%
• Decreasing returns to scale
• Occurs at sufficiently high levels of output
• Long-run average cost curve is increasing
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Relations between the SR and LR
• Derive SRTC from isoquants and factor prices
• Derive LRTC from isoquants and factor prices
• SRTC versus LRTC
– SRTC always at least as great as LRTC
• Multitude of short run situations
– Each has different level of fixed capital
– True for total cost and average cost
– Each point on long-run curve is associated with a
tangency point from a short-run curve
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EXHIBIT 6.13a Short-Run and Long-Run Total
Cost Curves
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EXHIBIT 6.13b Short-Run and Long-Run Total
Cost Curves continued
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EXHIBIT 6.15 Many Short-Run Average Cost
Curves
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