Transcript Production and Cost - BYU Marriott School

Production and Supply
MANEC 387
Economics of Strategy
David J. Bryce
David Bryce © 1996-2002
Adapted from Baye © 2002
The Structure of Industries
Threat of new
Entrants
Bargaining
Power of
Suppliers
Competitive
Rivalry
Threat of
Substitutes
From M. Porter, 1979, “How Competitive Forces Shape Strategy”
David Bryce © 1996-2002
Adapted from Baye © 2002
Bargaining
Power of
Customers
Production and Supply
• Firms acquire inputs from suppliers
• Economics of production determines demand
for inputs
• Inputs are transformed into outputs through
a productivity relationship defined by the
“production function”
• For example, consider the Cobb-Douglas
production function:
a b
Q = f(L,K) = AL K
David Bryce © 1996-2002
Adapted from Baye © 2002
Total Product
The Cobb-Douglas Production Function
Q = f(K,L) = K0.5L0.5
• Assume that in the very short run, capital (K)
is fixed at 16 units
• Short run production function:
Q = 160.5 L0.5 = 4 L0.5
• What is total product (output) when we
use 100 employees?
Q = 4 (1000.5) = 4 (10) = 40 units
David Bryce © 1996-2002
Adapted from Baye © 2002
Product of Labor
• Marginal product of labor – MPL = DQ/DL
– Measures the output produced by the last worker
– Slope of the production function
• Average product of labor – APL = Q/L
– Measures the output of an “average” worker
David Bryce © 1996-2002
Adapted from Baye © 2002
Productivity in Stages
Q
Increasing
Marginal
Returns
Diminishing
Marginal
Returns
Negative
Marginal
Returns
Q=F(K,L)
AP
MP
David Bryce © 1996-2002
Adapted from Baye © 2002
L
Optimal Choice of Input Levels
How much of an input do I need?
• Use enough input
such that marginal
benefit equals
marginal cost
• Logic – if one more
unit provides more
value (PQQ) than it
costs (PLL), firm is
better off – use
another unit
David Bryce © 1996-2002
Adapted from Baye © 2002
TVP
PLL
Q*
PQQ
L*
Input L
Tangency means MVP=MC
Marginal Rate of Technical
Substitution – Cobb-Douglas
• Isoquants represent the
combinations of inputs that
produce a particular level of
output
• Slope of isoquant gives the
rate at which we can trade
one input for another
leaving output unchanged –
marginal rate of technical
substitution (MRTS)
David Bryce © 1996-2002
Adapted from Baye © 2002
Input K
Q3
Q2
Q1
Input L
Q1 < Q2 < Q3
Linear Isoquants
Perfect substitutes – Perfect Complements
Leontief (fixed proportion) technology
K
K
Q3
Q2
Q1
Q2
Q1
Q3
L
David Bryce © 1996-2002
Adapted from Baye © 2002
L
Optimal Choice of Input
Combinations
• Choose optimal inputs
such that marginal rate
of technical substitution
equals the price ratio
• Logic – if MRTS > price
ratio, you can get more
production/$ from L
than from K. Add more
L until its marginal
contribution equals that
of K
Input K
K*
PL/PK
L*
Input L
Tangency means MRTS = price ratio
David Bryce © 1996-2002
Adapted from Baye © 2002
Input Factor Demands
How much do we need from suppliers?
Input K
When the price
of labor rises,
firm demand
for labor falls
and demand
for capital rises
K1
K0
PL/PK
L1
David Bryce © 1996-2002
Adapted from Baye © 2002
L0
Input L
Input Factor Demand
The firm’s demand for
an input (from a
supplier) is derived from
each new equilibrium
point found on the
isoquant as the price of
the input is varied.
K
L
$
P0
P1
DL
L0 L1
David Bryce © 1996-2002
Adapted from Baye © 2002
L
Elements of Cost
Firms Incur Costs Using Inputs
• Total cost is an (always)
increasing function of output
and assumes that firms
produce efficiently.
• Variable cost is the cost of
variable inputs (e.g., direct
labor, raw materials, sales
commissions) and varies
directly with output.
• Fixed costs remain constant
as output increases
$
TC(Q) = VC(Q) + FC
VC(Q)
FC
Q
David Bryce © 1996-2002
Adapted from Baye © 2002
Properties of Cost
• The properties of cost are
determined by the shape of
total cost function
• Average cost (AC(Q)) is the
average cost per unit
(TC(Q)/Q)
• Marginal cost (MC(Q)) is
the cost of the last unit and
defines the rate at which
cost changes as quantity
changes
David Bryce © 1996-2002
Adapted from Baye © 2002
$
MC
ATC
AVC
AFC
Q
Fixed Cost
Q0(ATC-AVC)
$
= Q0 AFC
MC
ATC
= Q0(FC/ Q0)
= FC
AFC
ATC
AVC
Fixed Cost
AVC
Q0
David Bryce © 1996-2002
Adapted from Baye © 2002
Q
Variable Cost
$
Q0AVC
MC
ATC
= Q0 [VC(Q0)/Q0]
= VC(Q0 )
AVC
ATC
AVC
Variable Cost
Q0
David Bryce © 1996-2002
Adapted from Baye © 2002
Q
Total Cost
$
Q0ATC
MC
ATC
= Q0 [TC(Q0)/Q0]
= TC(Q0 )
AVC
ATC
AVC
Total
Cost
Q0
David Bryce © 1996-2002
Adapted from Baye © 2002
Q
Time and Cost
• Once a firm commits to a
technology, it cannot
immediately change scale –
costs are more fixed in the
short-run
• In the long-run, firms can
change technology and
scale – costs are more
variable
• The long-run average cost is
the minimum of all short-run
cost curves over time.
David Bryce © 1996-2002
Adapted from Baye © 2002
Cost
SRAC
SRAC1
5
SRAC
3
LRAC
Quantity
Decision-Making and Cost
• Accounting costs inform external constituents.
• Economic costs inform internal decision
makers and include opportunity costs.
• Sunk costs have already been incurred and
cannot be avoided.
– Economic decisions depend on avoidable costs.
– When fixed costs can be redeployed or sold, they
are not entirely sunk.
– Sunk costs are the basis for strategic commitment.
David Bryce © 1996-2002
Adapted from Baye © 2002