Transcript Powerpoint Template

Chapter 7
Behind the Supply Curve:
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Recall:
Optimal Consumer Behavior

Consumer Behavior
– (behind the demand curve):
Consumption of G&S (Q) produces
satisfaction
 Satisfaction measured as utility
 Budget as constraint

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Optimal Consumer Behavior:
One product with no constraint
TU maximized when MU=0
 Two products, optimal consumption
bundle
MUx / Px = MUy / Py
 Two products with budget constraint
budget line and indifference curves
MUx / MUy = Px / Py = dY / dX

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Producer Behavior

Behind the supply curve:
– Inputs produces outputs
– Outputs measured as Q
– Cost of inputs as constraint
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Optimal Producer Behavior:
One input with no constraint
TP maximized when MP=0
 Two inputs, optimal input combination
MPL / w = MPk / r
 Two inputs with cost constraint
Iso-Cost lines and Iso-Quant Curves
MPL / MPk = w / r = dK / dL

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K: was fixed and is variable
--Long-Run:
The
period of time in
which all inputs are
variable.
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Optimal Input Combination:
Marginal Analysis
 Given
cost budget, buy L and K
at
MPL/w = MPK/r
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optimal choice
with two variable inputs
Two inputs, both variable
 Given input prices
 Given cost
 Iso-cost Line: a line that shows the
various combinations of inputs that cost
the same amount to purchase, given
input prices.

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Characteristics of Iso-cost lines:
C=wL+rK
 The slope of the Iso-cost curve is the
negative of the relative input price ratio,
-w/r.
 A change in total cost will lead to a
parallel shift of the Iso-cost curve.
 A change in an input price will rotate the
Iso-cost curve.

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Substitutability among Inputs
Variable Proportions Production: more
than one combinations of inputs are
possible (substitutions allowed)
 Fixed proportions Production: only one
combination of inputs is feasible (fixed
ratio, no substitutions)

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Iso-quant:
a
curve showing all
possible combinations
of inputs that would
produce the same level
of output.
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Characteristics of Iso-quant:
Downward sloping: to keep the same
total product.
 An infinite number of Iso-quants makes
up an Iso-quant map.
 The farther away from the origin, the
higher the output level it represents.

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Characteristics of Iso-quant: (cont.)

No two curves can intersect: Completeness and
Transitivity

Convex to origin: Diminishing marginal
rate of technical substitution (MRTS)
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Marginal rate of Technical
Substitution: MRTS

the rate at which one input is substituted for
another along an Iso-quant
 the slope of the Iso-quant
 MRTS= - (dK/dL)
 dQ=(MPL*dL)+(MPK*dK)
since dQ=0, (MPL*dL)= - (MPK*dK)
MPL/ MPK = - (dK / dL)
MRTS= - (dK/dL) = MPL/MPK
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Optimization:
Constrained Minimization
min C = wL + rK
 s.t Q = f(L, K)
by choosing L, K


Rule: cost of producing a certain level of
output will be minimized when MRTS = w/r
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Optimization (minimization):
Marginal Product Approach
MRTS = MPL/MPK
 cost is minimized
when MRTS = - w/r
 cost of producing a certain level of
output will be minimized when
MRTS=MPL/MPK=w/r, or
(MPL/w)=(MPK/r)

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Optimization:
Constrained Maximization

Max
Q = f(L, K)
 s.t. C = wL + rK
by choosing L, K

Rule: MRTS = MPL/MPK = w/r
or
MPL/w = MPK/r
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Expansion Path:

A curve or locus of points that shows the
cost-minimizing input combination for each
level of output, holding input prices
constant.
 Each point on the path is both technically
and economically efficient.
 MRTS = w/r everywhere on the path.
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Return to Scale:
Assume: Q = f(L, K)
and
zQ = f(cL, cK)
 there is constant return to scale if z=c.
 there is increasing return to scale if z>c.
 there is decreasing return to scale if z<c.
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Long-run Costs
 LTC
= wL + rK
 LAC = LTC/Q
 LMC = ΔLTC/ΔQ
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LTC, LAC, & LMC
Least Cost
Combination
Q
100
200
300
400
500
600
700
L
10
12
20
30
40
52
60
K
7
8
10
15
22
30
42
(w=5)
(r=10)
LTC
120
140
200
300
420
560
720
LAC
1.20
0.70
0.67
0.75
0.84
0.93
1.03
LMC
1.20
0.20
0.60
1.00
1.20
1.40
1.60
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LTC, LAC, & LMC
LMC<LAC,LAC;
LMC>LAC,LAC;
LMC=LAC,LAC min.
C
LMC
LAC
Q
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(Internal)
Economies of Scale
 LAC
decreases as output increases.
--specialization and division of labor
--technological factors
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(Internal)
Diseconomies of Scale

LAC increases as output increases.
--limitations to efficient management
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External Economy vs. External
Diseconomy
-industry development provides better
transportation, information, and human
resources.
*competition causes higher costs
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Economies of Scope:
there is economies of scope if
C(X, Y) < C(x) + C(Y), otherwise, there
is diseconomies of scope.
 SC = (C(X) + C(Y) - C(X, Y))/C(X, Y)
if SC>0, there exits economies of scope
if SC<0, there exits diseconomies of
scope.

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