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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 + rKLAC = LTC/QLMC = ΔLTC/ΔQ
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LTC, LAC, & LMC
Least Cost Combination
(w=5)
(r=10)
Q L K LTC LAC LMC
100 10 7 120 1.20 1.20
200 12 8 140 0.70 0.20
300 20 10 200 0.67 0.60
400 30 15 300 0.75 1.00
500 40 22 420 0.84 1.20
600 52 30 560 0.93 1.40
700 60 42 720 1.03 1.60
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LMC<LAC,LAC;
LMC>LAC,LAC;
LMC=LAC,LAC min.C
Q
LAC
LMC
LTC, LAC, & LMC
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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.