ie4229 lecture3 cost supply(2)
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IE4229 Special Topics in Logistics
Transportation Economics
Instructor: Dr. Liu Yang
3. Cost and Supply(2)
1
Review: Production Theory
Production Function
(Q is dependent variable)
Isoquants
(Q is constant)
Marginal Product MRTS=MPL/MPK
Average Product Elasticity of Substitution
(sigma)
Return to Scale
Productivity Substitutability
2
Average Product and Marginal Product
1. When the marginal product of an input is positive,
Q=f(L,K) is increasing in that input.
2. When the average product is decreasing, the
corresponding marginal product must be smaller than
the average product.
Can you convince yourself of the conclusion above?
Hints:
1. Q is increasing in L if MPL>0;
2. dAPL/dL<0 is equivalent to MPL<APL
3
Source:
McCarthy 2001Figure: Productivity Curves
Average product
maximized
Q maximized
where marginal
product is zero.Marginal
product
maximized
4
Average Product and Marginal Product
Q and MP
1. Q is increasing when MPL>0 ;
2. Q is decreasing when MPL<0 ;
3. Q is maximized when MPL=0 ;
MP and AP
1. APL is decreasing (dAPL/dL<0) when MPL<APL;
2. APL is increasing (dAPL/dL>0) when MPL>APL;
3. APL is maximized (dAPL/dL=0) when MPL=APL;
5
Fixed and Variable Costs
A cost is fixed when it can not be (easily) adjusted to the
size/scale of production.
In contrast, a cost is variable when it depends on Q.
Example.
The purchase of a lot to use to operate a restaurant is a
fixed cost.
The purchase of the different ingredients used to prepare
the meals is variable cost.
9
Short-Run Cost
In short term, some inputs are clearly fixed which result
in fixed cost
E.g., road infrastructure, rail tracks, seaport
Some inputs are variable which result in variable cost
E.g., labor, fuel, maintenance
10
Long-Run Cost
In long run, all the costs are variable
All inputs can vary to get the optimal cost
Including the infrastructure and equipment
Because of time delays and high costs of changing
transportation infrastructure, e.g., seaport infrastructure,
this may be a rather idealized concept in many systems
11
The (Long Run) Cost Minimization Problem
Suppose that a firm’s manager wishes to minimize costs
Let the desired output level be Q0
Production function (Technology): Q=f(L,K)
12
The (Long Run) Cost Minimization Problem
Manager’s decision problem
Min TC(K,L)=rK+wL
s.t. Q0=f(L,K)
Decision variables: optimal L and K
TC: total cost
r: price of K
w: wage of L
In long run, both K and L are variable
13
The (Long Run) Cost Minimization Problem
14
Optimal L* and K*
Where isocost curve
is tangent of isoquant
at tangency point E
Isocost curve rK+wL=C2