Transcript Minimizing Cost - Microeconomics

Minimizing Cost
The Long Run Cost Minimization Problem

Long run:
The period of time that is long enough for the
firm to vary the quantities of all of its inputs as
much as it desires.

Short run:
The period of time in which at least one of
the firm’s input quantities cannot be
changed.
The Long Run Cost Minimization Problem
(continued)

Min TC = wL + rK
of producing Q units of output.
Min = minimize.
TC = Total Cost.
w = the price of a unit of labor service.
r = the price per unit of capital services.
L = Labor.
K = Capital.
Isocost

Isocost:
The set of combinations of labor and capital
that yield the same total cost for the firm.
Figure 7.1. Page 232
The Solution To The Long Run Cost
Minimization Problem

When the isoquant is just tangen to an
isocost line
Figure 7.2. Page 233
Cost minimizing input combination
Slope Isoquant = Slope Isocost
(MPl / w) = (MPk / r)

Problem:
Production function Q = 50 (LK)1/2
w = 5; r = 20
What is the cost minimizing if the firm want to
produce Q = 1000?

Answer:
MPl = 25 (K/L)1/2
MPk = 25 (L/K)1/2
( MPl / w ) = (MPk / r)
[ 25 (K/L)1/2 / 5 ] = [ 25 (L/K)1/2 / 20 ]
L = 4K
K = 10
L = 40
TC = ?
Deriving The Input Demand Curves From
A Production Function

Problem:
The production function Q = 50 (LK)1/2
What are the demand curves for Labor and
Capital?
(MPl / w) = (MPk / r)
K = f (r, w, Q)
L = f (r, w, Q)
The Price Elasticity Of Demand For
Inputs

Price Elasticity Of Demand For Labor:
The percentage change in the cost
minimizing quantity of labor with respect to a
1 percent change in the price of labor.
e L,w = (DL / Dw) / (w / L)
The Price Elasticity Of Demand For
Inputs (continued)

Price Elasticity Of Demand For Capital:
The percentage change in the cost
minimizing quantity of labor with respect to a
1 percent change in the price of capital.
e L,w = (DK / Dr) / (r / K)
Tabel 7.1. Page 245
Price Elasticities Of Input Demand For Manufacturing
Industries In Alabama
Input
Industry
Capital
Production
Labor
Non
Production
Labor
Electricity
Textiles
-0.41
-0.50
-1.04
-0.11
Paper
-0.29
-0.62
-0.97
-0.16
Chemicals
-0.12
-0.75
-0.69
-0.25
Metals
-0.91
-0.41
-0.44
-0.69
Short Run Cost Minimization

TC = TVC + TFC
TC = Total Cost.
TVC = Total Variable Cost.
TFC = Total Fixed Cost.
Short Run Cost Minimization (continued)

TVC:
the sum of expenditures on variable inputs,
such as labor and materials, at the short run
cost minimizing input combination.

TFC:
the cost of fixed inputs, it does not vary with
output.
Figure 7.14 Page 248
Short Run Cost Minimization With One Fixed Input.

Figure 7.15. Page 249
Short Run Input Demand Versus Long Run
Input Demand.