Title: Minimizing Cost
1Minimizing Cost
2The 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 firms input quantities cannot be
- changed.
3The 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.
4Isocost
- Isocost
- The set of combinations of labor and capital
that yield the same total cost for the firm. - Figure 7.1. Page 232
5The 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)
6- 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?
7- 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 ?
-
8Deriving 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)
9The 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)
10The 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)
11Tabel 7.1. Page 245Price 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
12Short Run Cost Minimization
- TC TVC TFC
- TC Total Cost.
- TVC Total Variable Cost.
- TFC Total Fixed Cost.
13Short 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.
14Figure 7.14 Page 248Short Run Cost Minimization
With One Fixed Input.
15- Figure 7.15. Page 249
- Short Run Input Demand Versus Long Run Input
Demand.