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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 245Price Elasticities Of Input Demand For Manufacturing Industries In Alabama

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 7.15. Page 249

Short Run Input Demand Versus Long Run Input Demand.

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