Minimizing Cost The Long Run Cost Minimization Problem

Minimizing Cost

The Long Run Cost Minimization Problem n 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. n 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) n Min TC = w. L + r. K 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 n 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 n 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)

n 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?

n 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 = 4 K K = 10 L = 40 TC = ?

Deriving The Input Demand Curves From A Production Function n 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 n 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) n 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. 44 -0. 69

Short Run Cost Minimization n TC = TVC + TFC TC = Total Cost. TVC = Total Variable Cost. TFC = Total Fixed Cost.

Short Run Cost Minimization (continued) n TVC: the sum of expenditures on variable inputs, such as labor and materials, at the short run cost minimizing input combination. n 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.

n Figure 7. 15. Page 249 Short Run Input Demand Versus Long Run Input Demand.