Managerial Economics & Business Strategy Chapter 5 The Production Process and Costs

How do we know the OPTIMAL level of capital and labor in the long run Isoquant The combinations of inputs (K, L) that yield the producer the same level of output. Shape reflects how managers can substitute inputs and maintaining the same level of output.

Isoquants are Convex  K and L are not perfect substitutes Capital Increase Output Q2= 300 units Q1= 200 units Q0= 100 units Labor Substitute Labor for Capital

Marginal Rate of Technical Substitution (MRTS) Slope of the Isoquant How much of the “other” variable do you need to keep output constant? The rate at which two inputs are substituted while maintaining the same output level.

Linear Isoquants Capital and labor are perfect substitutes Q = aK + bL MRTSKL = b/a Substituted at a constant rate, independent of the input levels employed. Q3 Q2 Q1 Increasing Output L K

Leontief Isoquants Capital and labor are perfect complements. K Increasing Output Capital and labor are perfect complements. Capital and labor are used in fixed-proportions. Q = min {bK, cL} No input substitution along isoquants So…. no MRTSKL L

Cobb-Douglas Isoquants Inputs are not perfectly substitutable. Diminishing marginal rate of technical substitution. As less of one input is used in the production process, increasingly more of the other input must be employed to produce the same output level. Q = KaLb MRTSKL = MPL/MPK K Q3 Increasing Output Q2 Q1 L

Isocost The combinations of inputs that produce a given level of output at the same cost: wL + rK = C Rearranging, K= (1/r)C - (w/r)L For given input prices, isocosts farther from the origin are associated with higher costs. Slope is the ratio of input prices Price of labor / price of capital Changes in input prices change the slope of the isocost line. K New Isocost Line associated with higher costs (C0 < C1). C1/r C0 C0/w C0/r C1 L C1/w K New Isocost Line for a decrease in the wage (price of labor: w0 > w1). C/r C/w1 L C/w0

Cost Minimization Slope of the isoquant and isocost are equal What was the slope of the isoquant? Marginal Rate of Technical Substitution What was the slope of the isocost? Price ratio Marginal product per dollar spent should be equal for all inputs: But, this is just

Slope of Isocost = Slope of Isoquant Cost Minimization K Point of Cost Minimization Q L Slope of Isocost = Slope of Isoquant

Optimal Input Substitution If we start at point A at a cost of C0. Suppose w0 falls to w1. The isocost curve rotates counterclockwise Cannot use original level of capital like we did with consumption. Need to keep output constant Substitute Labor for capital because it’s cheaper Now can produce at point B using more labor and less capital to produce the same output K A K0 C1/w1 B K1 L1 Q0 L0 C0/w0 L

Cost Analysis Types of Costs Fixed costs (FC) Variable costs (VC) Total costs (TC) Sunk costs