Chapter 9 - Production and cost in the long run. In this chapter students will be able to: Draw a graph of a typical production isoquant and use the definition of an isoquant to explain why isoquants must be downward sloping, discuss the properties of an isoquant, construct isocost curves for a given level of expenditure on inputs,...
Managerial Economics ninth edition Thomas Maurice Chapter Production & Cost in the Long Run McGrawHill/Irwin McGrawHill/Irwin Managerial Economics, 9e Managerial Economics, 9e Copyright © 2008 by the McGrawHill Companies, Inc. All rights reserved Managerial Economics Production Isoquants • In the long run, all inputs are variable & isoquants are used to study production decisions • An isoquant is a curve showing all possible input combinations capable of producing a given level of output • Isoquants are downward sloping; if greater amounts of labor are used, less capital is required to produce a given output 92 Managerial Economics Typical Isoquants 93 (Figure 9.1) Managerial Economics Marginal Rate of Technical Substitution • The MRTS is the slope of an isoquant & measures the rate at which the two inputs can be substituted for one another while maintaining a constant level of output MRTS K L T h e m inus s ig n is ad d e d t o m ak e MRTS a po s it ive num b e r s inc e K L , t h e s lo pe o f t h e is o q uant , is ne g at ive 94 Managerial Economics Marginal Rate of Technical Substitution • The MRTS can also be expressed as the ratio of two marginal products: MRTS MPL MPK A s lab o r is s ub s t it ut e d f o r c apit al, MPL d e c line s & MPK r is e s c aus ing MRTS t o d im inis h MRTS 95 K L MPL MPK Managerial Economics Isocost Curves • Show various combinations of inputs that may be purchased for given level of expenditure ( C ) at given input prices ( w , r ) K C r w L r • Slope of an isocost curve is the negative of the input price ratio ( w r ) • K -intercept is C r 96 • Represents amount of capital that may be purchased if zero labor is purchased Managerial Economics Isocost Curves (Figures 9.2 & 9.3) 97 Managerial Economics Optimal Combination of Inputs • Minimize total cost of producing Q by choosing the input combination on the isoquant for which Q is just tangent to an isocost curve • Two slopes are equal in equilibrium • Implies marginal product per dollar spent on last unit of each input is the same MPL MPK 98 MPL w o r r w MPK r Managerial Economics Optimal Input Combination to Minimize Cost for Given Output (Figure 9.4) 99 Managerial Economics Optimization & Cost • Expansion path gives the efficient (least-cost) input combinations for every level of output • Derived for a specific set of input prices • Along expansion path, inputprice ratio is constant & equal to the marginal rate of technical substitution 9 Managerial Economics Returns to Scale f(cL, cK) = zQ • If all inputs are increased by a factor of c & output goes up by a factor of z then, in general, a producer experiences: • Increasing returns to scale if z > c; output goes up proportionately more than the increase in input usage • Decreasing returns to scale if z