Slide 1Chapter OutlineIntroductionThe Production FunctionShort-Run versus Long-Run Decisions: Fixed and Variable InputsMeasures of ProductivityMeasures of Productivity in ActionRelation between Productivity Measures in ActionThe Manager’s Role in the Production ProcessManager’s Role in the Production Process in ActionAlgebraic Forms of Production FunctionsAlgebraic Forms of Production Functions in ActionAlgebraic Measures of ProductivityAlgebraic Measures of Productivity in ActionIsoquants and Marginal Rate of Technical SubstitutionSlide 16Diminishing Marginal Rate of Technical Substitution in ActionIsocost and Changes in Isocost LinesIsocost LineChanges in the Isocost LineChanges in the Isocost LineCost-Minimization Input Rule in ActionCost Minimization and the Cost-Minimizing Input RuleCost-Minimizing Input Rule in ActionOptimal Input Substitution in ActionThe Cost FunctionShort-Run Costs in ActionAverage and Marginal CostsThe Relationship between Average and Marginal Costs in ActionFixed and Sunk CostsLong-Run CostsLong-Run Average Total Costs in ActionEconomies of ScaleEconomies and Diseconomies of Scale in ActionConstant Returns to Scale in ActionMultiple-Output Cost FunctionMultiple-Output Cost Function in ActionConclusionCHAPTER 5The Production Process and Costs© 2014 by McGraw-Hill Education. All Rights Reserved.Chapter Outline•The production function–Short- versus long-run decisions–Measures of productivity–Manager’s role in production process–Production function and productivity algebraic forms–Isoquants and isocosts–Cost minimization and optimal input substitution•The cost function–Short-run costs–Average and marginal costs–Relations among costs–Fixed and sunk costs–Cost function algebraic forms–Long-run costs and economies of scale•Multiple-output cost functions–Economies of scope and cost complementarityCopyright © 2013 by the McGraw-Hill Companies, Inc. All rights reserved.5-2Chapter OverviewIntroduction•Chapter 4 focused on how consumers adjust consumption decisions in reaction to price and income changes. The theory developed illustrates the underlying principles of individual and market demand curves.•This chapter examines how managers select the optimal mix of inputs that minimize production costs.Copyright © 2013 by the McGraw-Hill Companies, Inc. All rights reserved.5-3Chapter OverviewThe Production Function•Mathematical function that defines the maximum amount of output that can be produced with a given set of inputs., where – is the level of output.– is the quantity of capital input.– is the quantity of labor input.• Copyright © 2013 by the McGraw-Hill Companies, Inc. All rights reserved.5-4The Production FunctionShort-Run versus Long-Run Decisions: Fixed and Variable Inputs•Short-run–Period of time where some factors of production (inputs) are fixed, and constrain a manager’s decisions.•Long-run–Period of time over which all factors of production (inputs) are variable, and can be adjusted by a manager.Copyright © 2013 by the McGraw-Hill Companies, Inc. All rights reserved.5-5The Production FunctionMeasures of Productivity•Total product (TP)–Maximum level of output that can be produced with a given amount of inputs.•Average product (AP)–A measure of the output produced per unit of input.•Average product of labor: •Average product of capital: •Marginal product (MP)–The change in total product (output) attributable to the last unit of an input.•Marginal product of labor: •Marginal product of capital: • Copyright © 2013 by the McGraw-Hill Companies, Inc. All rights reserved.5-6The Production FunctionMeasures of Productivity in Action•Consider the following production function when 5 units of labor and 10 units of capital are combined produce: .•Compute the average product of labor. units per worker•Compute the average product of capital. units capital unit• Copyright © 2013 by the McGraw-Hill Companies, Inc. All rights reserved.5-7The Production FunctionRelation between Productivity Measures in ActionCopyright © 2013 by the McGraw-Hill Companies, Inc. All rights reserved.5-8Labor input(holding capital constant)0Total productAverage productMarginal productTotal product (TP)Average product (APL)Marginal product (MPL)Increasing marginal returns to laborDecreasing marginal returns to laborNegativemarginal returns to laborThe Production FunctionThe Manager’s Role in the Production Process•Produce output on the production function.–Aligning incentives to induce maximum worker effort.•Use the right mix of inputs to maximize profits.–To maximize profits when labor or capital vary in the short run, the manager will hire:•Labor until the value of the marginal product of labor equals the wage rate: , where •Capital until the value of the marginal product of capital equals the rental rate: , where • Copyright © 2013 by the McGraw-Hill Companies, Inc. All rights reserved.5-9The Production FunctionManager’s Role in the Production Process in Action•Suppose a firm sells its output in a competitive market where its output is sold at $5 per unit. If workers are also hired at a competitive wage of $200, what is the marginal productivity of the last worker?•Since, and , then, units–The marginal productivity of the last unit of labor is 40 units.–Alternatively, management should hire labor such that the last unit of labor produces 40 units.• Copyright © 2013 by the McGraw-Hill Companies, Inc. All rights reserved.5-10The Production FunctionAlgebraic Forms of Production Functions•Commonly used algebraic production function forms:–Linear: , where and are constants.–Leontief: , where and are constants.–Cobb-Douglas: , where and are constants.• Copyright © 2013 by the McGraw-Hill Companies, Inc. All rights reserved.5-11The Production FunctionAlgebraic Forms of Production Functions in Action•Suppose that a firm’s estimated production function is:•How much output is produced when 3 units of capital and 7 units of labor are employed? units• Copyright © 2013 by the McGraw-Hill Companies, Inc. All rights reserved.5-12The Production FunctionAlgebraic Measures of Productivity•Given the commonly used algebraic production function forms, we can compute the measures of productivity as follows:–Linear: •Marginal products: and •Average products: and –Cobb-Douglas: •Marginal products: and •Average products: and • Copyright © 2013