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Economics for Managers by y Paul Farnham Chapter 5: Production and Cost Analysis in the Short Run © 2005 Prentice Hall, Inc. 5.1 Defining the P d ti Production Function F ti The formula can be read as “quantity quantity of output is a function of the inputs listed inside the parentheses” Q = f (L, K, M…) where Q = quantity of output L = quantity of labor input K = quantity y of capital input M = quantity of materials input © 2005 Prentice Hall, Inc. 5.2 Fixed Inputs Versus V i bl Inputs Variable I t Fixed input: quantity a manager cannot change g during g a given g time Variable input: quantity a manager can change during a given time Amount of output would vary as managers made decisions regarding amounts of input © 2005 Prentice Hall, Inc. 5.3 Short-run Versus L Long-run P d ti Production Not expressed in terms of calendar time,, but in terms of fixed and variable inputs Short Short-run run production function: involves at least one fixed input Long-run Long run production function: production process in which all inputs are variable © 2005 Prentice Hall, Inc. 5.4 Managerial Rule of Thumb: Short-run Short run Production and Long-run Planning Managers operate in the short run, but must have long-run vision i i They need to be aware that the currentt amountt off fixed fi d inputs i t may not be appropriate as market conditions change Managers make more long run economic decisions © 2005 Prentice Hall, Inc. 5.5 Model of the Short-run P d ti Production Function F ti Total product: total quantity of output produced with a given quantity of fixed and variable inputs TP or Q = f (L, K) where TP or Q = total p product or quantity q y of output L = quantity of labor input K = quantity of capital input © 2005 Prentice Hall, Inc. 5.6 Average Product Average product: A d t amountt off output per unit of variable input AP = TP / L or Q / L where AP = The average product of labor © 2005 Prentice Hall, Inc. 5.7 Marginal Product Marginal M i l product: d t the th additional dditi l output produced with an additional unit of variable input MP = ΔTP / ΔL = ΔQ / ΔL where MP = The marginal product of labor © 2005 Prentice Hall, Inc. 5.8 Total Product: Short-run Production Function Figure 5.1a Law of diminishing returns where marginal product eventually decreases TP 0 © 2005 Prentice Hall, Inc. L1 L2 L3 L 5.9 TP: Short-run P d ti Production Function F ti TP increases rapidly up to level of labor input L1 then increases at a slower rate as labor input increases TP curve becomes flatter and flatter until it reaches maximum output level at L3 Curve implies that marginal product of labor first increases rapidly then decreases, eventually becoming zero or less © 2005 Prentice Hall, Inc. 5.10 AP and MP: Short-run Production Function Figure 5.1b MP AP 0 © 2005 Prentice Hall, Inc. L1 L2 L3 L 5.11 AP and MP: Short-run Production Function Between zero and L2, MP curve lies above AP curve, causing AP curve to increase Below L2, MP curve is below AP curve, causing AP curve to decrease Therefore, MP curve must intersect AP curve at maximum point i t off AP curve © 2005 Prentice Hall, Inc. 5.12 Economic Explanation Increasing marginal returns: region where MP curve is positive and d increasing i i Law of diminishing returns: region i where h marginal i l product d t curve is positive but decreasing Negative N ti marginal i l returns: t region i where product curve is negative so that TP is decreasing © 2005 Prentice Hall, Inc. 5.13 Law of Diminishing R t Returns Additional output generated by additional units of variable input p (MP) is decreasing Occurs because capital input and technologies are held constant © 2005 Prentice Hall, Inc. 5.14 Productivity Changes A Across I Industries d t i Q = f (K, L, E, M, t) where Q = industry output K = capital services L = labor services E = energy use M = materials use t = level of technology © 2005 Prentice Hall, Inc. 5.15 Model of Short-run C t Functions Costs F ti Cost function: shows relationship between cost of p production and level of output Opportunity cost: reflects use of resources in one activity while foregoing g g another © 2005 Prentice Hall, Inc. 5.16 Model of Short-run C t Functions Costs F ti Explicit cost: payment to an individual that is recorded in an accounting system Implicit costs: value of using a resource that is not explicitly paid out,, is often difficult to measure,, and not recorded in an accounting system © 2005 Prentice Hall, Inc. 5.17 Measuring O Opportunity t it Cost C t Prices that a firm pays for input reflects opportunity cost If managers do not recognize opportunity costs, they may have t too much h invested i t d in i buildings b ildi or other assets Historic Hi t i cost: t amountt off money a firm paid for an input when it was purchased © 2005 Prentice Hall, Inc. 5.18 Accounting Profit and E Economic i Profit P fit Profit: difference between total revenue and total cost of production d ti Accounting profit: difference b t between total t t l revenue and d total t t l explicit cost Economic E i profit: fit difference diff between total revenue and total costs, both implicit and explicit © 2005 Prentice Hall, Inc. 5.19 Managerial Rule of Thumb: I Importance t off Opportunity O t it Costs C t Measuring opportunity costs can be difficult because accountants are trained to examine explicit costs Managers need to take into account both types yp of costs (explicit and opportunity costs) © 2005 Prentice Hall, Inc. 5.20 Short-run Short run Cost Functions Short-run cost function: shows relationship p between output p and costs based on underlying shortrun production function It is a cost function for short-run production process p p in which there is at least one fixed unit of production © 2005 Prentice Hall, Inc. 5.21 Costs Total fixed cost: cost of using fixed input p Total variable cost: price per unit of labor times quantity of labor input Total cost: sum of total fixed cost plus total variable costs © 2005 Prentice Hall, Inc. 5.22 Costs Average A fi fixed d cost: totall fixed fi d cost per unit of output Average variable cost: total variable cost per unit of output Average total cost: total cost per unit of output plus average variable cost Marginal cost: additional cost of producing additional units of output © 2005 Prentice Hall, Inc. 5.23 Total, Average, and M Marginal i l Cost C t AFC decreases continuously as more output p is produced p Since TFC is constant, AFC must decline as output increases AVC and ATC first decrease then increase ATC always equals AFC plus AVC © 2005 Prentice Hall, Inc. 5.24 TC, TCV, TFC Functions Figure 5.2a TC TVC TFC 0 © 2005 Prentice Hall, Inc. Q1 Q2 Q3 Q 5.25 MC, ATC, AVC, and d AFC Functions F ti Figure 5.2b MC ATC AVC 0 © 2005 Prentice Hall, Inc. Q1 Q2 Q3 AFC Q 5.26 Short-run P d ti Production and d Cost C t MC AVC AP 0 MP L1 © 2005 Prentice Hall, Inc. L2 L 0 Q1 Q2 Q 5.27 Managerial Rule of Thumb: U d Understanding t di Your Y Costs C t M Managers need d to t understand d t d • Technology and prices paid for iinputs t off production d ti • Difference between variable and fixed costs t • Difference between average costs (costs per unit of output) and marginal costs (additional costs of producing p g additional units of output) p ) © 2005 Prentice Hall, Inc. 5.28 Econometric Estimation off C Costt F Functions ti Dean’s D ’ studies t di off a furniture f it factory, f t a leather belt shop, 1976 Johnston’s J h t ’ study t d off British B iti h electric l ti generating plants, road passenger transport and food processing firm, transport, firm 1960 Hall, Hall 1986 Blinder, et al, 1990s © 2005 Prentice Hall, Inc. 5.29 Summary of Key Terms Accounting profit Explicit cost Average g fixed Fixed input p cost Average product Average total cost Average variable costt Cost function Economic profit © 2005 Prentice Hall, Inc. Historic cost Implicit cost Marginal returns Diminishing returns Long-run production functions 5.30 Summary of Key Terms Marginal cost Total T t l costt Marginal product Total fixed cost Negative N ti marginal i l Total product returns pp y Production function Opportunity cost Short-run production function Total variable cost Short-run cost function Variable input p © 2005 Prentice Hall, Inc. 5.31