This is a PowerPoint presentation on the production process and associated costs. A left mouse click or the enter key will add and element to a slide or move you to the next slide. The back space key will take you back an element or slide. If you wish to exit the presentation, the escape key will do it! R. Larry Reynolds ã 1997

Principles of Microeconomics Production Production is an activity where resources are altered or changed and there is an increase in the ability of these resources to satisfy wants. change in physical characteristics change in location change in time change in ownership Fall ‘ 97 Principles of Microeconomics

Principles of Microeconomics Production and Cost Production is a technical relationship between a set of inputs or resources and a set of outputs or goods. QX = f( inputs [land, labour, capital], technology, . . . ) [Legal and social/cultural institutions influence the production function.] Cost functions are the pecuniary relationships between outputs and the costs of production; Cost = f(QX {inputs, technology} , prices of inputs, . . . ) Cost functions are determined by input prices and production relationships. It is necessary to understand production functions if you are to interpret cost data. Fall ‘ 97 Principles of Microeconomics

Principles of Microeconomics Costs Costs are incurred as a result of production. The important concept of cost is opportunity cost [marginal cost]. These are the costs associated with an activity. When inputs or resources are used to produce one good, the other goods they could have been used to produce are sacrificed. Costs may be in real or monetary terms; implicit costs explicit costs Fall ‘ 97 Principles of Microeconomics

Principles of Microeconomics Implicit Costs Opportunity costs or MC should include all costs associated with an activity. Many of the costs are implicit and difficult to measure. A production activity may adversely affect a person’s health. This is an implicit cost that is difficult to measure. Another activity may reduce the time for other activities. It may be possible to make a monetary estimate of the value. Fall ‘ 97 Principles of Microeconomics

Principles of Microeconomics Explicit Costs Explicit costs are those costs where there is an actual expenditure in a market. The costs of labour or interest payments are examples. Some implicit costs are estimated and used in the decision process. Depreciation is an example. Fall ‘ 97 Principles of Microeconomics

Principles of Microeconomics Normal Profit In neoclassical economics, all costs should be included: wages represent the cost of labour interest represents the cost of Kapital rent represents the cost of land “normal profit [ P ]” represents the cost of entrepreneurial activity normal profit includes risk Fall ‘ 97 Principles of Microeconomics

Principles of Microeconomics Production Function A production function expresses the relationship between a set of inputs and the output of a good or service. The relationship is determined by the nature of the good and technology. A production function is “like” a recipe for cookies; it tells you the quantities of each ingredient, how to combine and cook, and how many cookies you will produce. Fall ‘ 97 Principles of Microeconomics

Principles of Microeconomics QX = f(L, K, R, technology, . . . ) QX = quantity of output L = labour input K = Kapital input R = natural resources [land] Decisions about alternative ways to produce good X require that we have information about how each variable influences QX. One method used to identify the effects of each variable on output is to vary one input at a time. The use of the ceteris paribus convention allows this analysis. The time period used for analysis also provides a way to determine the effects of various changes of inputs on the output. Fall ‘ 97 Principles of Microeconomics

Principles of Microeconomics Technology The production process [and as result, costs] is divided up into various time periods; the “very long run” is a period sufficiently long enough that technology used in the production process changes. In shorter time periods [long run, short run and market periods], technology is a constant. Fall ‘ 97 Principles of Microeconomics

Principles of Microeconomics Long Run The long run is a period that: is short enough that technology is unchanged. all other inputs [labour, kapital, land, . . . ] are variable, i.e. can be altered. these inputs may be altered in fixed or variable proportions. This may be important in some production processes. If inputs are altered, the output changes. QX = f(L, K, R, . . . ) technology is constant Fall ‘ 97 Principles of Microeconomics

Principles of Microeconomics Short Run The short run is a period in which at least one of the inputs has become a constant and at least one of the inputs is a variable. If kapital [K] and land [R] are fixed or constant in the short run, labour [L] is the variable input. Output is changed by altering the labour input. QX = f(L) Technology, K and R are fixed or constant. Fall ‘ 97 Principles of Microeconomics

Principles of Microeconomics Market Period When Alfred Marshall included time into the analysis of production and cost, he included a “market period” in which inputs, technology and consequently outputs could not be varied. The supply function would be perfectly inelastic in this case. Fall ‘ 97 Principles of Microeconomics

Principles of Microeconomics Production in the Short Run Consider a production process where K, R and technology are fixed: As L is changed, the output changes, QX= f(L) Production of Good X L APL MPL TPL L = labour input TPL = QX = output of good X APL = average product [TP/L] MPL = Marginal product [DTP/ DL] -- DTPL=4 DL = 1 1 4 4 4 2 10 5 6 APL = TPL L APL = TPL L APL = TPL L 3 20 6.67 10 MPL = DTPL DL MPL = DTPL DL 4 25 6.25 5 5 6 7 9 8 29 32 34 35 5.8 5.3 4.87 4.37 3.89 4 3 2 1 APL = TPL L = output input = Efficiency Maximum of APL is at the 3 input of labour. Fall ‘ 97 Principles of Microeconomics

Principles of Microeconomics Production in the Short Run APL = TPL L = output input Efficiency of labour Production of Good X L APL MPL TPL 5 6 7 9 8 -- 1 4 2 10 3 20 6.67 25 6.25 29 32 34 35 5.8 5.3 4.87 4.37 3.89 Notice that the APL increases as the first three units of labour are added to the fixed inputs of K and R. The maximum efficiency of Labour or maximum APL , given our technology, plant and natural resources is with the third worker. As additional units of labour are added beyond the third worker the output per worker [APL ] declines. Fall ‘ 97 Principles of Microeconomics

Principles of Microeconomics Graphically TPL can be shown: TPL initially increases at an increasing rate; it is convex from below. L 5 6 7 9 8 1 2 3 4 TPL 10 20 25 29 32 34 35 . . . . TPL . 1 2 3 4 5 6 7 8 9 Labour Output, QX 5 10 15 20 25 30 35 . Maximum output . After some point it then increases at a decreasing rate and reaches a maximum level of output, . . . and declines Fall ‘ 97 Principles of Microeconomics

Principles of Microeconomics Given the TP , the APL can calculated: TPL 4 10 20 25 29 32 34 35 L 5 6 7 9 8 1 2 3 4 APL 4 5 6.67 6.25 5.8 5.3 4.87 4.37 3.89 APL = TPL L = output input Efficiency of labour APL 1 2 3 4 5 6 7 8 9 Labour 2 4 6 8 10 . . . . . . . . . . APL Fall ‘ 97 Principles of Microeconomics

Principles of Microeconomics . . . 1 2 3 4 5 6 7 8 9 Labour Output, QX 5 10 15 20 25 30 35 Z Z W . . TPL The APL is the slope of a ray from the origin to the TPL . . Graphically the relationship between APL and TPL can be shown: . M 1 unit of L produces 4Q, APL is 4/1 = 4 or the slope of line 0H. H . rise/run = 5 2 units of L produces 10Q, rise/run = 4 APL is 10/2 = 5 or the slope of line 0M. . . 3 units of L produces 20Q, 4 APL is 20/3 = 6.67 or the slope of line 0Z. APL . 4 units of L produces 25Q, 1 2 3 4 5 6 7 8 9 Labour 2 4 6 8 10 . . APL is 25/4 = 6.25 or the slope of line 0W. . . . . . . As additional units of L are added, the AP falls. . The maximum AP is where the ray with the greatest slope is tangent to the TP. APL Fall ‘ 97 Principles of Microeconomics

Principles of Microeconomics 4 . 1 2 3 4 5 6 7 8 9 Labour Output, QX 5 10 15 20 25 30 35 1 2 3 4 5 6 7 8 9 2 6 8 TPL APL Given TPL , the APL was calculated and graphed. MPL was calculated as the change in TPL given a change in L. L 5 6 7 9 8 1 2 3 4 MPL -- 4 6 10 5 3 2 1 APL 4 5 6.67 6.25 5.8 5.3 4.87 4.37 3.89 TPL 4 10 20 25 29 32 34 35 4-0 The first unit of labour added 4 units of output. “Between” the 1st and 2cd units of labour, Q increases by 6. . . Note: Where MPL = APL, APL is a maximum. . MPL = APL . . . . . . MPL Remember: MP is graphed at “between” units of L. Fall ‘ 97 Principles of Microeconomics

Principles of Microeconomics 4 . 1 2 3 4 5 6 7 8 9 Labour Output, QX 5 10 15 20 25 30 35 1 2 3 4 5 6 7 8 9 2 6 8 TPL APL MPL Z Useful things to notice: 1. MPL is the slope of TPL. 2. When TPL increases at an increasing rate, MPL increases. At the inflection point in the TPL , MPL is a maximum. When TPL increases at a decreasing rate, MPL is decreasing. 3. The APL is a maximum when: a. MPL = APL , b. the slope of the ray from origin is tangent to TPL . 4. When MPL > APL the APL is increasing. When MPL < APL the APL is decreasing. 5. When MPL is 0, the slope of TPL is 0, and TP is a maximum. Fall ‘ 97 Principles of Microeconomics

Principles of Microeconomics Summary: TPL , MPL and APL Z In many production processes Q initially increases at an increasing rate. This is due to division of labour and a “better” mix of the variable input with the fixed inputs. TPL TPL At the inflection point Diminishing marginal product As Q [TPL ]increases at an increasing rate, MP increases. L As Q [TPL ]increases at a decreasing rate, MPL decreases. MPL APL MPL is a max {MP< AP, AP falls} Where 0Z is tangent to TPL , APL is a maximum; APL = MPL . When TPL is a maximum, MPL is zero. APL When TPL is decreasing, MPL is negative. MPL {MP> AP, AP rises} L1 L2 L3 L Fall ‘ 97 Principles of Microeconomics

Principles of Microeconomics PRODUCTION LABOUR KAPITAL OUTPUT MP AP 5 1 8 2 23 3 42 4 57 67 6 74 7 79 82 9 83 10 To calculate AP: APL = TPL L AP is a maximum when L = 4. 0 ¸ 0 = ? DTPL = 8 DL= 1 8 8.0 8 ¸ 1 = 8 DTPL = 15 DL= 1 15 11.5 23 ¸ 2 = 11.5 DTPL = 19 Note that MP is 15 between 3rd & 4th units of L, it is 10 between 4th & 5th, so it equals AP = 14.25 at L=4. DL= 1 19 42 ¸ 3 = 14 14.0 DTPL = 15 DL= 1 57¸4 = 14.25 15 14.25 DTPL = 10 DL= 1 67 ¸ 5 = 13.4 10 13.4 DTPL = 7 DL= 1 7 12.33 5 11.28 3 10.25 To calculate MP: 1 9.22 MPL = DTPL DL -1 8.2 MP is a maximum between 2cd and 3rd unit of L. Fall ‘ 97 Principles of Microeconomics

Principles of Microeconomics PRODUCTION LABOUR KAPITAL OUTPUT MP AP 5 1 8 2 23 3 42 4 57 67 6 74 7 79 82 9 83 10 8.0 11.5 14.0 14.25 13.4 12.33 11.28 10.25 9.22 8.2 15 19 -1 As L is added to production process, output per worker [AP] increases. to a maximum “efficiency” [output/input which occurs at L = 4. MP increases to a max between the 2cd & 3rd units of L. When MP > AP the output per worker is increasing. Division of Labour and a more efficient mix of L, K & R causes AP to increase. Output per worker decreases after the 4th worker. “Too many” workers for K, R & tech, MP< AP. Diminishing Marginal Productivity begins with the 4rth unit of L. Fall ‘ 97 Principles of Microeconomics

Principles of Microeconomics The price of labour [PL] is $4 per unit and the price of kapital [PK] is $6 per unit. Calculate the cost functions for this production process. TFC = PK x K = $6K = 6 x5 = $30, This cost does not change in the short run. TVC = PL x L = $4L, as L changes TVC and Output change. PRODUCTION AND COST LABOUR KAPITAL OUTPUT AP MP TFC TVC TC AFC AVC ATC 5 -- 1 8 2 23 11.5 15 3 42 14 19 4 57 14.25 67 13.4 10 6 74 12.33 7 79 11.28 82 10.25 9 83 9.22 8.2 -1 TC = TVC+TFC x $4 = $30 + =$30 $ 0 x $4 = + =$34 $ 4 x $4 = + =$38 $ 8 x $4 = + =$42 $12 x $4 = + =$46 $16 x $4 = + =$50 $20 + =$54 $24 + =$58 $28 + =$62 $32 + =$66 $36 + =$70 $40 Fall ‘ 97 Principles of Microeconomics

Principles of Microeconomics PRODUCTION AND COST LABOUR KAPITAL OUTPUT AP MP TFC TVC TC AFC AVC ATC 5 -- 1 8 2 23 11.5 15 3 42 14 19 4 57 14.25 67 13.4 10 6 74 12.33 7 79 11.28 82 10.25 9 83 9.22 8.2 -1 The price of labour [PL] is $4 per unit and the price of kapital [PK] is $6 per unit. Calculate the cost functions for this production process. $30 $ 0 $ 4 $ 8 $12 $16 $20 $24 $28 $32 $36 $40 $38 $42 $46 $50 $54 $58 $62 $66 $70 $34 AFC = TFC¸Q = $30¸Q ATC = AVC + AFC = TC¸Q AVC = TVC ¸ Q $3.75 $ .50 $4.25 $1.30 $ .35 $1.65 $ .71 $ .29 $1.00 $ .53 $ .28 $.81 $ .45 $ .30 $.75 $ .41 $ .32 $.729 $ .38 $ .35 $.734 $ .37 $ .39 $.76 $ .36 $ .43 $.79 $ .37 $ .49 $.86 Fall ‘ 97 Principles of Microeconomics

Principles of Microeconomics PRODUCTION AND COST LABOUR KAPITAL OUTPUT AP MP TFC TVC TC AFC AVC ATC 5 -- 1 8 2 23 11.5 15 3 42 14 19 4 57 14.25 67 13.4 10 6 74 12.33 7 79 11.28 82 10.25 9 83 9.22 8.2 -1 $30 $ 0 $ 4 $ 8 $12 $16 $20 $24 $28 $32 $36 $40 $38 $42 $46 $50 $54 $58 $62 $66 $70 $34 $3.75 $1.30 $ .71 $ .53 $ .45 $ .41 $ .38 $ .37 $ .36 $ .50 $ .35 $ .29 $ .28 $ .30 $ .32 $ .39 $ .43 $ .49 $4.25 $1.65 $1.00 $.81 $.75 $.729 $.734 $.76 $.79 $.86 Things to note . . . As AP increases, AVC decreases. Since AFC declines, it will “pull” the ATC down as Q increases beyond the minimum of the AVC. When AP is a maximum, AVC is a minimum. AFC declines so long as Q or output increases. {Up to the point where TP becomes negative.} Fall ‘ 97 Principles of Microeconomics

Principles of Microeconomics L x PL = TVC TPL is Q L x PL = TVC Z TVC = L x PL TVC TPL = Q TPL TPL When TP or Q increases at an increasing rate, Z’ L2 x PL TVC TVC increases at a decreasing rate. TPL [a mirror image] L2 x PL L1 x PL [a mirror image] Q* is the output with the lowest AVC! [Max AP] TPL = Q Q L1 L2 L3 L Q* At L1 [inflection point] the MP is a maximum; the point of Diminishing Marginal productivity begins, each additional worker increases output, but at a smaller and smaller amount. At L2 the AP is a maximum; output per worker is a maximum, “maximum efficiency;” additional units of labour are less “productive.” At L3 the TP is a maximum; this is the maximum amout of output [Q] that can be produced given the size of the plant [fixed input K]. Additional [marginal] L is negative. Fall ‘ 97 Principles of Microeconomics

Principles of Microeconomics The average variable cost [AVC] and marginal cost [MC] are “mirror” images of the AP and MP functions. MPL APL APL APL MPL APL MPL L1 L2 L3 L3 L The maximum of the AP is consistent with the minimum of the AVC. $ MC = 1 MP x PL APL MPL MC AVC AVC = 1 AP x PL AVC Q APL x L2 Fall ‘ 97 Principles of Microeconomics

Principles of Microeconomics $ MC will intersect the AVC at the minimum of the AVC [always]. MC ATC AVC ATC* R J MC will intersect the ATC at the minimum of the ATC. TC = ATC* x Q** AVC* The vertical distance between ATC and AVC at any output is the AFC. At Q** AFC is RJ. TVC = AVC* x Q* Q* Q** Q At Q* output, the AVC is at a minimum AVC* [also max of APL]. At Q** the ATC is at a MINIMUM. Fall ‘ 97 Principles of Microeconomics

Principles of Microeconomics The Long Run The long run is a period of time where: technology is constant All inputs are variable The long run period is a series of short run periods. [For each short run period there is a set of TP, AP, MP, MC, AFC, AVC, ATC, TC, TVC & TFC for each possible scale of plant] Fall ‘ 97 Principles of Microeconomics

Principles of Microeconomics LONG RUN COSTS Plant ATC* is the optimal size! MC1 LRMC $ ATC! LRAC MC2 ATC6 ATC2 ATC5 ATC3 ATC* ATC* There is a long run marginal cost function. Cmin At Q* the cost per unit are minimized [the least inputs used]. Q* Q For Plant size 1, the costs are ATC1 and MC1 : For a bigger Plant 2, the unit costs move out and down. It is more cost effective. As bigger plants are built the ATC moves out and down. Eventually, the plant size is “too large,” the ATC moves out but also up! An “envelope curve” is constructed to represent the long run AC [LRAC]. Fall ‘ 97 Principles of Microeconomics

Principles of Microeconomics The LRAC LRAC is “U-Shaped” The LRAC initially decreases due to “economies of scale” economies of scale are due to division of labour. Eventually, “diseconomies of scale” begin usually lack of adequate information to manage the production process Fall ‘ 97 Principles of Microeconomics

Principles of Microeconomics Calculation of LRAC With a little mathematics, the long run cost functions can be calculated. It is easier to use equations rather than tables and graphs. If consumer behavior, production and cost is understood, you can then think about how to achieve your objectives. Fall ‘ 97 Principles of Microeconomics