1 Production, Costs, and Supply Principles of Microeconomics Professor Dalton ECON 202 – Fall 2013

2 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

3 Production and Cost  Production is a technical relationship between a set of inputs or resources and a set of outputs or goods. Q X = f( inputs [land, labor, 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(Q X {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.

4 Costs  Costs are incurred as a result of production. 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

5 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.

6 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.

7 Normal Profit  In neoclassical economics, all costs should be included: wages represent the cost of labor Rental rate of capital represents the cost of capital Rental rate of land represents the cost of land “normal profit [ π ]” represents the cost of entrepreneurial activity  normal profit includes reward for risk-bearing

8 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.

9 QX QX = f(L, K, R, technology,... ) Q X = quantity of output L = labor input K = capital input R = natural resources [land] Decisions about alternative ways to produce good X require that we have information about how each variable influences Q X. 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.

10 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.

11 Long Run  The long run is a period that: is short enough that technology is unchanged. all other inputs [labor, capital, 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. Q X = f(L, K, R,... ) technology is constant

12 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 capital [K] and land [R] are fixed or constant in the short run, labor [L] is the variable input. Output is changed by altering the labour input. Q X = f(L) Technology, K and R are fixed or constant.

13 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.

14 Production in the Short Run Consider a production process where K, R and technology are fixed: As L is changed, the output changes, Q X = f(L) L = labor input TP L = Q X = output of good X AP L = average product [TP/L] MP L = Marginal product [  TP/  L] Production of Good X LAP L MP L TP L 00 AP L = TP L L MP L =  TP L LL Maximum of AP L is at the 3 input of labor.

15 Production in the Short Run Production of Good X LAP L MP L TP L Notice that the AP L increases as the first three units of labor are added to the fixed inputs of K and R. The maximum efficiency of Labor or maximum AP L, given our technology, plant and natural resources is with the third worker. As additional units of labor are added beyond the third worker the output per worker [AP L ] declines.

16 L TP L Labor Output, Q X Graphically TP L can be shown: TP L TP L initially increases at an increasing rate; it is convex from below. After some point it then increases at a decreasing rate and reaches a maximum level of output, Maximum output and declines

Labor Given the TP, the AP L can calculated: AP L = TP L L L AP L AP L

18 1 unit of L produces 4Q, 4 AP L is 4/1 = 4 or the slope of line 0H. H rise/run = 4 2 units of L produces 10Q, AP L is 10/2 = 5 or the slope of line 0M. M rise/run = 5. Z 3 units of L produces 20Q,. AP L is 20/3 = 6.67 or slope of line 0Z. As additional units of L are added, AP falls Labor Output, Q X Labor TP L... AP L Graphically the relationship between AP L and TP L can be shown: 0 AP L The AP L is the slope of a ray from the origin to the TP L. The maximum AP is where the ray with the greatest slope is tangent to the TP. Z

Labor Output, Q X Labor TP L... AP L TP L MP L was calculated as the change in TP L given a change in L. MP L The first unit of labor added 4 units of output Remember: MP is graphed at “between” units of L. “ Between” the 1st and 2cd units of labor, Q increases by MP L Note: Where MP L = AP L, AP L is a maximum. MP L = AP L

Labor Output, Q X Labor TP L... AP L MP L Useful things to notice: 1. MP L is the slope of TP L. 2. When TP L increases at an increasing rate, MP L increases. At the inflection point in the TP L, MP L is a maximum. When TP L increases at a decreasing rate, MP L is decreasing. 3. The AP L is a maximum when: a. MP L = AP L, b. the slope of the ray from origin is tangent to TP L. 4. When MP L > AP L the AP L is increasing. When MP L < AP L the AP L is decreasing. 5. When MP L is 0, the slope of TP L is 0, and TP is a maximum. Z

21 To calculate AP: AP L = TP L L To calculate MP: MP L =  TP L LL AP is a maximum when L = 4. MP is a maximum between 2cd and 3rd unit of L. Note that MP is 15 between 3rd & 4th units of L, it is 10 between 4th & 5th, so it equals AP = at L=4.

22 PRODUCTION LABOURCAPITALOUTPUT MPAP 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.

23 The price of labour [P L ] is $4 per unit and the price of kapital [P K ] is $6 per unit. Calculate the cost functions for this production process. TFC = P K x K = $6K = 6 x5 = $30, This cost does not change in the short run. $30 TVC = P L x L = $4L, as L changes TVC and Output change. $ 0 $ 4 $ 8 $12 $16 $20 $24 $28 $32 $36 $40 TC = TVC+TFC + =$30 + =$34 + =$38 + =$42 + =$46 + =$50 + =$54 + =$58 + =$62 + =$66 + =$70

24 PRODUCTION AND COST LABORCAPITALOUTPUTAPMPTFCTVCTCAFCAVCATC The price of labor [P L ] is $4 per unit and the price of capital [P K ] is $6 per unit. Calculate the cost functions for this production process. $30 $ 0 $ 4 $ 8 $12 $16 $20 $24 $28 $32 $36 $40 $30 $38 $42 $46 $50 $54 $58 $62 $66 $70 $34 AFC = TFC  Q = $30  Q $3.75 $1.30 $.71 $.53 $.45 $.41 $.38 $.37 $.36 $.37 AVC = TVC  Q $.50 $.35 $.29 $.28 $.30 $.32 $.35 $.39 $.43 $.49 ATC = AVC + AFC = TC  Q $4.25 $1.65 $1.00 $.81 $.75 $.729 $.734 $.76 $.79 $.86

25 PRODUCTION AND COST LABORCAPITALOUTPUTAPMPTFCTVCTCAFCAVCATC $30 $ 0 $ 4 $ 8 $12 $16 $20 $24 $28 $32 $36 $40 $30 $38 $42 $46 $50 $54 $58 $62 $66 $70 $34 $3.75 $1.30 $.71 $.53 $.45 $.41 $.38 $.37 $.36 $.37 $.50 $.35 $.29 $.28 $.30 $.32 $.35 $.39 $.43 $.49 $4.25 $1.65 $1.00 $.81 $.75 $.729 $.734 $.76 $.79 $.86 Things to note... As AP increases, AVC decreases. 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.} Since AFC declines, it will “pull” the ATC down as Q increases beyond the minimum of the AVC.

26 MP L AP L L MP L AP L L3L3 The average variable cost [AVC] and marginal cost [MC] are “mirror” images of the AP and MP functions. L1L1 L2L2 L3L3 Q $ AP L MP L AP L MP L MC AVC MC = 1 MP L x w AVC = 1 AP L x w AP L AP L x L 2 AVC The maximum of the AP is consistent with the minimum of the AVC.

27 Q $ MC AVC MC will intersect the AVC at the minimum of the AVC [always]. Q* At Q* output, the AVC is at a minimum AVC* [also max of AP L ]. AVC* ATC Q** ATC* MC will intersect the ATC at the minimum of the ATC. At Q** the ATC is at a MINIMUM. The vertical distance between ATC and AVC at any output is the AFC. At Q** AFC is RJ. R J

28  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. The Long Run

29 LONG RUN COSTS $ Q For Plant size 1, the costs are ATC 1 and MC 1 : ATC ! MC 1 For a bigger Plant 2, the unit costs move out and down. It is more cost effective. ATC 2 MC 2 As bigger plants are built the ATC moves out and down. ATC 3 ATC* Eventually, the plant size is “too large,” the ATC moves out but also up! ATC 5 ATC 6 An “envelope curve” is constructed to represent the long run AC [LRAC]. LRAC There is a long run marginal cost function. LRMC Plant ATC* is the optimal size! ATC* At Q* the cost per unit are minimized [the least inputs used]. Q* C min

30 Long Run Average Costs  LRAC is “U-Shaped”  The LRAC initially decreases due to “economies of scale” economies of scale are due to division of labor.  Eventually, “diseconomies of scale” begin usually lack of adequate information to manage the production process

31 Calculating 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.