AGEC 603. Conditions for Perfect Competition. Classification of Inputs. Production and Cost Relationships. Homogeneous products

Transcription

1 AGEC 603 Production and Cost Relationships Conditions for Perfect Competition Homogeneous products Products from different producers are perfect substitutes No barriers to entry or exit Resources are free to move in and out of the sector Large number of buyers and sellers No market power price takers Perfect information Including quantities, prices, quality, sources of resources etc. Classification of Inputs Land - includes renewable (forests) and nonrenewable (minerals) resources Labor - all owner and hired labor services, excluding management Capital - manufactured goods such as fuel, chemicals, tractors and buildings Management - production decisions designed to achieve specific economic goal 1

2 Output What Are Production Functions? Mathematical relationship that characterizes the physical relationship between the use of inputs and the level of outputs Output = f(capital labor, land, and management) Start with one variable input Assume all other inputs fixed at their current levels Data - Barlowe Land Capital TPP APP MPP TPP Curve Capital Land unit 2

3 MPP Marginal Physical Product (MPP) Land Capital TPP MPP (2-0)/(1-0) = (6-2)/(2-1) = The change in the level of output associated with the change in the use of an input. Slope small changes output MPP input Partial derivative δ TPP MPP = δ input 20 MPP - Three Segments 1 Increasing and positive 10 Decreasing but positive Negative and decreasing Capital Land unit Law of Diminishing Marginal Product As successive units of a variable input are added to a production process with the other inputs held constant, the marginal physical product (MPP) eventually declines 3

4 APP Data Land Capital TPP APP MPP Average Physical Product (APP) Land Capital TPP APP /1 = /2 = /3 = Represents the output per unit of input total output APP totalinput APP Graphically 20 1 Increasing and positive Decreasing but never goes negative Capital Land unit 4

5 Data Land Capital TPP APP MPP Question Professor William Saupe of the University of Wisconsin has a trophy in his office certifying he won the Northwest Iowa Corn Contest. When he says Look what I won for driving the marginal physical product of nitrogen to zero? What does he mean? A) He added nitrogen such that he maximized his yields by causing MPP to be zero. B) He should have added more nitrogen as the MPP was zero. C) He should have added less nitrogen as the MPP was zero. D) He does not understand the relationship between nitrogen and corn yields. E) MPP is a separate curve from the TPP curve, therefore, any relationship is ambiguous. Question Professor William Saupe of the University of Wisconsin has a trophy in his office certifying he won the Northwest Iowa Corn Contest. When he says Look what I won for driving the marginal physical product of nitrogen to zero? What does he mean? A) He added nitrogen such that he maximized his yields by causing MPP to be zero. B) He should have added more nitrogen as the MPP was zero. C) He should have added less nitrogen as the MPP was zero. D) He does not understand the relationship between nitrogen and corn yields. E) MPP is a separate curve from the TPP curve, therefore, any relationship is ambiguous.

6 Output MPP / APP 20 1 Stages of Production MPP APP Stage I: MPP > APP Stage II: MPP = or < APP; MPP = 0 Stage III: MPP < Stage I Stage II Stage III - Capital Land unit Relationships - Know 11 TPP TPP APP MPP Stage I Stage II Stage III MPP APP Capital Land unit Question Assume a firm is producing where the MPP is negative. At this point of production, we know the APP and TPP curves are A) Both are negative. B) One is negative and the other is positive but the relationship is unknown without further information. C) Production is elastic at this point. D) TPP is negative and APP is positive. E) Both positive. 6

7 Corn dozen ~ Corn Dozen ` Question Assume a firm is producing where the MPP is negative. At this point of production, we know the APP and TPP curves are Positive 160 TPP A) Both are negative. 100 B) One is negative and the other 80 Stage I Stage II Stage III is positive but the relationship is unknown without further 20 information C) Production is elastic at this 3 point. 30 Positive 2 D) TPP is negative and APP is 20 APP positive E) Both positive. APP and TPP are always positive. KNOW WHY? Pickers per Day Question What is TPP at X= 11? What is MPP at input level of 14? What is APP at input level of? Why is input level 17 irrelevant to a rational economic decision maker? A) 200, 0, 10, and beyond max TPP B) 10, 200, 0, and beyond max TPP C) 10, 200, 10, and before max TPP D) 100, 14, 10, and before max TPP E) 10, 0, 10, and beyond max TPP Output input Question What is TPP at X= 11? What is MPP at input level of 14? What is APP at input level of? Why is input level 17 irrelevant to a rational economic decision maker? Read TPP directly Max TPP slope =MPP is 0 A) 200, 0, 10, and beyond max TPP B) 10, 200, 0, and beyond max TPP C) 10, 200, 10, and before max TPP D) 100, 14, 10, and before max TPP E) 10, 0, 10, and beyond max TPP off the graph Output input APP = TPP/ input = 0/= 10 Beyond Max TPP Increasing input decreases TPP so why use? 7

8 Profit Maximization Value Product Analysis Assumptions Previous TPP Output price fixed at $1 / unit Capital price constant at $7 / unit Close to perfect competition TVP Land Capital TPP APP MPP TVP *2 = *6 = TVP = price * TPP Note price = $1 Not generally the case MVP Land Capital TPP APP MPP TVP MVP *2 = *4 = MVP = price * MPP or change in TVP / change in input Marginal return per unit of input Note price = $1 Not generally the case 8

9 AVP Land Capital TPP APP MPP TVP MVP AVP *2 = *3 = AVP = price * APP or TVP / total input Note price = $1 Not generally the case Total Variable Cost - TVC Land Capital TPP APP MPP TVP MVP AVP TC *2 = 2 7*1 = *3 = 3 7*2 = TC = price of input * input level AFC and MFC Land Capital TPP APP MPP TVP MVP AVP TC AFC MFC *2 = 2 7 7/1 = 7 7/1 = *3 = 3 (14-7)/ 14 14/2 = 7 (2-1)=7 MFC 1 = marginal factor cost 7 13 = additional cost associated 1 4 with the application of 10 each successive variable input = in TC / input AFC 1 = average factor 14 cost 78 = cost 14 per 9.70 unit of input = 1 TC / input 9 91 level In 1 this case the AFC = MFC = constant = $ Why?

10 Dollars Net Returns or Profit Land Capital TPP APP MPP TVP MVP AVP TC Net AFC MFC Returns = = Net Returns = TVP TC Net Returns or Profit Land Capital TPP APP MPP TVP MVP AVP TVC Net AFC MFC Returns = = Net Returns Maximization TVP TVC Net Returns MFC MVP Net returns max at greatest distance between TVP and TC Occurs at input level in which MFC = MVP Captial 10

11 Dollars Net Returns Graph MFC MVP Net Returns Input level that MFC = MVP maximizes net returns Capital Land unit Short-Run Costs Fixed costs do not vary with the level of input use Variable costs vary with the level of input use Similar to production can obtain curves such as total, average, and marginal costs Note on Fixed Costs Fixed costs = 0 in Barlowe With only two inputs, land and capital the profits we are generating are returns to the fixed input land Usually TC = TVC + FC but our case FC = 0, therefore TC = TVC OK returns to land fixed costs do not influence decision making 11

12 Dollars Total Costs Recall capital costs = $7 / unit Land Capital TPP FC TVC FC+ TVC =TC * 7 = = * 7 = = 14 Note, * 7 = Will ignore Land and FC in proceeding slides! Total Costs - Graphically After max TTP decreases but costs still increase. Produce in Stage III? Cost increase at decreasing rate Cost increase at increasing rate. 0 Output or TPP Average / Marginal Costs Average cost = total cost / output Marginal cost = change in total costs / change in output Capital TPP TC ATC /2 = 3.0 (7-0)/(2-0) = /6 = 2.33 (14-7)/(6-2) = /13 = 1.62 (21-14)/(13-6) = Why is not relevant in stage III!

13 Dollars Marginal / Average Costs Output or TPP Cost / Production Relationships Decreasing is associated with increasing MPP Increasing is associated with diminishing marginal returns decreasing MPP Decreasing is associated with increasing APP Increasing is associated with decreasing APP = at minimum Question What is the shape of your curve between input levels of 12 and 10 pounds of fertilizer to your spinach field? Why? A) Upward sloping, MPP is increasing is stage 2. B) Upward sloping, MPP is decreasing in stage 2. C) Downward sloping, MPP is increasing in stage 2. D) Downward sloping, MPP is decreasing in stage 2. E) Upward sloping, the stage Stage 1 Stage 3 of production is irrelevant. Stage 2 13

14 Dollars Question What is the shape of your curve between input levels of 12 and 10 pounds of fertilizer to your spinach field? Why? A) Upward sloping, MPP is increasing is stage 2. B) Upward sloping, MPP is decreasing in stage 2. C) Downward sloping, MPP is increasing in stage 2. D) Downward sloping, MPP is decreasing in stage 2. E) Upward sloping, the stage Stage 1 Stage 3 of production is irrelevant. Stage Net Returns = TVP - TC TC TVP Net returns max at greatest distance between TVP and TC Output or TPP Short-Run Decisions Similar to what we have been doing Total Revenue (TVP) = price x quantity WHY? Average Revenue revenue per unit of output Marginal Revenue change in total revenue as output changes total revenue revenue AR MR total output output Objective maximize net returns given fixed land unit 14

15 Dollars Average / Marginal Revenues Recall price of $1 TPP TPP * price = TR AR MR * 1 = /2 = 1.00 (2-0)/(2-0) = * 1 = /6 = 1.00 (6-2)/(6-2) = Level of Output = MR Perfect competition in the short run produce at the point = MR MR Net revenue maximizing point = MR Output or TPP Level of Output = MR Why? Examine MR and curves A > MR Produce less Why? MR = MR Correct output level Why? b < MR Produce more Why? 1

16 TR and TC Areas Note change in y-axis for clarity Total Returns Gray area = TR = P * Q Total Cost Red area TC = x Q 16

17 Net Returns Green area net returns TR - TC Breakeven Price Breakeven price - price that just covers total costs TR = TC implies economic profits are zero Price = $0.69 = min Breakeven Price Breakeven price - price that just covers total costs TR = TC implies economic profits are zero Price = $0.69 = min Gray area TR 17

18 Breakeven Price Breakeven price - price that just covers total costs TR = TC implies economic profits are zero Price = $0.69 = min Red area TC Notice profits = 0 Question At a price of $2.0, how much of total costs are being covered? Dollars A) None Quantity B) Can not tell, because you need to know quantity C) Some but not all D) Curves are average curves and you can not obtain totals from averages E) All Question At a price of $2.0, how much of total costs are being covered? Total costs Total Revenue Dollars A) None Quantity B) Can not tell, because you need to know quantity C) Some but not all D) Curves are average curves and you can not obtain totals from averages E) All 18

19 Question At a price of $.00, how much of total costs are being covered? Dollars A) None Quantity B) Can not tell, because you need to know quantity C) Some but not all D) Curves are average curves and you can not obtain totals from averages E) All Question At a price of $.00, how much of total costs are being covered? Total costs Total Revenue Dollars ATC AVC A) None Quantity B) Can not tell, because you need to know quantity C) Some but not all D) Curves are average curves and you can not obtain totals from averages E) All Question At which point would a profit maximizing firm produce if price =$? Why? Dollars.00 A) A B) B C) C D) D E) E A B C D E Quantity 19

20 Question At which point would a profit maximizing firm produce if price =$? Why? Dollars.00 A B C D E A) A MR = but decreasing -- not in stage 2 Quantity B) B MR does not = C) C MR does not = D) D MR does not = E) E MR= and increasing -- stage 2 Question What area gives the total costs? Dollars G F A B C A) AE0 B) BE0G C) CE0F D) ABG E) BCFG 0 E Quantity Question What area gives the total costs? Dollars G F A B C A) AE0 B) BE0G C) CE0F D) ABG E) BCFG 0 E Quantity 20

21 Question What area gives the total revenue? Dollars G F A B C A) AE0 B) BE0G C) CE0F D) ABG E) BCFG 0 E Quantity Question What area gives the total revenue? Dollars G F A B C AVC A) AE0 B) BE0G C) CE0F D) ABG E) BCFG 0 E Quantity Question What area gives profits? Dollars G F A B C A) AE0 B) BE0G C) CE0F D) ABG E) BCFG 0 E Quantity 21

22 Question What area gives profits? Dollars G F A B C A) AE0 B) BE0G C) CE0F D) F E) BCFG 0 E Quantity Intensity of Land Use Land the fixed factor Short Run - land usually assumed fixed Long Run - land is variable Define economic land use Intensity Refers to the relative amount of capital and labor combined with units of land in the production process - relative amounts of capital and labor high ratio implies intensive use downtown vs. ranch Two Concepts Intensive margin Extensive margin Intensive Margin of Land Concept applies to all uses of land Intensive Margin Input level associated with maximizing net returns MFC = MVP or = MR Give same point We will concentrate in cost curves 22

23 PRICE PRICE Price Intensive Margin Good Assume occurs at 1 units of capital 30 2 Green box = net returns Produce at MR = MR Intensive margin Area of insufficient input use Area of too much input use Output Intensive Margin - Average 30 Assume occurs at 10 units of capital 2 MR 20 1 Intensive margin 10 Area of insufficient input use Area of too much input use Output Intensive Margin - Marginal Net returns = Assume occurs at units of capital MR Area of insuffici ent input use Intensive margin Area of too much input use Output 23

24 Economic Capacity of Land Price Price Price Extensive Margin of Land Use Extensive margin large land area (low capital and labor) break even tract lowest grade of land least accessible site Occurs when operator is applying intensive level of inputs (MR=) for a given land use and finds they are using the lowest grade of land they can afford to operate Extensive Margin Good Average Marginal Intensive margins Extensive margin MR MR MR Output Output Output Continuum 1 Intensive margins 10 Extensive margin Good Average Marginal Decreasing Land Capacity 24

25 Price Price Economic Capacity of Land Economic Capacity of Land Continuum 1 10 Intensive margins for Best land Sub average land Good Average Marginal Decreasing Land Capacity Price Decrease / Cost Increase Good land uses less inputs 1 Average land uses less inputs 10 Marginal land taken out of production Extensive margin shifts to left Good Average Marginal Decreasing Land Capacity Price Decrease Good Intensive margin before MR before Marginal Intensive margin before MR before MR after MR after Intensive margin after Output Would not produce after Output 2

26 Price Price Economic Capacity of Land Price Increase / Cost Decrease Good land uses more inputs Average land uses more inputs 1 Marginal land uses more inputs 10 Sub marginal land put into production Extensive margin shifts to right Good Average Marginal Decreasing Land Capacity Good Price Increase Sub marginal Intensive margin after MR after Intensive margin after MR after MR before MR before Intensive margin before Output Intensive margin before Not producing Output Factors Influencing Intensity Type of use Commercial vs. residential vs. farming Technology For a given use Characteristics of the land Changing economic conditions Owners expectations and attitudes Technology 26

27 Equi-marginal Principle Equi-marginal principle If a resources is limited, maximum net returns occur when MVP is at least equal to the next best alternative (opportunity cost) MVP will be equal Example Assumptions Three tracts of land - not homogenous 30 units of the input available TVP and MVP varying between the tracts next table Input costs = $3 / unit = MFC # of Variable Inputs Different Land First Tract Second Tract Third Tract TVP MVP TVP MVP TVP MVP 1 $10 $ $ # of Variable Inputs No Constraints MFC = MVP First Tract Second Tract Third Tract TVP MVP TVP MVP TVP MVP 1 $10 $

28 No constraints Tract Units TVP MVP Total Constrained to 30 units Use 10 units / grade Tract Units TVP MVP Constrained to 30 units Use to intensive margin on best land first Tract Units TVP MVP Total net returns = 281 3*38 = $167 net returns = 232 3*30 = $142 Constrained to 30 units Equi-marginal principle Tract Units TVP MVP Total Total net returns = 234 3*30 = $144 net returns = 248 3*30 = $18 # of Variable Inputs Equi-marginal Principle First Tract Second Tract Third Tract TVP MVP TVP MVP TVP MVP 1 $10 $ $ Long Run Average Cost Curve The long run average cost (L) curve reflects points of tangency with a series of short run average total cost (S) curves. The point on the L where the following holds is the long run equilibrium position (Q LR ) of the firm: S = L = S = P LR where P LR represents the long run price and S short run marginal costs. 28

29 Developing the L Economies of Size Increasing returns to size increase in output is more than proportional increase in input use L is decreasing when firm is expanded Decreasing returns to size - increase in output is less than proportional increase in input use L is increasing when firm is expanded Constant returns to size - increase in output is equal to the proportional increase in input use L is horizontal when firm is expanded Returns to Size Increasing Decreasing Constant 29

30 What can we say about the four firms in this graph? Size 1 would lose money at price P WHY? Q 3 Firm size 2, 3 and 4 would earn a profit at price P. WHY? Q 3 30

31 Firm #2 s profit would be the area shown below Q 3 Firm #3 s profit would be the area shown below Q 3 Firm #4 s profit would be the area shown below Q 3 31

32 If price were to fall to P LR, only size 3 would not lose money; it would break-even. Size 4 would have to down size its operations! Size 1 and 2 would have to increase operations. 32