Introduction to Production and Resource Use Chapter 6

Topics of Discussion Conditions of perfect competition Classification of productive inputs Important production relationships (Assume one variable input in this chapter) Assessing short run business costs Economics of short run production decisions 2

Conditions for Perfect Competition Homogeneous products  i.e., Corn grain, mined low-sulfur coal No barriers to entry or exit  No regulatory barriers  No extremely high fixed costs Large number of sellers  How large is large? Perfect information Information cost is relatively small No one firm has access to information that others don’t Page 86 3

Classification of Inputs Economists view the production process as one where a variety of inputs are combined to produce a single or multiple outputs  Cheese plant example  Many inputs: Labor, stainless steel cheese vats, raw milk, energy, starter cultures, cutting and wrapping tables, water, etc.  Multiple outputs: Cheese, dry whey, whey protein concentrates are produced by the plant Pages

Classification of Inputs Land: includes renewable (forests) and non-renewable (minerals) resources Labor: all owner and hired labor services, excluding management Capital: Manufactured goods such as fuel, chemicals, tractors and buildings that may have an extended lifetime Management: Makes production decisions designed to achieve specific economic goals Pages

Classification of Inputs Inputs can also be classified depending on whether amount of input used changes with production level  Fixed inputs: The amount of input used does not change with output level  Up to a point the size of milking parlor does not change with ↑ milk production/cow or for initial ↑ in herd size  Variable Inputs: The amount of input used changes directly with the level of output  Usually the amount of labor supplied is a variable input (i.e., car assembly plant that ↑ the speed of assembly line to ↑ production/hour Pages

Production Function Output = f(labor | capital, land, and management) Page 88 Start with one variable input Start with one variable input f() is general functional notation  Could be any functional form Assume remaining inputs fixed at current levels Assume remaining inputs fixed at current levels 7 “given the level of”

Page 89 PointLabor (hr)Output A101.0 B163.0 C204.8 D226.5 E268.1 F329.6 G H I J Production Function We can graph the relationship between output and amount of labor used  Known as the Total Physical Product (TPP) curve  Purely a physical relationship, no economics involved  X lbs of fertilizer/acre generates a yield of Y 8

Page 89 Total Physical Product (TPP) Curve Variable input Maximum Output Decreasing output 9 Data from previous table

Other Physical Relationships The following derivations of the TPP curve play an important role in decision-making  Marginal Physical Product (MPP) =  Average Physical Product (APP) = Page 90 10

MPP = Change in output as you change input use Page 89 Production Function Point Labor [1] Output [2] ∆Labor [3] ∆Output [4] MPP [5] = [4] ÷ [3] A B C D E F G H I J ↓MPP ↑MPP

Page 89 Total Physical Product (TPP) Curve  Input MPP = 1.8/4.0 =.45  Output ↑ from 3.0 to 4.8 units = 1.8  Labor ↑ from 16 to 20 units = 4.0  Output Data from previous table

Law of Diminishing Marginal Returns Pertains to what happens to the MPP with increased use of a single variable input  If there are other inputs their level of use is not changed Diminishing Marginal Returns  The MPP ↑ with initial use of a variable input  At some point, MPP reaches a maximum with greater input use  Eventually MPP ↓ as input use continues to ↑ Page 93 13

Point Labor [1] Output [2] ∆Labor [3] ∆Output [4] MPP [5] = [4] ÷ [3] ∆MPP A B C D E F G H I J Production Function 14

Plotting the MPP Curve Page 91 Change in output associated with a change in inputs Change from A to B on the production function → a MPP of Data from previous table

Page 91 Plotting the MPP Curve 16 Q of Output Q of Input 0 ∆I* MPP = Slope of the line tangent at a point (A) on the TPP curve = ∆Q*/∆I* A ∆Q*

Page 91 Plotting the MPP Curve 17 Q of Output Q of Input 0 ∆I* At A, MPP = ∆Q/∆I = 0/∆I* = 0 A TPP is at a maximum when MPP = 0 TPP is at a maximum when MPP = 0

Page 89 Point Labor [1] Output [2] ∆Labor [3] ∆Output [4] APP [6] = [2] ÷ [1] A B C D E F G H I J Production Function Average Physical Product (APP) = Amount of output ÷ amount of inputs used = Output/unit of input used Average Physical Product (APP) = Amount of output ÷ amount of inputs used = Output/unit of input used 18

Page 89 Total Physical Product (TPP) Curve APP =.31 (= 8÷26) with labor use = 26 Output Input 19 Data from previous table

Page 91 Plotting the APP Curve APP = output level divided by level of input use APP = output level divided by level of input use Output divided by labor use at B (3 ÷ 16) =0.19 Output divided by labor use at B (3 ÷ 16) = Data from previous table

Page 91 Plotting the APP Curve 21 Q of Output Q of Input 0 A Q* I* APP = Q*/I* = Slope of the line from the origin to the point on the TPP curve At I**, APP is at a maximum, as line OB is just tangent to the TPP curve I** B

Page 91 Relationship Between APP and MPP 22 MPP APP Q of Output Q of Input 0 APP is at a maximum at input level where APP = MPP APP is at a maximum at input level where APP = MPP I* APP*

Page 91 Definition of the Three Stages of Production APP is increasing in Stage I Stage I: MPP > APP APP is ↑ Stage I: MPP > APP APP is ↑ 23

Page 91 Definition of the Three Stages of Production Stage II: MPP < APP MPP > 0 Stage II: MPP < APP MPP > 0 24

Page 91 Definition of the Three Stages of Production Stage III: MPP < 0 25

Page 91 The Three Stages of Production 26 MPP APP Stage I Stage II Stage III Q of Output Q of Input 0  Stage II starts at input use where APP is at a maximum (pt A)  Stage II ends at input where MPP = 0 (or TPP is at a maximum)  Stage II starts at input use where APP is at a maximum (pt A)  Stage II ends at input where MPP = 0 (or TPP is at a maximum)

Page 91 The Three Stages of Production 27 MPP APP Stage I Stage II Stage III Q of Output Q of Input 0 Why are using the amount of input in Stage I and Stage III of production irrational from the producer’s perspective?

Page 91 The Three Stages of Production 28 MPP APP Stage I Stage II Stage III Q of Output Q of Input 0 Average productivity is increasing as more inputs are being used so why stop if the average return is greater than cost? Can increase output by using less inputs: → More output and less cost

Page 91 The Three Stages of Production 29 MPP APP Stage I Stage II Stage III Q of Output Q of Input 0 The producer’s economic question: What level of input amount contained in Stage II should the I use to maximize profits? The producer’s economic question: What level of input amount contained in Stage II should the I use to maximize profits?

Economic Dimension To answer the above question  We need to account for the price of the product being produced  We also need to account for the cost of the inputs used to produce the above product 30

Key Cost Relationships The following cost concepts play key roles in determining where in Stage II a producer will want to produce  Total Variable Cost (TVC) = the total value of costs that change with the level of output (e.g. energy costs, labor costs, material costs, etc.)  Total Fixed Cost (TFC) = total value of costs that do not changed with the level of output (e.g. property taxes)  Total Costs (TC) = the sum of total variable and fixed costs  TC = TVC + TFC Page

Key Cost Relationships The following cost concepts play key roles in determining where in Stage II a producer will want to produce  Marginal Cost (MC) =  total cost of production ÷  output produced as output level changes =  variable cost of production ÷  output produced given that total fixed costs by definition do not change with output = ∆TC/∆Q = ∆TVC/∆Q  Average Variable Cost (AVC) = total variable cost of production ÷ total amount of output produced = TVC/Q Page

Key Cost Relationships The following cost concepts play key roles in determining where in Stage II a producer will want to produce  Average Fixed Cost (AFC) = total fixed cost of production ÷ total amount of output produced = TFC/Q  Average Total Cost (ATC) = total cost of production ÷ total amount of output produced = TC/Q = AVC + ATC Page

From TPP curve on page 113 From TPP curve on page 113 Page 94 34

Fixed costs are $100 no matter the level of production Fixed costs are $100 no matter the level of production Page 94 35

Page Total fixed costs (Col. 2) ÷ by total output (Col. 1) Total fixed costs (Col. 2) ÷ by total output (Col. 1)

Page Costs that vary with level of production Costs that vary with level of production

Page Total variable cost (Col. 4) ÷ by total output (Col. 1)

Page Total Fixed Cost (Col. 2) + Total Variable Cost (Col.4)

Page 94 Change in Total Cost (Col. 4 or 6) associated with a change in output (Col. 1) 40

Page 94 [Total Cost (Col. 6) ÷ by Total Output (Col. (1)] or [Avg. Variable Cost + Avg. Fixed Cost] 41

Let’s Graph the Above Cost Items Contained in the Previous Table 42

Page 95 Table 6.3 Cost Relationships MC = min(ATC) and min(AVC) Vertical distance between ATC and AVC = AFC Input Use Cost ($) 43 AFC

Key Revenue Concepts The following revenue concepts play key roles in determining where in Stage II a producer will want to produce  Total Revenue (TR) =Multiplication of total amount of output produced by the sale price ($)  Average Revenue (AR) = Total revenue ÷ total amount of output produced ($/unit of output) = TR/Q  Marginal Revenue (MR) = ∆ total revenue ÷ ∆ total amount of output produced = ∆TR ÷ ∆Q  How much revenue is generated by one additional unit of output?  Under perfect competition, it is the per unit price 44

Now let’s assume this firm can sell its product for $45/unit 45

Page 98 Remember we are assuming perfect competition  The firm takes price as given  Price (Col. 2) = MR (Col. 7)  What is the AR value? Key Revenue Concepts 46

Page 98 With perfect competition, where would the firm maximize profit in the above example? Profit Maximization 47

Let’s see this in graphical form 48

Page 99 P=MR=AR $ Profit maximizing Output where MR=MC 49

The previous graph indicated that Profit is maximized at 11.2 units of output MR ($45) equals MC ($45) at 11.2 units of output Profit maximizing output occurs between points G and H At 11.2 units of output profit would be $ Let’s do the math…. Profit Maximization 50

Profit at Price of $45? 28 P =45 $ Q 11.2 MC ATC AVC Revenue = $45  11.2 = $ Total cost = $28  11.2 = $ Profit = $ – $ = $ Since P = MR = AR Average profit = $45 – $28 = $17 Profit = $17  11.2 = $ Revenue = $45  11.2 = $ Total cost = $28  11.2 = $ Profit = $ – $ = $ Since P = MR = AR Average profit = $45 – $28 = $17 Profit = $17  11.2 = $

Profit at Price of $45? 28 P =45 $ Q 11.2 MC ATC AVC Revenue = $45  11.2 = $ Total cost = $28  11.2 = $ Profit = $ – $ = $ Since P = MR = AR Average profit = $45 – $28 = $17 Profit = $17  11.2 = $ Revenue = $45  11.2 = $ Total cost = $28  11.2 = $ Profit = $ – $ = $ Since P = MR = AR Average profit = $45 – $28 = $17 Profit = $17  11.2 = $ $

Page 99 P=MR=AR Zero economic profit if price falls to P BE Firm would only produce output O BE where AR (MR) ≥ ATC Zero economic profit if price falls to P BE Firm would only produce output O BE where AR (MR) ≥ ATC 53

Profit at Price of $28? P=28 45 $ Q MC ATC AVC Revenue = $28  10.3 = $ Total cost = $28  10.3 = $ Profit = $ – $ = $0 Since P = MR = AR Average profit = $28 – $28 = $0 Profit = $0  10.3 = $0 (break even) 54

Page 99 P=MR=AR Firm can just cover variable cost if price falls to P SD. Firm would shut down if price falls below P SD Firm can just cover variable cost if price falls to P SD. Firm would shut down if price falls below P SD 55

Profit at Price of $18? 28 P=18 45 $ Q MC ATC AVC Revenue = $18  8.6 = $ Total cost = $28  8.6 = $ Profit = $ – $ = –$86 Since P = MR = AR Average profit = $18 – $28 = –$10 Profit = –$10  8.6 = –$86 (Loss) 56

Profit at Price of $10? 28 P= $ Q MC ATC AVC Revenue = $10  7.0 = $70.00 Total cost = $30  7.0 = $ Profit = $70.00 – $ = – $ Since P = MR = AR Average profit = $10 – $30 = –$20 Profit = –$20  7.0 = –$140 Average variable cost = $19 Variable costs = $19  7.0 = $ Revenue – variable costs = –$63 Not covering variable costs!!!!!!

The Firm’s Supply Curve $ Q MC ATC AVC Profit Maximizing Output Levels

Page 99 We know that so long as P (= MR) > AVC some of the fixed costs can be covered  Better economic position then shutting down altogether, WHY? We know that when P (= MR)=MC, the firm maximizes profit Portion of MC curve defined by output level that generates the minimum AVC is referred to as the firm’s supply curve The Firm’s Supply Curve 59

The Firm’s Supply Curve $ Q ATC AVC Firm Supply Curve MC 60

Now let’s look at the demand for a single input: Labor 61

Key Input Relationships The following input-related derivations play key roles in determining amount of variable input to use to maximize profits  Marginal Value Product (MVP) = MPP × Product Price  MPP → ∆Output ÷ ∆Input Use  Product Price → ∆Revenue ÷ ∆Output  MVP → ∆Revenue ÷ ∆Input Use (Additional output value generated by the last increment in input use)  Marginal Input Cost (MIC) = wage rate, rental rate, seed cost, etc. Page

Page B C E F G H J MVP=MPP x Output Price Wage rate is labor’s MIC I D 63

Page B C D E F G H I J Profit maximizing input use rule  Use a variable input up to the point where  Value received from another unit of input (MVP)  Equals cost of another unit of input (MIC)  → MVP=MIC 64

Page B C D E F G H I J The area below the green lined MVP curve and above the red lined MIC curve represents cumulative net benefit 65

Page 100 MVP = MPP × $45 66

Page 100 Profit are maximized where MVP = MIC or where MVP =$5 and MIC = $5 Profit are maximized where MVP = MIC or where MVP =$5 and MIC = $5 67

Page 100 Marginal net benefit (Col. 5) = MVP (Col. 3) – labor MIC (Col. 4) = Value of additional output from last unit of input net of the cost of that input = – 68

Page 100 The cumulative net benefit (Col. 6) of input use = the sum of successive marginal net benefits (Col. 5) = the grey area in previous graph. The cumulative net benefit (Col. 6) of input use = the sum of successive marginal net benefits (Col. 5) = the grey area in previous graph. 69

Page 100 For example… $25.10 = $ $15.25 $58.35 = $ $33.25 For example… $25.10 = $ $15.25 $58.35 = $ $

Page 100 = – Cumulative net benefit is maximized where MVP=MIC at $5 71

Page B C D E F G H I J If you stopped at point E on the MVP curve, for example, you would be foregoing all of the potential profit lying to the right of that point up to where MVP=MIC. 72

Page B C D E F G H I J If you use labor beyond the point where MVP =MIC, you begin incurring losses as the return to another unit of labor is < $5.00, its per unit cost 73

A Final Thought One final relationship needs to be made. The level of profit-maximizing output (O MAX ) in the graph on page 99 where MR = MC corresponds directly with the variable input level (L MAX ) in the graph on page 101 where MVP = MIC. Going back to the production function on page 88, this means that: O MAX = f(L MAX | capital, land and management) 74

In Summary… Features of perfect competition Factors of production (Land, Labor, Capital and Management) Key decision rule: Profit maximized at output MR=MC Key decision rule: Profit maximized where MVP=MIC 75

Chapter 7 focuses on the choice of inputs to use and products to produce…. 76