Module 14 Cost in the Short Run

Objectives: Understand the relationship between the short run production function and short run costs. Define total cost, total variable cost and total fixed cost. Define average total cost, average variable cost, average fixed cost and marginal cost. Know and be able to use the cost formulas to calculate costs. Understand the relationship between marginal product and marginal cost of production. 2

Objectives…cont’d. Understand the relationship between marginal product and marginal cost of production. Understand the relationship between marginal cost and average total cost and marginal cost and average variable cost. Understand what happens to average fixed cost as output increases and what this implies about the average total cost and average variable cost curves. Be able to graph the cost curves. 3

Objective 1 Understand the relationship between the short run production function and short run costs Costs are derived from the production function. Consider a simple 2-input short run production function, like the one we used for the Acme Box Company: Q = f (L, K0) where L= the variable input, labor and K0 = the fixed input, capital From the production function we can write an expression for total cost. Total Cost = Labor Costs + Capital Cost = Total Variable Cost + Total Fixed Cost 4

Define Total Fixed Cost, …. Objective 2 Define Total Fixed Cost, …. Total Fixed Costs (TFC) refers to the total expenditure by the firm for fixed inputs. Fixed costs do not change when firms increase or decrease their output. The lay person thinks of fixed costs as overheads. 5

Objective 2: …total variable cost and total cost Total Variable Costs (TVC) refer to total expenditure on variable inputs, for example, the wages paid for labor services and the cost of raw materials purchased to produce the product. Total Costs (TC) refer to the total expenditure on all inputs used to produce a product. It is the sum of fixed costs and variable costs. 6

Objective 2: ….fixed cost, variable cost and total cost Total Cost = Total Fixed Cost + Total Variable Cost

Can you determine these values? 8

Objective 3 Define average total cost, average variable cost, average fixed cost and marginal cost Average costs tells you how much a product costs per unit of output. In the short run, there are three average cost variables, one corresponding to each category of costs. 1. Average Fixed cost (AFC) 2. Average Variable Cost (AVC) 3. Average Total Cost (ATC) or simply Average Cost (AC) 9

Objective 3…the three “average” cost variables.. Total Cost = Average Total Cost x Quantity    10

Since fixed cost is constant, the equation above equals: Marginal Cost is the addition to total cost resulting from producing one more unit of output. Since fixed cost is constant, the equation above equals: In the short run, marginal cost is independent of fixed costs. 11

Know and be able to use the cost formulas to Objective 4 Know and be able to use the cost formulas to calculate costs. Example: We will revisit the Acme Box Company. Suppose Acme’s Fixed Costs equals $1,000 and the firm hires labor at a constant wage of $60 per unit. Ratha, I worked on trying to get the table that you had created input here for quite a while (see next slide) but I had trouble. I was able to do it for the last module, but it was smaller and for some reason, the numbers lined up easier than on this one. Maybe you are able to input it easier with the programs that you have? I’m sorry I’m not able to complete this part for you. -Sara 12

Objective 4: Calculating Costs … Suppose Acme’s fixed costs equals $1,000. Labor (L) Total Product or Output (Q) Marginal Product of labor (MPL) Total Fixed Cost (TFC) $ 1000 1 8 2 23 15 3 42 19 4 57 5 67 10 6 74 7 79 82 9 83 13

Objective 4: Calculating Costs … Acme’s hires labor at a constant wage of $60 per unit of labor. Its labor are its variable cost. Labor Costs = wage rate x labor units (1) (2) (3) (4) (5)=(1)x$60 Labor (L) Total Product (Q) Marginal Product (MPL) Total Fixed Cost (TFC) $ Total Variable Cost (TVC) 1000 1 8 1x60=60 2 23 15 2x60=120 3 42 19 3x60=180 4 57 240 5 67 10 300 6 74 7 360 79 420 82 480 9 83 540 14

Objective 4: Calculating Costs … Acme’s Total Cost = Fixed Cost + Variable Cost (1) (2) (3) (4) (5) (6)=(4) +(5) Labor (L) Total Product (Q) Marginal Product (MPL) Total Fixed Cost (TFC) $ Total Variable Cost (TVC) Total Cost (TC) 1000 1 8 60 1000+60=1060 2 23 15 120 1000+120=1120 3 42 19 180 1000+180=1180 4 57 240 1240 5 67 10 300 1300 6 74 7 360 1360 79 420 1420 82 480 1480 9 83 540 1540 15

Objective 4: Calculating Costs … Average Fixed Cost = Fixed Cost ÷ Output (1) (2) (3) (4) (5) (6)=(4) +(5) (7)=(4) ÷(2) Labor (L) Total Product or Output (Q) Marginal Product (MPL) Total Fixed Cost (TFC) $ Total Variable Cost (TVC) Total Cost (TC) Average Fixed Cost (AFC) 1000 -- 1 8 60 1060 1000 ÷8=125 2 23 15 120 1120 1000 ÷23=43.5 3 42 19 180 1180 1000 ÷42=23.8 4 57 240 1240 17.5 5 67 10 300 1300 14.9 6 74 7 360 1360 13.5 79 420 1420 12.7 82 480 1480 12.2 9 83 540 1540 12.1 16

Objective 4: Calculating Costs … Average Variable Cost = Total Variable Cost ÷ Output (1) (2) (3) (4) (5) (6) (7) (8)=(5) +(2) Labor (L) Total Product or Output (Q) Marginal Product (MPL) Total Fixed Cost (TFC) $ Total Variable Cost (TVC) Total Cost (TC) Average Fixed Cost (AFC in $) Average Variable Cost (AVC in $) 1000 -- 1 8 60 1060 125 60 ÷8=7.5 2 23 15 120 1120 43.5 120 ÷23=48.7 3 42 19 180 1180 23.8 180 ÷42=28.1 4 57 240 1240 17.5 21.8 5 67 10 300 1300 14.9 19.4 6 74 7 360 1360 13.5 18.4 79 420 1420 12.7 18.0 82 480 1480 12.2 18.1 9 83 540 1540 12.1 18.5 17

Objective 4: Calculating Costs … Average Total Cost = Total Cost ÷ Output , or Average Total Cost = Average Fixed Cost + Average Variable Cost (1) (2) (3) (4) (5) (6) (7) (8) (9)=(6) ÷(2) Labor (L) Total Product or Output (Q) Marginal Product (MPL) Total Fixed Cost (TFC) $ Total Variable Cost (TVC) Total Cost (TC) Average Fixed Cost (AFC in $) Average Variable Cost (AVC in $) Average Total Cost (ATC in $) 1000 -- 1 8 60 1060 125 60 ÷8=7.5 1060÷ 8=132.5 2 23 15 120 1120 43.5 120 ÷23=5.2 1120 ÷23=48.7 3 42 19 180 1180 23.8 180 ÷42=4.3 1180 ÷ 42=28.1 4 57 240 1240 17.5 4.2 21.8 5 67 10 300 1300 14.9 4.5 19.4 6 74 7 360 1360 13.5 4.9 18.4 79 420 1420 12.7 5.3 18.0 82 480 1480 12.2 5.9 18.1 9 83 540 1540 12.1 6.5 18.5 18

Objective 4: Calculating Costs … Marginal Cost = ∆Total Cost ÷ ∆Output, or in the short run, Marginal Cost = ∆Variable Cost ÷ ∆Output (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)=∆(5)÷(3) Labor (L) Total Product or Output (Q) Marginal Product (MPL) Fixed Cost (TFC) $ Variable Cost (TVC) Total Cost (TC) Average Fixed Cost (AFC) Average Variable Cost (AVC) $ Average Total Cost (ATC) Marginal Cost (MC) 1000 -- 1 8 60 1060 125 7.5 132.5 60÷ 8=7.5 2 23 15 120 1120 43.5 5.2 48.7 60÷ 15=4 3 42 19 180 1180 23.8 4.3 28.1 60÷ 19=3.2 4 57 240 1240 17.5 4.2 21.8 5 67 10 300 1300 14.9 4.5 19.4 6 74 7 360 1360 13.5 4.9 18.4 8.6 79 420 1420 12.7 5.3 18.0 12 82 480 1480 12.2 5.9 18.1 20 9 83 540 1540 12.1 6.5 18.5 19

Understand the relationship between marginal Objective 5 Understand the relationship between marginal product and marginal cost of production. Below is a segment of the Table for the Acme Box Company. Labor (L) Total Product or Output (Q) Marginal Product of labor (MPL) Marginal Cost (MC) $ -- 1 8 7.5 2 23 15 4 3 42 19 3.2 57 5 67 10 6 74 7 8.6 79 12 82 20 9 83 60 Increasing Marginal Returns segment Diminishing Marginal Returns segment 20

Objective 5: ..the relationship between marginal product and marginal cost of production. In the increasing marginal returns segment, when marginal product is rising, marginal cost is falling. In the diminishing marginal returns segment, when marginal product is falling, marginal cost is rising. In the negative marginal returns segment, what do you think is happening to marginal cost? Yes, it is rising fast! 21

What then is the shape of the marginal cost curve? It is U-shaped. Objective 5: ..the law of diminishing marginal returns and the shape of the marginal cost curve What then is the shape of the marginal cost curve? It is U-shaped. 22

Understand the relationship between marginal cost Objective 6: Understand the relationship between marginal cost average total cost and average variable cost When marginal cost (MC) is less than either average total cost (ATC) or average variable cost (AVC), it causes ATC or AVC to fall. When MC is greater than either ATC or AVC, it causes ATC or AVC to rise. The MC curve intersects both the AVC and ATC curves at their minimum points. 23

The average total cost and average variable curves are also U-shaped. Objective 6: …the marginal cost, average total cost and average variable cost curves The average total cost and average variable curves are also U-shaped. Like the marginal cost curve, their shapes are also influenced by the law of diminishing marginal returns. 24

Understand what happens to average fixed Cost as output increases. Objective 7 Understand what happens to average fixed Cost as output increases. Average fixed costs falls as output increases.....think of this as “spreading your overheads”. 25

ATC = AVC + AFC AFC = ATC – AVC As output expands, AFC gets smaller and smaller, which means that the difference between the ATC and the AVC curves decreases. 26

Be able to graph the cost curves Objective 8 Be able to graph the cost curves Graph the cost curves using the data for the Acme Box Company. Can you identify the curves in the diagram? 27

E = Marginal Cost curve a = minimum point on the marginal cost curve. Diminishing marginal returns set in at this point. 28

F = Average Total Cost curve C = minimum point on the average total cost curve. The marginal cost curve cuts the average total cost at this point. 29

G = Average variable Cost curve b = minimum point on the average variable cost curve. The marginal cost curve cuts the average variable cost curve at this point. 30

H = Average Fixed Cost curve 31

You should be able to draw and identify these graphs. 32