1 Module 14 Cost in the Short Run. ObjectivesObjectives Understand the relationship between the...

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Module 14Module 14Module 14Module 14

Cost in the Short Cost in the Short RunRun


ObjectivesObjectivesObjectivesObjectives

Understand the relationship between the short run Understand the relationship between the short run production function and short run costs.production function and short run costs.


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Define total cost, total variable cost and total fixed Define total cost, total variable cost and total fixed cost.cost.



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Define average total cost, average variable cost, Define average total cost, average variable cost, average fixed cost and marginal cost.average fixed cost and marginal cost.




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Know and be able to use the cost formulas to Know and be able to use the cost formulas to calculate costs.calculate costs.





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Understand the relationship between marginal Understand the relationship between marginal product and marginal cost of production.product and marginal cost of production.





Understand the relationship between marginal Understand the relationship between marginal product and marginal cost of production.product and marginal cost of production.

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Understand the relationship between marginal cost Understand the relationship between marginal cost and average total cost, and marginal cost and and average total cost, and marginal cost and average variable cost.average variable cost.

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Objectives continuedObjectives continuedObjectives continuedObjectives continued


Understand what happens to average fixed cost as Understand what happens to average fixed cost as output increases and what this implies about the output increases and what this implies about the average total cost and average variable cost curves. average total cost and average variable cost curves.

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Be able to graph the cost curves. Be able to graph the cost curves.



Be able to graph the cost curves. Be able to graph the cost curves.

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Costs are derived from the production function.Costs are derived from the production function.

Objective 1Objective 1Objective 1Objective 1

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Understand the relationship between the short Understand the relationship between the short run production function and short run costsrun production function and short run costsUnderstand the relationship between the short Understand the relationship between the short run production function and short run costsrun production function and short run costs


Consider a simple 2-input short run production function,Consider a simple 2-input short run production function,like the one we used for the Acme Box Company:like the one we used for the Acme Box Company:

Q = f (L, KQ = f (L, K00))

where L= the variable input, labor and Kwhere L= the variable input, labor and K00 = the fixed = the fixed input, capital.input, capital.


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Consider a simple 2-input short run production function,Consider a simple 2-input short run production function,like the one we used for the Acme Box Company:like the one we used for the Acme Box Company:

Q = f (L, KQ = f (L, K00))

where L= the variable input, labor and Kwhere L= the variable input, labor and K00 = the fixed = the fixed input, capital.input, capital.

From the production function, we can write an From the production function, we can write an expression for total cost.expression for total cost.

Total Cost = Labor Costs + Capital CostTotal Cost = Labor Costs + Capital Cost = Total Variable Cost + Total Fixed Cost= Total Variable Cost + Total Fixed Cost


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Total Fixed Costs (TFC)Total Fixed Costs (TFC) refer to the total expenditure by the firm for fixed inputs.


Define Total Fixed Cost …Define Total Fixed Cost …Define Total Fixed Cost …Define Total Fixed Cost …

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Total Fixed Costs (TFC)Total Fixed Costs (TFC) refer 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 overheadsoverheads.



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Total Fixed Costs (TFC)Total Fixed Costs (TFC) refers to the total expenditure refers to the total expenditure by the firm for fixed inputs. by the firm for fixed inputs.

Fixed costs do not change when firms increase or Fixed costs do not change when firms increase or decrease their output. The lay person thinks of fixed decrease their output. The lay person thinks of fixed costs as costs as overheadsoverheads. .



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Total Variable CostsTotal Variable Costs (TVC) (TVC) refer to total expenditure refer to total expenditure on variable inputs, for example, the wages paid for on variable inputs, for example, the wages paid for labor services and the cost of raw materials labor services and the cost of raw materials purchased to produce the product. purchased to produce the product.

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Objective 2: … total variable cost and total costObjective 2: … total variable cost and total costObjective 2: … total variable cost and total costObjective 2: … total variable cost and total cost

Total Variable CostsTotal Variable Costs (TVC) (TVC) refer to total expenditure refer to total expenditure on variable inputs, for example, the wages paid for on variable inputs, for example, the wages paid for labor services and the cost of raw materials labor services and the cost of raw materials purchased to produce the product. purchased to produce the product.

Total CostsTotal Costs (TC) (TC) refer to therefer to the total expenditure on all total expenditure on all inputs used to produce a product. It is the sum of inputs used to produce a product. It is the sum of fixed costs and variable costs.fixed costs and variable costs.

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Objective 2: … total variable cost and total costObjective 2: … total variable cost and total costObjective 2: … total variable cost and total costObjective 2: … total variable cost and total cost

Objective 2: … fixed cost, variable cost and Objective 2: … fixed cost, variable cost and total costtotal cost

Objective 2: … fixed cost, variable cost and Objective 2: … fixed cost, variable cost and total costtotal cost

Total Cost = Total Fixed Cost + Total Variable CostTotal Cost = Total Fixed Cost + Total Variable Cost

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Can you Can you determine determine

these these values?values?

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Average costsAverage costs tells you how much a product costs per tells you how much a product costs per unit of output. In the short run, there are three average unit of output. In the short run, there are three average cost variables,cost variables, one corresponding to each category of one corresponding to each category of costs.costs.

Define average total cost, average variable cost, average Define average total cost, average variable cost, average fixed cost and marginal costfixed cost and marginal costDefine average total cost, average variable cost, average Define average total cost, average variable cost, average fixed cost and marginal costfixed cost and marginal cost

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1.1. Average Fixed cost (AFC)Average Fixed cost (AFC)


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2.2. Average Variable Cost (AVC)Average Variable Cost (AVC)


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2.2. Average Variable Cost (AVC)Average Variable Cost (AVC)

3.3. Average Total Cost (ATC) or simply Average Cost Average Total Cost (ATC) or simply Average Cost (AC)(AC)


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Total Cost = Average Total Cost Total Cost = Average Total Cost Quantity Quantity

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Total CostAverage Total Cost =Quantity

Objective 3: … the three “average” cost variables..Objective 3: … the three “average” cost variables..Objective 3: … the three “average” cost variables..Objective 3: … the three “average” cost variables..


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Total Cost Fixed Cost Variable Cost= +Quantity Quantity Quantity



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Total Cost Fixed Cost Variable Cost= +Quantity Quantity Quantity

Average Average Average Total = Fixed + Variable Cost Cost Cost


Marginal CostMarginal Cost is the addition to total cost resulting from producing one more unit of output.

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Objective 3: … define marginal cost Objective 3: … define marginal cost Objective 3: … define marginal cost Objective 3: … define marginal cost


ΔTotal CostMarginal Cost =ΔQuantity


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= +ΔTotal Cost ΔFixed Cost ΔVariable CostMarginal Cost =ΔQuantity ΔQuantity ΔQuantity

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Since fixed cost is constant, the equation above equals:Since fixed cost is constant, the equation above equals:



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=ΔTotal Cost ΔVariable CostMarginal Cost =ΔQuantity ΔQuantity


Since fixed cost is constant, the equation above equals:Since fixed cost is constant, the equation above equals:



In the In the short runshort run,, marginal cost is independent of fixed marginal cost is independent of fixed costs. costs.

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=ΔTotal Cost ΔVariable CostMarginal Cost =ΔQuantity ΔQuantity

Objective 4Objective 4 Objective 4Objective 4 Know and be able to use the cost formulas to Know and be able to use the cost formulas to

calculate costs calculate costs Know and be able to use the cost formulas to Know and be able to use the cost formulas to

calculate costs calculate costs

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Objective 4Objective 4 Objective 4Objective 4

Example:Example: We will revisit the Acme Box Company. We will revisit the Acme Box Company. Suppose Acme’s Fixed Costs equals $1,000 and the Suppose Acme’s Fixed Costs equals $1,000 and the firm hires labor at a constant wage of $60 per unit. firm hires labor at a constant wage of $60 per unit.

Know and be able to use the cost formulas to Know and be able to use the cost formulas to calculate costs calculate costs

Know and be able to use the cost formulas to Know and be able to use the cost formulas to calculate costs calculate costs

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Suppose Acme’s fixed costs equals $1,000. Suppose Acme’s fixed costs equals $1,000.

Objective 4: Calculating Costs …Objective 4: Calculating Costs …Objective 4: Calculating Costs …Objective 4: Calculating Costs …

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(1) (2) (3) (4)

LaborLabor(L)(L)

Total Total ProductProduct

(Q)(Q)

Marginal Marginal Product Product

(MPL)(MPL)

Total Fixed Total Fixed Cost (TFC)Cost (TFC)

$$

0 0 0 1000

1 8 8 1000

2 23 15 1000

3 42 19 1000

4 57 15 1000

5 67 10 1000

6 74 7 1000

7 79 5 1000

8 82 3 1000

9 83 1 1000

Acme’sAcme’s hires labor at a constant wage of $60 per unit of labor. hires labor at a constant wage of $60 per unit of labor. Its labor costs are its only variable costs.Its labor costs are its only variable costs.

Labor Costs = Variable Costs = wage rate Labor Costs = Variable Costs = wage rate labor units labor units

(1) (2) (3) (4) (5)=(1)x$60

LaborLabor(L)(L)


(Q)(Q)


(MPL)(MPL)


$$

Total Variable Total Variable Cost (TVC)Cost (TVC)

$$

0 0 0 1000 0

1 8 8 1000 1x60=60

2 23 15 1000 2x60=120

3 42 19 1000 3x60=180

4 57 15 1000 240

5 67 10 1000 300

6 74 7 1000 360

7 79 5 1000 420

8 82 3 1000 480

9 83 1 1000 54035


Acme’s Total Cost = Fixed Cost + Variable CostAcme’s Total Cost = Fixed Cost + Variable Cost


(1) (2) (3) (4) (5) (6)=(4) +(5)(6)=(4) +(5)

LaborLabor(L)(L)


(Q)(Q)


(MPL)(MPL)


$$

Total Variable Total Variable Cost (TVC)Cost (TVC)

$$

Total Cost Total Cost

(TC)(TC)

$$

0 0 0 1000 0 1000

1 8 8 1000 60 1000+60=1060

2 23 15 1000 120 1000+120=1120

3 42 19 1000 180 1000+180=1180

4 57 15 1000 240 1240

5 67 10 1000 300 1300

6 74 7 1000 360 1360

7 79 5 1000 420 1420

8 82 3 1000 480 1480

9 83 1 1000 540 1540

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Average Fixed Cost = Fixed Cost ÷ OutputAverage Fixed Cost = Fixed Cost ÷ Output


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(1) (2) (3) (4) (5) (6)=(4) +(5)(6)=(4) +(5) (7)=(4) (7)=(4) ÷(2)(2)

LaborLabor(L)(L)

Total Total Product orProduct or

Output (Q)Output (Q)


(MPL)(MPL)


$$

Total Variable Total Variable Cost (TVC) Cost (TVC)

$$

Total Cost Total Cost

(TC)(TC)

$$

Average Fixed Average Fixed Cost (AFC)Cost (AFC)

$$

0 0 0 1000 0 1000 ----

1 8 8 1000 60 1060 1000 ÷8=125

2 23 15 1000 120 1120 1000 ÷23=43.5

3 42 19 1000 180 1180 1000 ÷42=23.8

4 57 15 1000 240 1240 17.5

5 67 10 1000 300 1300 14.9

6 74 7 1000 360 1360 13.5

7 79 5 1000 420 1420 12.7

8 82 3 1000 480 1480 12.2

9 83 1 1000 540 1540 12.1

Average Variable Cost = Total Variable Cost ÷ OutputAverage Variable Cost = Total Variable Cost ÷ Output


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(1) (2) (3) (4) (5) (6)(6) (7)(7) (8)=(5) ÷(2)(8)=(5) ÷(2)

LaborLabor(L)(L)

Total Total Product orProduct orOutput (Q)Output (Q)

Marginal Marginal Product Product (MPL)(MPL)


$$


$$

Total Cost Total Cost (TC)(TC)

$$

Average Average Fixed Cost Fixed Cost (AFC in $) (AFC in $)

Average Variable Average Variable Cost (AVC in $)Cost (AVC in $)

0 0 0 1000 0 1000 ---- 0

1 8 8 1000 60 1060 125 60 ÷8=7.5

2 23 15 1000 120 1120 43.5 120 ÷23=5.2

3 42 19 1000 180 1180 23.8 180 ÷42=4.3

4 57 15 1000 240 1240 17.5 4.2

5 67 10 1000 300 1300 14.9 4.5

6 74 7 1000 360 1360 13.5 4.9

7 79 5 1000 420 1420 12.7 5.3

8 82 3 1000 480 1480 12.2 5.9

9 83 1 1000 540 1540 12.1 6.5

Average Total Cost = Average Fixed Cost + Average Variable Cost, orAverage Total Cost = Average Fixed Cost + Average Variable Cost, orAverage Total Cost = Total Cost ÷ OutputAverage Total Cost = Total Cost ÷ Output


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(1) (2) (3) (4) (5) (6)(6) (7)(7) (8)(8) (9)=(6) (9)=(6) ÷(2)(2)

LaborLabor(L)(L)




$$


$$

Total Cost Total Cost (TC)(TC)

$$

Average Average Fixed Cost Fixed Cost (AFC in $)(AFC in $)

Average Average Variable Cost Variable Cost

(AVC in $)(AVC in $)

Average Total Average Total Cost (ATC in Cost (ATC in

$)$)

0 0 0 1000 0 1000 ---- 0 ----

1 8 8 1000 60 1060 125 60 ÷8=7.5 1060÷ 8=132.5

2 23 15 1000 120 1120 43.5 120 ÷23=5.2 1120 ÷23=48.7

3 42 19 1000 180 1180 23.8 180 ÷42=4.3 1180 ÷ 42=28.1

4 57 15 1000 240 1240 17.5 4.2 21.8

5 67 10 1000 300 1300 14.9 4.5 19.4

6 74 7 1000 360 1360 13.5 4.9 18.4

7 79 5 1000 420 1420 12.7 5.3 18.0

8 82 3 1000 480 1480 12.2 5.9 18.1

9 83 1 1000 540 1540 12.1 6.5 18.5

Marginal Cost = Marginal Cost = ∆∆Total Cost ÷ Total Cost ÷ ∆∆Output, or in the short run,Output, or in the short run,Marginal Cost = Marginal Cost = ∆∆Variable Cost ÷ Variable Cost ÷ ∆∆OutputOutput


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(1) (2) (3) (4) (5) (6)(6) (7)(7) (8)(8) (9)(9) (10)=∆(5)÷(3)(10)=∆(5)÷(3)

LaborLabor(L)(L)



Fixed Cost Fixed Cost (TFC)(TFC)

$$

Variable Variable Cost (TVC)Cost (TVC)

$$

TotalTotalCost Cost (TC)(TC)

$$

Average Average Fixed Cost Fixed Cost

(AFC) (AFC) $$

Average Average Variable Variable

Cost (AVC) Cost (AVC) $$

Average Average Total Cost Total Cost

(ATC) (ATC) $$

Marginal Cost Marginal Cost (MC) (MC)

$$

0 0 0 1000 0 1000 ---- 0 ---- ----

1 8 8 1000 60 1060 125 7.5 132.5 60÷ 8=7.5

2 23 15 1000 120 1120 43.5 5.2 48.7 60÷ 15=4

3 42 19 1000 180 1180 23.8 4.3 28.1 60÷ 19=3.2

4 57 15 1000 240 1240 17.5 4.2 21.8 4

5 67 10 1000 300 1300 14.9 4.5 19.4 6

6 74 7 1000 360 1360 13.5 4.9 18.4 8.6

7 79 5 1000 420 1420 12.7 5.3 18.0 12

8 82 3 1000 480 1480 12.2 5.9 18.1 20

9 83 1 1000 540 1540 12.1 6.5 18.5 60


Understand the relationship between marginal Understand the relationship between marginal product and marginal cost of productionproduct and marginal cost of productionUnderstand the relationship between marginal Understand the relationship between marginal product and marginal cost of productionproduct and marginal cost of production

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Below is a segment of the Table for the Acme Box Company.Below is a segment of the Table for the Acme Box Company.


LaborLabor(L)(L)

Total Product Total Product or Output or Output

(Q)(Q)


of Labor (MPL)of Labor (MPL)

Marginal Cost Marginal Cost (MC)(MC)

$$

0 0 0 ----

1 8 8 7.5

2 23 15 4

3 42 19 3.2

4 57 15 4

5 67 10 6

6 74 7 8.6

7 79 5 12

8 82 3 20

9 83 1 6042

(1) (2) (3) (4)




LaborLabor(L)(L)


(Q)(Q)




$$

0 0 0 ----

1 8 8 7.5

2 23 15 4

3 42 19 3.2

4 57 15 4

5 67 10 6

6 74 7 8.6

7 79 5 12

8 82 3 20

9 83 1 60

Increasing Increasing Marginal Marginal Returns Returns segmentsegment

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LaborLabor(L)(L)


(Q)(Q)




$$

0 0 0 ----

1 8 8 7.5

2 23 15 4

3 42 19 3.2

4 57 15 4

5 67 10 6

6 74 7 8.6

7 79 5 12

8 82 3 20

9 83 1 60

Increasing Increasing Marginal Marginal Returns Returns segmentsegment

Diminishing Diminishing Marginal Marginal ReturnsReturnssegmentsegment

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In the In the increasing marginal returnsincreasing marginal returns segment, when segment, when marginal product is rising, marginal cost is falling.marginal product is rising, marginal cost is falling.

Objective 5: … the relationship between marginal Objective 5: … the relationship between marginal product and marginal cost of productionproduct and marginal cost of productionObjective 5: … the relationship between marginal Objective 5: … the relationship between marginal product and marginal cost of productionproduct and marginal cost of production

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In the In the diminishing marginal returnsdiminishing marginal returns segment, when segment, when marginal product is falling, marginal cost is rising.marginal product is falling, marginal cost is rising.


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In the In the diminishing marginal returnsdiminishing marginal returns segment, when segment, when marginal product is falling, marginal cost is rising.marginal product is falling, marginal cost is rising.

In the In the negative marginal returnsnegative marginal returns segment, what do segment, what do you think is happening to marginal cost? Yes, it is you think is happening to marginal cost? Yes, it is rising fast!rising fast!


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What then is the shape of the marginal cost curve? What then is the shape of the marginal cost curve?

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Objective 5: … the relationship between marginal Objective 5: … the relationship between marginal product and marginal cost of productionproduct and marginal cost of production

Objective 5: … the relationship between marginal Objective 5: … the relationship between marginal product and marginal cost of productionproduct and marginal cost of production

What then is the shape of the marginal cost curve? What then is the shape of the marginal cost curve? It is U-shaped.It is U-shaped.

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Objective 6: … the relationship between marginal product Objective 6: … the relationship between marginal product and marginal costand marginal costObjective 6: … the relationship between marginal product Objective 6: … the relationship between marginal product and marginal costand marginal cost


Understand the relationship between marginal cost,Understand the relationship between marginal cost, average total cost, and average variable costaverage total cost, and average variable cost


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When marginal cost (MC) is When marginal cost (MC) is lessless than either average than either average total cost (ATC) or average variable cost (AVC), it total cost (ATC) or average variable cost (AVC), it causes ATC or AVC to fall.causes ATC or AVC to fall.




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When MC is When MC is greatergreater than either ATC or AVC, it than either ATC or AVC, it causes ATC or AVC to rise.causes ATC or AVC to rise.





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The MC curve The MC curve intersectsintersects both the AVC and ATC both the AVC and ATC curves at their respective minimum points.curves at their respective minimum points.



The MC curve The MC curve intersectsintersects both the AVC and ATC both the AVC and ATC curves at their respective minimum points.curves at their respective minimum points.



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The average total cost and average variable curves The average total cost and average variable curves are also U-shaped.are also U-shaped.

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Objective 6: … the marginal cost, average total cost and Objective 6: … the marginal cost, average total cost and average variable cost curvesaverage variable cost curvesObjective 6: … the marginal cost, average total cost and Objective 6: … the marginal cost, average total cost and average variable cost curvesaverage variable cost curves

The average total cost and average variable curves The average total cost and average variable curves are also U-shaped.are also U-shaped.

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Objective 6: … the marginal cost, average total cost and Objective 6: … the marginal cost, average total cost and average variable cost curvesaverage variable cost curvesObjective 6: … the marginal cost, average total cost and Objective 6: … the marginal cost, average total cost and average variable cost curvesaverage variable cost curves

Like the marginal cost curve, their shapes are also Like the marginal cost curve, their shapes are also influenced by the law of diminishing marginal returns.influenced by the law of diminishing marginal returns.

Objective 7Objective 7Objective 7Objective 7Understand what happens to average fixed Understand what happens to average fixed

cost as output increasescost as output increases.Understand what happens to average fixed Understand what happens to average fixed

cost as output increasescost as output increases.

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Average fixed costs falls as output increases.....think of this as “spreading your overheads”. Average fixed costs falls as output increases.....think of this as “spreading your overheads”.

Objective 7Objective 7Objective 7Objective 7Understand what happens to average fixed Understand what happens to average fixed

cost as output increasescost as output increases.Understand what happens to average fixed Understand what happens to average fixed

cost as output increasescost as output increases.

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Fixed CostAverage Fixed Cost =Quantity

ATC = AVC + AFC ATC = AVC + AFC AFC = ATC – AVCAFC = ATC – AVC

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If average fixed cost falls as output increases, If average fixed cost falls as output increases, what does this imply about the average what does this imply about the average variable cost and average total cost curves?variable cost and average total cost curves?

ATC = AVC + AFC ATC = AVC + AFC

AFC = ATC – AVCAFC = ATC – AVC

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

ATC = AVC + AFC ATC = AVC + AFC

AFC = ATC – AVCAFC = ATC – AVC

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

Objective 8:Objective 8: Be able to graph the cost curvesBe able to graph the cost curvesObjective 8:Objective 8: Be able to graph the cost curvesBe able to graph the cost curves

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Graph the cost curves using the data for the Acme Graph the cost curves using the data for the Acme Box Company. Box Company.

Graph the cost curves using the data for the Acme Graph the cost curves using the data for the Acme Box Company. Box Company.


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(2) (4) (5) (6)(6) (7)(7) (8)(8) (9)(9) (10)=∆(5)÷(3)(10)=∆(5)÷(3)


Fixed Cost Fixed Cost (TFC)(TFC)

$$

Variable Variable Cost (TVC)Cost (TVC)

$$

TotalTotalCost Cost (TC)(TC)

$$

Average Average Fixed Cost Fixed Cost

(AFC) (AFC) $$

Average Average Variable Variable

Cost (AVC) Cost (AVC) $$

Average Average Total Cost Total Cost

(ATC) (ATC) $$

Marginal Cost Marginal Cost (MC) (MC)

$$

0 1000 0 1000 ---- 0 ---- ----

8 1000 60 1060 125 7.5 132.5 7.5

23 1000 120 1120 43.5 5.2 48.7 4

42 1000 180 1180 23.8 4.3 28.1 3.2

57 1000 240 1240 17.5 4.2 21.8 4

67 1000 300 1300 14.9 4.5 19.4 6

74 1000 360 1360 13.5 4.9 18.4 8.6

79 1000 420 1420 12.7 5.3 18.0 12

82 1000 480 1480 12.2 5.9 18.1 20

83 1000 540 1540 12.1 6.5 18.5 60

Can you identify the curves in the diagram?Can you identify the curves in the diagram? Can you identify the curves in the diagram?Can you identify the curves in the diagram?


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H = Average Fixed Cost curve

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E = Marginal Cost curve

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F = Average Total Cost curve

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G = Average variable Cost curve

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E = Marginal Cost curve

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

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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.

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F = Average Total Cost curve

C = minimum point on the average total cost curve. The marginal cost curve cuts the average total cost curve at this point.

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You should be able to draw and identify these graphs.

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7272

End of Module 14End of Module 14End of Module 14End of Module 14



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