Cost of Production

Mankiw 13

Firm’s Goal

• Profit maximization

• Profits are Revenue( P*q)-Costs

• What are firm’s costs ?

Costs

• Economic costs are the full costs of production including a normal rate of return on investment and the opportunity costs of each factor of production.

• A normal rate of return is what you could have earned on your next best investment

Accounting Costs vs. Economic Costs

• Accounting costs are explicit costs– Costs the firm gets a bill for like wages,

interests on loans, rent

• Economic costs include opportunity cost

• Consider identical firms, one managed by owner and one with a hired manager.– Accounting costs will be higher for one with

hired manager, but economic costs will not be

Use the correct costs

• Accounting costs must be easily measured to reduce the ability to cheat for tax and other purposes.

• Firms must take into account implicit costs as well as explicit costs to make correct decisions.– Say you inherit a sum of money, should you

think of it as free money and use it to start a business?

Alexander owns a small factory that makes fishing lures. He can make 1,000 lures per year and sell them for $100 each. Alexander pays $25,000 for raw materials to produce the 1,000 lures. He

invested a total of $100,000 in the building and equipment: $50,000 of his own savings and $50,000 borrowed at 10 percent; his own money was earning 10 percent interest too. Alexander

could work at a competing factory for $40,000. According to this information, Alexander's accounting profit is

1 2 3 4 5

20% 20% 20%20%20%

1. $30,000.

2. $35,000.

3. $70,000.

4. $75,000.

5. $80,000.

Alexander owns a small factory that makes fishing lures. He can make 1000 lures per year and sell them for $100 each. Alexander pays $25,000 for raw materials to produce the 1000 lures. He invested a total of $100,000 in the building and equipment: $50,000 of his own savings and

$50,000 borrowed at 10 percent; his own money was earning 10 percent interest too. Alexander could work at a competing factory for $40,000. According to this information, Alexander's

economic profit is

1 2 3 4 5

20% 20% 20%20%20%

1. $25,000.

2. $30,000.

3. $35,000.

4. $70,000

5. $75,000.

What makes up costs?

• Price of inputs– An input is anything the firm buys to produce

its product, like labor, raw materials, machines etc

• Production technology– determines how many inputs are necessary to

produce given amount of output

Production

• Remember that we need to know about production to find the firms costs

• We assume there are just two inputs, capital and labor, but that the can be used in various combinations to produce output.– Can dig a ditch in an hour with 5 men and

shovel or one man and ditch digging machine.

Production Function

• A production function expresses the relationship between inputs and outputs.

• Q=F(L,K)

• Q=output

• L=labor

• K=capital

Short Run

• The short run is a period of time that is short enough so that at least one input is fixed– The capital input is usually assumed fixed– Actual time period is different for different industries.

• Like assuming plant size is fixed.• Production function is simpler.

– Say capital is fixed at 10 units, Q=F(L,10)

• As L increases what will happen to Q?

Ice Cream Store

• .What does production function of an ice cream shop look like in the short run?

• We assume the size of the shop is fixed

• We need workers to sell ice cream, we add the first one or two and we sell a lot more ice cream.

Diminishing Returns

• At some point we add another worker, sales go up but not by as much.

• Why?– We have a fixed size of shop– We have a fixed number of cash registers

• This is what we call the principle of diminishing returns

Diminishing Returns

• Diminishing Returns must happen in short run because capital is fixed

• Does not matter what the industry is

• Important to remember that additional workers add less to output because they have less capital per worker– Quality is the same.

ExampleAre these numbers for output consistent with diminishing returns?

Yes output increases at decreasing rate

Would the firm ever hire 8 workers?

No output decreases

K L Q

5 0 0

5 1 9

5 2 32

5 3 63

5 4 96

5 5 125

5 6 144

5 7 147

5 8 128

Graph

Total Product Curve

0

20

40

60

80

100

120

140

160

0 1 2 3 4 5 6 7 8 9

Lablor

Ou

tpu

t

Marginal and Average Product

L Q AP MP

0 0 - -

1 9 9 9

2 32 16 23

3 63 21 31

4 96 24 33

5 125 25 29

6 144 24 19

7 147 21 3

8 128 16 -19

Average Product=Q/L If L=1, AP=9/1=9 If L=2, AP=32/2=16 Marginal Product=∆Q/∆L If L=1,MP=9-0/1-0=9 If L=2, MP=32-9/2-1=23 Where is diminishing returns?

With 5th worker, when MP falls

Graph of Marginal and Average Product

Average and Marginal Product

-30

-20

-10

0

10

20

30

40

0 5 10

labor

APMP

Diminishing returns

Diminishing returns

• Begins when marginal product falls• Is equal to the slope of the total product curve• MP=∆q/∆L

Marginal Product is slope of Total Product Curve

Total Product Curve

0

20

40

60

80

100

120

140

160

0 1 2 3 4 5 6 7 8 9

Lablor

Ou

tpu

t

923

1. 2. 3 4. 5.

20% 20% 20%20%20%

According to the table below, the marginal product of hiring the third worker is

1. 50.

2. 38.

3. 16.7.

4. 12.

5. 4.

Short Run

• Capital is fixed

• Diminishing Returns is inevitable

• In short run, TP and MP will always have the shapes of the curves in the previous slides

Total Product and Costs

• How do we go from the information about production to the cost curves?

• Two types of inputs in the short run lead to two types of costs, fixed and variable

Fixed Costs

• Since firm always has the same amount of capital, even if it produces nothing, it will always have to pay the costs of that capital

• In the example, firm has 5 units of capital if the cost of capital is $50 per unit, its fixed cost will always be $250

Fixed Costs

• Fixed Costs are costs that do not change when output changes

• Sunk costs are a special kind of fixed costs.– Costs that cannot be recovered– Example would be a subway tunnel. Once it is

built it has not other uses. – Sunk costs are not relevant to decisions

Variable Costs

• Variable costs are costs that vary with output

• Variable costs come from labor

• Amount of labor needed to produce a given output multiplied by the price of labor

• What if Pl=$100?

Which of the following is most likely a fixed cost in the short run?

1 2 3 4 5

20% 20% 20%20%20%1. Wages paid to workers who

assemble computers

2. Performance bonuses for sales staff of a pharmaceutical company

3. Payments for gasoline for company cars driven by the sales staff

4. Interest payments on funds borrowed by a farmer to finance farm machinery

5. Payments for chemicals in the production of drugs at a pharmaceutical company

Total Product

K L Q

5 0 0

5 1 9

5 2 32

5 3 63

5 4 96

5 5 125

5 6 144

5 7 147

CostsFC VC Q

250 0 0

250 100 9

250 200 32

250 300 63

250 400 96

250 500 125

250 600 144

250 700 147

FC=Pk*K

FC=50*5

VC=Pl*L

VC=100*l

Total Product Curve

0

20

40

60

80

100

120

140

160

0 1 2 3 4 5 6 7 8 9

Labor

Ou

tpu

t

VC=L*100

Variable Costs

0

20

40

60

80

100

120

140

160

0 1 2 3 4 5 6 7 8 9

Costs

Ou

tpu

t

00 00 00 00 00 00 00 00 00

TP to VC

• Graph has not really changed shape when L is multiplied by 100 (Pl)

• Shape of VC is determined by principle of diminishing returns

• Convention is axis are reversed

Short Run Costs

FC

VC

Q

$

250

Short Run Costs

FC

VC

Q

$

250

TC

TC=FC=VC

CostsQ

F C

V C TC AFC AVC ATC MC

0 250 0 250

9 250 100 350 27.78 11.11 38.8911.1

1

32 250 200 450 7.81 6.25 14.06 4.35

63 250 300 550 3.97 4.76 8.73 3.23

96 250 400 650 2.60 4.17 6.77 3.03

125 250 500 750 2.00 4.00 6.00 3.45

144 250 600 850 1.74 4.17 5.90 5.26

147 250 700 950 1.70 4.76 6.4633.3

3

FC=Pk*K

VC=PL*L

TC=FC+VC

ATC=TC/Q

AVC=VC/Q

AFC=FC/Q

MC=∆TC/∆Q

According to the table below, the marginal cost of producing the fifth unit is

1 2 3 4 5

20% 20% 20%20%20%

1. $3.60.

2. $8.00.

3. $10.00.

4. $40.00.

5. $18.00.

What will graph of Average Cost Curves look like?

• AFC=FC/Q, FC is constant as Q ↑, so AFC↓

• AVC =VC/Q is more difficult, both VC and Q are ↑

• AVC could ↑ or ↓or stay the same depending on which increases faster

• Must look at shape of VC

Short Run Costs

VC

Q

$

50

VC increases slowly at first. Since VC is ↑ more slowly than q, AVC ↓. LaterVC increases faster than q and AVC ↑.

Average Cost Curves

AFC

AVC

Q

$

Average Total Cost

• Total Cost has the same shape as Variable cost (TC=FC+VC)

• ATC=AFC+AVC

• ATC>AVC, ATC will be above AVC

• ATC will have the same shape as AVC

• ATC-AVC=AFC

Average Cost Curves

AFC

AVC

Q

$ ATCAFC

Marginal Cost

• Marginal Cost will ↑– MC is slope of TC curve, slope is increasing– MC increases because amount of labor to

produce additional units of output is increasing due to diminishing returns

1 2 3 4 5

20% 20% 20%20%20%

Over the range indicated, the production process in the table below exhibits _________ marginal product of labor, and the marginal cost

curve for this firm would be _________.

1. increasing; downward sloping.

2. increasing; upward sloping.

3. decreasing; downward sloping.

4. decreasing; upward sloping.

5. constant; downward sloping then upward sloping.

Answer

• When labor increases from 0 to 1, output increases by 22. Each unit of output takes 1/22 unit of labor

• When labor increases from 1 to 2, output increases by 18. Each unit of output takes 1/18 unit of labor

MC intersects AC at the minimum

• If MC<AC, AC falls– If your semester grades are lower than your GPA, GPA

falls

• If MC>AC, AC rises– If your semester grades are higher than your GPA, GPA

rises

• If MC=AC, AC stays the same– If your semester grades are the same as your GPA,

GPA stays the same

Average Cost Curves

AVC

Q

$ ATC

MC

When marginal cost is above average total cost,

1 2 3 4

25% 25%25%25%1. average total cost is

rising.

2. average total cost is falling.

3. average total cost is minimized.

4. average fixed cost is rising.

Long Run Cost Curves

• In Long Run all costs are variable because there are not fixed inputs

• Usually Long Run Curves have the same shape as Short Run Curves

• Diminishing returns is not the reason for the shape of long run curves – No fixed inputs

Returns to scale

• Economies of scale refer to the property where long-run average total cost falls as the quantity of output increases.

• Diseconomies of scale refer to the property where long-run average total cost rises as the quantity of output increases.

• Constant returns to scale refers to the property where long-run average total cost stays the same as the quantity of output increases

Average Total Cost in the Short and Long Runs

Long Run Costs

• We think most cost curves in long run are U shaped because in most industries we do not see many small firms or just one big firm.

The short run is a period of time less than three months long.

1 2

50%50%

1. True

2. False

The long run average cost curve is U-shaped because the principle of

diminishing returns.

1 2

50%50%

1. True

2. False