The Costs of Production and Profit Maximization

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THE COSTS OF
PRODUCTION
 
13
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THE COSTS OF PRODUCTION
Total Revenue, Total Cost, Profit
 
We assume that 
the firm’s goal is to maximize profit
.
 
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THE COSTS OF PRODUCTION
Costs:  Explicit vs. Implicit
 
Explicit costs
 require an outlay of money,
e.g.
, paying wages to workers.
Implicit costs
 do not require a cash outlay,
e.g.
, the opportunity cost of the owner’s time.
Remember one of the Ten Principles:
     
The cost of something is
     what you give up to get it
.
This is true whether the costs are implicit or explicit.  Both
matter for firms’ decisions.
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THE COSTS OF PRODUCTION
Explicit vs. Implicit Costs:  An Example
 
You need $100,000 to start your business.
The interest rate is 5%.
Case 1:  borrow $100,000
explicit cost = $5000 interest on loan
Case 2:  use $40,000 of your savings,
borrow the other $60,000
explicit cost = $3000 (5%) interest on the loan
implicit cost = $2000 (5%) 
foregone
 interest you could have
earned on your $40,000.
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THE COSTS OF PRODUCTION
Economic Profit  vs. Accounting Profit
 
Accounting profit
=
 
total revenue minus total explicit costs
Economic profit
=
 
total revenue minus total costs (including explicit
and implicit costs)
Accounting profit ignores implicit costs,
so it’s higher than economic profit.
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THE COSTS OF PRODUCTION
The Production Function
 
A 
production function
 shows the relationship between the quantity of
inputs used to produce a good and the quantity of output of that good.
It can be represented by a table, equation, or graph.
Example 1:
Farmer Jack grows wheat.
He has 5 acres of land.
He can hire as many workers as he wants.
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THE COSTS OF PRODUCTION
Example 1:  Farmer Jack’s Production Function
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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THE COSTS OF PRODUCTION
Marginal Product
 
If Jack hires one more worker, his output rises by the 
marginal product of
labor
.
The 
marginal product
 
of any input is the increase in output arising from an
additional unit of that input, holding all other inputs constant.
Notation:
   
 (delta) = “change in…”
 
Examples:
Q
 = change in output, 
L
 = change in labor
Marginal product of labor (
MPL
) =
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THE COSTS OF PRODUCTION
EXAMPLE 1:
  Total & Marginal Product
 
200
 
400
 
600
 
800
 
1000
MPL
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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THE COSTS OF PRODUCTION
EXAMPLE 1: 
MPL = Slope of Prod Function
 
MPL equals the
slope of the
production function.
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THE COSTS OF PRODUCTION
Why MPL Is Important
 
Recall one of the Ten Principles:
    
 
Rational people think at the margin.
When Farmer Jack hires an extra worker,
his costs rise by the wage he pays the worker
his output rises by 
MPL
Comparing them helps Jack decide whether he would benefit
from hiring the worker.
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THE COSTS OF PRODUCTION
Why MPL Diminishes
 
Farmer Jack’s output rises by a smaller and smaller amount for
each additional worker.  Why?
As Jack adds workers, the average worker has less land to work
with and will be less productive.
In general, 
MPL
 diminishes as 
L
 rises
whether the fixed input is land or capital (equipment, machines,
etc.).
Diminishing marginal product
:
the marginal product of an input declines as the quantity of the
input increases (other things equal)
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THE COSTS OF PRODUCTION
EXAMPLE 1:  
Farmer Jack’s Costs
 
Farmer Jack must pay $1000 per month for the land, regardless
of how much wheat he grows.
The market wage for a farm worker is $2000 per month.
So Farmer Jack’s costs are related to how much wheat he
produces….
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THE COSTS OF PRODUCTION
EXAMPLE 1:  
Farmer Jack’s Costs
Total
Cost
 
3000
5
2800
4
2400
3
1800
2
1000
1
0
0
Cost of
labor
Cost of
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THE COSTS OF PRODUCTION
EXAMPLE 1:  
Farmer Jack’s Total Cost Curve
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THE COSTS OF PRODUCTION
Marginal Cost
 
Marginal Cost
 (
MC
)
is the increase in Total Cost from
producing one more unit:
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THE COSTS OF PRODUCTION
EXAMPLE 1:  
Total and Marginal Cost
 
$10.00
 
$5.00
 
$3.33
 
$2.50
 
$2.00
 
Marginal
Cost (
MC
)
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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THE COSTS OF PRODUCTION
EXAMPLE 1:  
The Marginal Cost Curve
 
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THE COSTS OF PRODUCTION
Why MC Is Important
 
Farmer Jack is rational and wants to maximize
his profit.  To increase profit, should he produce more
or less wheat?
To find the answer, Farmer Jack needs to
“think at the margin.”
If the cost of additional wheat (
MC
) is less than
the revenue he would get from selling it,
then Jack’s profits rise if he produces more.
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THE COSTS OF PRODUCTION
Fixed and Variable Costs
 
Fixed costs
 
(
FC
)
 do not vary with the quantity of output
produced.
For Farmer Jack, 
FC
 = $1000 for his land
Other examples:
cost of equipment, loan payments, rent
Variable costs (
VC
)
 vary with the quantity produced.
For Farmer Jack, 
VC
 = wages he pays workers
Other example:  cost of materials
Total cost (
TC
)
  =  
FC
  +  
VC
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THE COSTS OF PRODUCTION
EXAMPLE 2:
  Costs
 
7
6
5
4
3
2
1
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TC
VC
FC
Q
$0
$100
$200
$300
$400
$500
$600
$700
$800
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2
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4
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VC
TC
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EXAMPLE 2:
  Marginal Cost
 
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THE COSTS OF PRODUCTION
EXAMPLE 2:
  Average Fixed Cost
100
7
100
6
100
5
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4
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3
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2
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1
$100
0
AFC
FC
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THE COSTS OF PRODUCTION
EXAMPLE 2:
  Average Variable Cost
520
7
380
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2
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1
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AVC
VC
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THE COSTS OF PRODUCTION
EXAMPLE 2:
  Average Total Cost
ATC
620
7
480
6
380
5
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4
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3
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2
170
1
$100
0
TC
Q
 
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   ATC
 = 
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 + 
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undefined
THE COSTS OF PRODUCTION
EXAMPLE 2:
  Average Total Cost
 
Usually, as in this example,
the 
ATC
 curve is U-shaped.
 
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76
77.50
86.67
110
$170
n/a
ATC
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TC
Q
undefined
THE COSTS OF PRODUCTION
EXAMPLE 2:
  
The Various Cost Curves Together
 
undefined
THE COSTS OF PRODUCTION
EXAMPLE 2:
  Why ATC Is Usually U-Shaped
 
 
A
s
 
Q
 
r
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s
:
Initially,
falling 
AFC
pulls 
ATC
 down.
Eventually,
rising 
AVC
pulls 
ATC
 up.
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THE COSTS OF PRODUCTION
EXAMPLE 2:
  ATC and MC
 
 
When 
MC
 < 
ATC
,
ATC
 is falling.
When 
MC
 > 
ATC
,
ATC
 is rising.
The 
MC
 curve
crosses the
ATC
 curve at
the 
ATC
 curve’s
minimum.
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THE COSTS OF PRODUCTION
Costs in the Short Run & Long Run
 
Short run:
Some inputs are fixed (
e.g.,
 factories, land).
The costs of these inputs are 
FC
.
Long run:
All inputs are variable
(
e.g.,
 firms can build more factories,
or sell existing ones).
In the long run, 
ATC
 at any 
Q
 is cost per unit using the most
efficient mix of inputs for that 
Q
 (
e.g
., the factory size with the
lowest 
ATC
).
undefined
THE COSTS OF PRODUCTION
EXAMPLE 3:
  LRATC with 3 factory Sizes
 
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Each size has its
own 
SRATC
 curve.
The firm can
change to a
different factory
size in the long
run, but not in the
short run.
undefined
THE COSTS OF PRODUCTION
EXAMPLE 3:
  LRATC with 3 factory Sizes
 
LRATC
 
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undefined
THE COSTS OF PRODUCTION
A Typical LRATC Curve
 
In the real world,
factories come in
many sizes,
each with its own
SRATC
 curve.
So a typical
LRATC
 curve
looks like this:
undefined
THE COSTS OF PRODUCTION
How ATC Changes as
the Scale of Production Changes
 
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THE COSTS OF PRODUCTION
How ATC Changes as
the Scale of Production Changes
 
Economies of scale occur when increasing production allows greater
specialization:
workers more efficient when focusing on a narrow task.
More common when 
Q
 is low.
Diseconomies of scale are due to coordination problems in large
organizations.
E.g
., management becomes stretched, can’t control costs.
More common when 
Q
 is high.
undefined
THE COSTS OF PRODUCTION
CONCLUSION
 
Costs are critically important to many business decisions, including
production, pricing, and hiring.
This chapter has introduced the various cost concepts.
The following chapters will show how firms use these concepts to maximize
profits in various market structures.
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Explore the concept of costs of production in business, distinguishing between explicit and implicit costs. Learn the difference between economic profit and accounting profit, and understand the importance of considering all costs in maximizing profit. Dive into examples and the production function to grasp these fundamental economic principles.

  • Production Costs
  • Profit Maximization
  • Economic Profit
  • Accounting Profit
  • Business Economics

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  1. 13 C H A P T E R THE COSTS OF PRODUCTION

  2. Total Revenue, Total Cost, Profit We assume that the firm s goal is to maximize profit. Profit = Total revenue Total cost the amount a firm receives from the sale of its output the market value of the inputs a firm uses in production THE COSTS OF PRODUCTION

  3. Costs: Explicit vs. Implicit Explicit costs require an outlay of money, e.g., paying wages to workers. Implicit costs do not require a cash outlay, e.g., the opportunity cost of the owner s time. Remember one of the Ten Principles: The cost of something is what you give up to get it. This is true whether the costs are implicit or explicit. Both matter for firms decisions. THE COSTS OF PRODUCTION

  4. Explicit vs. Implicit Costs: An Example You need $100,000 to start your business. The interest rate is 5%. Case 1: borrow $100,000 explicit cost = $5000 interest on loan Case 2: use $40,000 of your savings, borrow the other $60,000 explicit cost = $3000 (5%) interest on the loan implicit cost = $2000 (5%) foregone interest you could have earned on your $40,000. In both cases, total (exp+ imp) costs are $5000. THE COSTS OF PRODUCTION

  5. Economic Profit vs. Accounting Profit Accounting profit = total revenue minus total explicit costs Economic profit = total revenue minus total costs (including explicit and implicit costs) Accounting profit ignores implicit costs, so it s higher than economic profit. THE COSTS OF PRODUCTION

  6. The Production Function A production function shows the relationship between the quantity of inputs used to produce a good and the quantity of output of that good. It can be represented by a table, equation, or graph. Example 1: Farmer Jack grows wheat. He has 5 acres of land. He can hire as many workers as he wants. THE COSTS OF PRODUCTION

  7. Example 1: Farmer Jacks Production Function L Q 3,000 (no. of workers) (bushels of wheat) 2,500 Quantity of output 0 0 2,000 1 1000 1,500 2 1800 1,000 3 2400 500 4 2800 0 0 1 2 3 4 5 5 3000 No. of workers THE COSTS OF PRODUCTION

  8. Marginal Product If Jack hires one more worker, his output rises by the marginal product of labor. The marginal product of any input is the increase in output arising from an additional unit of that input, holding all other inputs constant. Notation: (delta) = change in Examples: Q = change in output, L = change in labor Marginal product of labor (MPL) = Q L THE COSTS OF PRODUCTION

  9. EXAMPLE 1: Total & Marginal Product L Q (no. of workers) (bushels of wheat) MPL 0 0 1000 Q = 1000 L = 1 1 1000 800 Q = 800 L = 1 2 1800 600 L = 1 Q = 600 3 2400 Q = 400 400 L = 1 4 2800 200 L = 1 Q = 200 5 3000 THE COSTS OF PRODUCTION

  10. EXAMPLE 1: MPL = Slope of Prod Function L Q MPL equals the slope of the production function. 3,000 MPL (no. of workers) (bushels of wheat) 2,500 Quantity of output 0 0 2,000 Notice that MPL diminishes as L increases. 1,000 1000 1 1000 1,500 800 2 1800 This explains why the production function gets flatter as L increases. 0 1 No. of workers 600 3 2400 500 400 4 2800 0 200 2 3 4 5 5 3000 THE COSTS OF PRODUCTION

  11. Why MPL Is Important Recall one of the Ten Principles: Rational people think at the margin. When Farmer Jack hires an extra worker, his costs rise by the wage he pays the worker his output rises by MPL Comparing them helps Jack decide whether he would benefit from hiring the worker. THE COSTS OF PRODUCTION

  12. Why MPL Diminishes Farmer Jack s output rises by a smaller and smaller amount for each additional worker. Why? As Jack adds workers, the average worker has less land to work with and will be less productive. In general, MPL diminishes as L rises whether the fixed input is land or capital (equipment, machines, etc.). Diminishing marginal product: the marginal product of an input declines as the quantity of the input increases (other things equal) THE COSTS OF PRODUCTION

  13. EXAMPLE 1: Farmer Jacks Costs Farmer Jack must pay $1000 per month for the land, regardless of how much wheat he grows. The market wage for a farm worker is $2000 per month. So Farmer Jack s costs are related to how much wheat he produces . THE COSTS OF PRODUCTION

  14. EXAMPLE 1: Farmer Jacks Costs L Q Cost of land Cost of labor Total Cost (no. of workers) (bushels of wheat) 0 0 $1,000 $0 $1,000 1 1000 $1,000 $2,000 $3,000 2 1800 $1,000 $4,000 $5,000 3 2400 $1,000 $6,000 $7,000 4 2800 $1,000 $8,000 $9,000 5 3000 $1,000 $10,000 $11,000 THE COSTS OF PRODUCTION

  15. EXAMPLE 1: Farmer Jacks Total Cost Curve $12,000 Q Total Cost (bushels of wheat) $10,000 $8,000 0 $1,000 Total cost $6,000 1000 $3,000 $4,000 1800 $5,000 $2,000 2400 $7,000 $0 2800 $9,000 0 1000 Quantity of wheat 2000 3000 3000 $11,000 THE COSTS OF PRODUCTION

  16. Marginal Cost Marginal Cost (MC) is the increase in Total Cost from producing one more unit: TC Q MC = THE COSTS OF PRODUCTION

  17. EXAMPLE 1: Total and Marginal Cost Q Total Cost Marginal Cost (MC) (bushels of wheat) 0 $1,000 $2.00 TC = $2000 Q = 1000 1000 $3,000 $2.50 TC = $2000 Q = 800 1800 $5,000 $3.33 TC = $2000 Q = 600 2400 $7,000 $5.00 TC = $2000 Q = 400 2800 $9,000 $10.00 TC = $2000 Q = 200 3000 $11,000 THE COSTS OF PRODUCTION

  18. EXAMPLE 1: The Marginal Cost Curve $12 Q (bushels of wheat) TC MC MC usually rises as Q rises, as in this example. $10 Marginal Cost ($) $8 0 $1,000 $2.00 $6 1000 $3,000 $2.50 $4 1800 $5,000 $3.33 2400 $7,000 $2 $5.00 2800 $9,000 $0 $10.00 0 1,000 2,000 3,000 3000 $11,000 Q THE COSTS OF PRODUCTION

  19. Why MC Is Important Farmer Jack is rational and wants to maximize his profit. To increase profit, should he produce more or less wheat? To find the answer, Farmer Jack needs to think at the margin. If the cost of additional wheat (MC) is less than the revenue he would get from selling it, then Jack s profits rise if he produces more. THE COSTS OF PRODUCTION

  20. Fixed and Variable Costs Fixed costs (FC) do not vary with the quantity of output produced. For Farmer Jack, FC = $1000 for his land Other examples: cost of equipment, loan payments, rent Variable costs (VC) vary with the quantity produced. For Farmer Jack, VC = wages he pays workers Other example: cost of materials Total cost (TC) = FC + VC THE COSTS OF PRODUCTION

  21. EXAMPLE 2: Costs $800 FC VC TC Q FC VC TC $700 0 $100 $0 $100 $600 1 100 70 170 $500 Costs 2 100 120 220 $400 3 100 160 260 $300 4 100 210 310 $200 5 100 280 380 $100 6 100 380 480 $0 7 100 520 620 0 1 2 3 4 5 6 7 Q THE COSTS OF PRODUCTION

  22. EXAMPLE 2: Marginal Cost Recall, Marginal Cost (MC) is the change in total cost from producing one more unit: $175 $200 Q TC MC 0 $100 $70 $150 1 170 TC Q 50 $125 MC = 2 220 Costs 40 $100 Usually, MC rises as Q rises, due to diminishing marginal product. $50 3 260 50 $75 4 310 70 Sometimes (as here), MC falls before rising. $25 5 380 100 6 480 (In other examples, MC may be constant.) 0 1 140 $0 7 620 2 3 4 5 6 7 Q

  23. EXAMPLE 2: Average Fixed Cost Average fixed cost (AFC) is fixed cost divided by the quantity of output: $150 Q FC AFC $200 $175 0 $100 n/a 1 100 $100 AFC = FC/Q $125 Costs 2 100 50 $100 3 100 33.33 Notice that AFC falls as Q rises: The firm is spreading its fixed costs over a larger and larger number of units. $0 0 1 2 $75 4 100 25 $50 5 100 20 $25 6 100 16.67 7 100 14.29 3 4 5 6 7 Q THE COSTS OF PRODUCTION

  24. EXAMPLE 2: Average Variable Cost Average variable cost (AVC) is variable cost divided by the quantity of output: $150 Q VC AVC $200 $175 0 $0 n/a 1 70 $70 AVC = VC/Q $125 Costs 2 120 60 $100 3 160 53.33 As Q rises, AVC may fall initially. In most cases, AVC will eventually rise as output rises. $25 $75 4 210 52.50 $50 5 280 56.00 6 380 63.33 $0 0 1 2 3 4 5 6 7 7 520 74.29 Q THE COSTS OF PRODUCTION

  25. EXAMPLE 2: Average Total Cost Average total cost (ATC) equals total cost divided by the quantity of output: Q TC ATC AFC AVC 0 $100 n/a n/a n/a 1 170 $170 $100 $70 2 220 110 50 60 ATC = TC/Q 3 260 86.67 33.33 53.33 Also, 4 310 77.50 25 52.50 ATC = AFC + AVC 5 380 76 20 56.00 6 480 80 16.67 63.33 7 620 88.57 14.29 74.29 THE COSTS OF PRODUCTION

  26. EXAMPLE 2: Average Total Cost Q TC ATC $200 Usually, as in this example, the ATC curve is U-shaped. $150 $175 0 $100 n/a 1 170 $170 $125 Costs 2 220 110 $100 3 260 86.67 $75 4 310 77.50 $50 5 380 76 $25 6 480 80 $0 0 1 2 3 4 5 6 7 7 620 88.57 Q THE COSTS OF PRODUCTION

  27. EXAMPLE 2:The Various Cost Curves Together $200 $175 $150 ATC $125 AVC Costs $100 AFC MC $75 $50 $25 $0 0 1 2 3 4 5 6 7 Q THE COSTS OF PRODUCTION

  28. EXAMPLE 2: Why ATC Is Usually U-Shaped As Q rises: $200 Initially, falling AFC pulls ATC down. $175 $150 $125 Costs Eventually, rising AVC pulls ATC up. $100 $75 $50 Efficient scale: The quantity that minimizes ATC. $25 $0 0 1 2 3 4 5 6 7 Q THE COSTS OF PRODUCTION

  29. EXAMPLE 2: ATC and MC When MC < ATC, ATC is falling. ATC MC $200 $175 When MC > ATC, ATC is rising. $150 $125 Costs The MC curve crosses the ATC curve at the ATCcurve s minimum. $100 $75 $50 $25 $0 0 1 2 3 4 5 6 7 Q THE COSTS OF PRODUCTION

  30. Costs in the Short Run & Long Run Short run: Some inputs are fixed (e.g., factories, land). The costs of these inputs are FC. Long run: All inputs are variable (e.g., firms can build more factories, or sell existing ones). In the long run, ATC at any Q is cost per unit using the most efficient mix of inputs for that Q (e.g., the factory size with the lowest ATC). THE COSTS OF PRODUCTION

  31. EXAMPLE 3: LRATC with 3 factory Sizes Avg Total Cost Firm can choose from 3 factory sizes: S, M, L. ATCMATCL ATCS Each size has its own SRATC curve. The firm can change to a different factory size in the long run, but not in the short run. Q THE COSTS OF PRODUCTION

  32. EXAMPLE 3: LRATC with 3 factory Sizes Avg Total Cost To produce less than QA, firm will choose size S in the long run. To produce between QA and QB, firm will choose size M in the long run. To produce more than QB, firm will choose size L in the long run. ATCMATCL ATCS LRATC Q QA QB THE COSTS OF PRODUCTION

  33. A Typical LRATC Curve In the real world, factories come in many sizes, each with its own SRATC curve. ATC LRATC So a typical LRATC curve looks like this: Q THE COSTS OF PRODUCTION

  34. How ATC Changes as the Scale of Production Changes Economies of scale: ATC falls as Q increases. ATC LRATC Constant returns to scale: ATC stays the same as Q increases. Diseconomies of scale: ATC rises as Q increases. Q THE COSTS OF PRODUCTION

  35. How ATC Changes as the Scale of Production Changes Economies of scale occur when increasing production allows greater specialization: workers more efficient when focusing on a narrow task. More common when Q is low. Diseconomies of scale are due to coordination problems in large organizations. E.g., management becomes stretched, can t control costs. More common when Q is high. THE COSTS OF PRODUCTION

  36. CONCLUSION Costs are critically important to many business decisions, including production, pricing, and hiring. This chapter has introduced the various cost concepts. The following chapters will show how firms use these concepts to maximize profits in various market structures. THE COSTS OF PRODUCTION

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