1. Economic Analysis for Business Session XI: The Costs of Production
Instructor Sandeep Basnyat

2. Objectives of the firms
Varieties of objectives:
Profit maximization
Sales Revenue maximization
Utility maximization
Corporate growth maximization
Etc…

3. Most Important economic Objective- Profit Maximization
The economic goal of the firm is to maximize profits.
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

4. Sequence of Presentation
Understanding Costs, Production functions and their relationship
Derive various cost curves
A concept of Revenue
How firms behave if they are in different market structures?

5. Costs: Explicit vs. Implicit
Explicit costs – require an outlay of money, e.g. paying wages to workers
Accounting profit
= total revenue minus total explicit costs
Implicit costs (Opportunity Costs) – do not require a cash outlay e.g. the cost of the owner’s time
Economic profit
= total revenue minus total costs (including explicit and implicit costs)

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.
In the following slides, Example 1 will be used to illustrate the production function, marginal product, and a first look at the costs of production.

7. Simple Example: Production Function
500
1,000
1,500
2,000
2,500
3,000 1 2 3 4 5
No. of workers
Quantity of output
Q (bushels of wheat)
L (no. of workers)
1000 1
1800 2
2400 3
2800 4
3000 5

8. Properties of Production Functions: Returns to Scale
Increasing Returns to Scale
When inputs are increased by m, output increases by more than m.
Eg: A 10% increase in labour/capital increases the output by more than 10%
Constant Returns to Scale
When inputs are increased by m, output increases by exactly m.
Decreasing Returns to Scale
When inputs are increased by m, output increases by less than m.
Note: Assuming that the value of multiplier >1 (positive)

9. Properties of Production Functions: Returns to Scale
Find if the followings production functions have increasing, constant or decreasing returns to scale.
(i) Q = 3L (ii) Q = L0.5 (iii) Q = L2
Q = 3L = 3 (mL) = m . 3L = m. Q (Constant)
Q = L0.5 = (mL)0.5 = m0.5L0.5 = m0.5Q (Decreasing)
Q = L2 = (mL)2 = m2L2 = m2Q (Increasing)

10. Marginal Product
The marginal product of any input is the increase in output arising from an additional unit of that input, holding all other inputs constant.
Marginal product of labor (MPL) =
∆Q = change in output, ∆L = change in labor ∆Q ∆L

11. EXAMPLE :Marginal Product
3000 5
2800 4
2400 3
1800 2
1000 1
Q (bushels of wheat)
L (no. of workers)
MPL
∆Q = 1000
∆L = 1
1000
∆Q = 800
∆L = 1
800
∆Q = 600
∆L = 1
600
∆Q = 400
∆L = 1
400
∆Q = 200
∆L = 1
200

12. Relationship between Production Function and MPL
500
1,000
1,500
2,000
2,500
3,000 1 2 3 4 5
No. of workers
Quantity of output
L (no. of workers)
Q (bushels of wheat)
MPL
1000 1
1000
800 2
1800
600 3
2400
400 4
2800
200 5
3000
Diminishing MPL: This property explains why Production Function flatters as output increases.

13. Why MPL Diminishes
Diminishing marginal product: the marginal product of an input declines as the quantity of the input increases (other things equal)
E.g.: Output rises by a smaller and smaller amount for each additional worker. Why?
If the number of workers increased but not land, the average worker has less land to work with, so will be less productive.
In general, MPL diminishes as L rises whether the fixed input is land or capital (equipment, machines, etc.).

14. Deriving Costs curves Q FC VC TC 100 $100 520 380 280 210 160 120 70
$800 FC Q FC VC TC VC
$700
100
$100
520
380
280
210
160
120 70 $0
620
480
380
310
260
220
170
$100 TC
$600 1
$500 2
Costs
$400 3
$300 4
$200 5
Point out that the TC curve is parallel to the VC curve, but is higher by the amount FC.
$100 6 $0 7 1 2 3 4 5 6 7
Example:
FC = Cost of land
VC = Wages to labor Q

15. Marginal Cost curve ∆TC MC = ∆Q
Marginal Cost (MC) is the change in total cost from producing one more unit:
$100
$70 1
170
∆TC ∆Q
MC = 50 2
220 40 3
260
Usually, MC rises as Q rises, due to diminishing marginal product.
Sometimes, MC falls before rising.
(In rare cases, MC may be constant.) 50 4
310 70 5
380
100 6
480
140 7
620

16. EXAMPLE : Rising Marginal Cost Curve
Q (bushels of wheat) TC MC
$1,000
$10.00
$5.00
$3.33
$2.50
$2.00
1000
$3,000
1800
$5,000
2400
$7,000
2800
$9,000
3000
$11,000

17. Average Fixed Cost curveQ FC
AFC
Average fixed cost (AFC) is fixed cost divided by the quantity of output:
AFC = FC/Q
$100
14.29
16.67 20 25
33.33 50
$100
n.a. 1
100 2
100 3
100 4
100 5
Most students readily grasp the following example.
Suppose FC = $1 million for a factory that produces cars.
If the firm produces Q = 1 car, then AFC = $1 million.
If the firm produces 2 cars, AFC = $500,000.
If the firm produces 5 cars, AFC = $200,000.
If the firm produces 100 cars, AFC = $10,000.
The more cars produced at the factory, the smaller is the cost of the factory per car.
100 6
100 7
100

18. Average Variable Cost curveQ VC
AVC
Average variable cost (AVC) is variable cost divided by the quantity of output:
AVC = VC/Q $0
74.29
63.33
56.00
52.50
53.33 60
$70
n.a. 1 70 2
120 3
160
As Q rises, AVC may fall initially. In most cases, AVC will eventually rise as output rises. 4
210 5
280 6
380 7
520

19. Average Total Cost curve
Average total cost (ATC) equals total cost divided by the quantity of output:
ATC = TC/Q Q TC
ATC
74.29
14.29
63.33
16.67
56.00 20
52.50 25
53.33
33.33 60 50
$70
$100
n.a.
AVC
AFC
$100
88.57 80 76
77.50
86.67
110
$170
n.a. 1
170 2
220 3
260
Also,
ATC = AFC + AVC 4
310
Many students have heard the terms “cost per unit” or “unit cost” in other business courses. ATC means the same thing. 5
380 6
480 7
620

20. Average Total Cost Curves$0
$25
$50
$75
$100
$125
$150
$175
$200 1 2 3 4 5 6 7 Q
Costs Q TC
ATC
Usually, the ATC curve is U-shaped.
$100
n.a. 1
170
$170 2
220
110 3
260
86.67 4
310
77.50 5
380 76 6
480 80 7
620
88.57

21. Why ATC Is Usually U-shaped$0
$25
$50
$75
$100
$125
$150
$175
$200 1 2 3 4 5 6 7 Q
Costs
As Q rises:
Initially, falling AFC pulls ATC down.
Eventually, rising AVC pulls ATC up.

22. The Various Cost Curves Together$0
$25
$50
$75
$100
$125
$150
$175
$200 1 2 3 4 5 6 7 Q
Costs
ATC
AVC
AFC MC

23. Important Economic Relation: ATC and MC$0
$25
$50
$75
$100
$125
$150
$175
$200 1 2 3 4 5 6 7 Q
Costs
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.
ATC MC
The textbook gives a nice analogy to help students understand this. A student’s GPA is like ATC. The grade she earns in her next course is like MC. If her next grade (MC) is less than her GPA (ATC), then her GPA will fall. If her next grade (MC) is greater than her GPA (ATC), then her GPA will rise.
I suggest letting students read the GPA example in the book, and giving them the following example in class:
You run a pizza joint. You’re producing 100 pizzas per night, and your cost per pizza (ATC) is $3. The cost of producing one more pizza (MC) is $2. If you produce this pizza, what happens to ATC? Most students will understand immediately that ATC falls (albeit by a small amount). Instead, suppose the cost of producing one more pizza (MC) is $4. Then, producing this additional pizza causes ATC to rise.

24. A C T I V E L E A R N I N G 3: Costs
Fill in the blank spaces of this table. Q VC TC
AFC
AVC
ATC MC
$50
n.a.
n.a.
n.a.
$10 1 10
$10
$60.00 2 30 80 30 3
16.67 20
36.67 4
100
150
12.50
37.50 5
150 30 60 6
210
260
8.33 35
43.33 24

25. A C T I V E L E A R N I N G 3: AnswersQ VC TC
AFC
AVC
ATC MC $0
$50
n.a.
n.a.
n.a.
$10 1 10 60
$50.00
$10
$60.00 20 2 30 80
25.00 15
40.00 30 3 60
110
16.67 20
36.67 40 4
100
150
12.50 25
37.50 50 5
150
200
10.00 30
40.00 60 6
210
260
8.33 35
43.33 25

26. Numerical Problem on Costs
Given the cost function:
TC = Q - 0.9Q Q3
Find:
1) MC, TVC, AVC functions
2) Discarding the previous TC function, consider that the existing AVC function became the ATC function for the firm. Find Q when AVC is minimum.

27. Worked out Problem
TC = Q - 0.9Q Q3 1) MC = ΔTC / ΔQ = d(TC) / dQ = Q+ 0.12Q2 2) TVC = TC –TFC = Q - 0.9Q Q3 – 1000 = 10Q - 0.9Q Q3 3) AVC = TVC / Q =(10Q - 0.9Q Q3 )/Q = Q Q2 4) Since AVC function is the ATC function, Q at Minimum AVC when: AVC = MC Q Q2 = Q+ 0.12Q2 Or, Q Q = 0 Or, Q(- 0.08Q+ 0.9) = 0 Or, Q =0 and Q+ 0.9 = 0 i.e, Q = (Minimum AVC)

28. 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)

29. LRATC with 3 Factory Sizes
Firm can choose from 3 factory sizes: S, M, L.
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
Avg Total Cost
ATCS
ATCM
ATCL

30. EXAMPLE 3: LRATC with 3 Factory Sizes
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. Q
Avg Total Cost
ATCS
ATCM
ATCL
LRATC QA QB
The following might be helpful:
After the first paragraph displays, pick a Q a little to the left of QA. From this Q, go up to the ATC curves. Notice that cost per unit is lower for the small factory than the medium one. The firm may be stuck with a medium factory in the short run, but in the long run – if it wishes to produce this level of output – it will choose the small factory to have the lowest cost per unit. Hence, for Q < QA, the LRATC curve is the portion of ATCS from 0 to QA.
After the second paragraph displays, pick a Q a little to the right of QA. From this Q, go up to the ATC curves. Notice that cost per unit is lower for the medium factory than the small one. The firm may be stuck with a small factory in the short run, but in the long run – if it wishes to produce this level of output – it will choose the medium factory to have the lowest cost per unit. Hence, for QA < Q < QB, the LRATC curve is the portion of ATCM from QB to QA.
The same type of argument illustrates the logic in the third paragraph.

31. 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: Q
ATC
LRATC

32. How ATC Changes as the Scale of Production Changes
Economies of scale: ATC falls as Q increases.
Constant returns to scale: ATC stays the same as Q increases.
Diseconomies of scale: ATC rises as Q increases. Q
ATC
LRATC

33. The Revenue of a Competitive Firm
Total revenue (TR)
Average revenue (AR)
Marginal Revenue (MR): The change in TR from selling one more unit.
TR = P x Q TR Q
AR =
= P
∆TR ∆Q
MR =
These revenue concepts are analogous to the cost concepts (TC, ATC, MC) in the previous chapter.

34. How do firms behave in different market structures?
Perfectly Competitive Market
Monopoly Market
Oligopoly Market
Monopolistically Competitive Market

35. Perfectly Competitive Market
1. Many buyers and many sellers
2. The goods offered for sale are largely the same.
3. Firms can freely enter or exit the market.
Because of 1 & 2, each buyer and seller is a “price taker” – takes the price as given.
“Firms can freely enter or exit the market” means there are no barriers or impediments to entry or exit. E.g., the government does not restrict the number of firms in the market.

36. Sample Data Notice that MR = P Q P TR = P x Q TR Q AR = ∆TR ∆Q MR =
$10
$30
$20
$10 $0
n.a.
Notice that MR = P
$10 1
$10
$10 2
$10
$10 3
$10 4
$10
$40
$10 5
$10
$50 36

37. MR = P for a Competitive Firm
A competitive firm can keep increasing its output without affecting the market price.
So, each one-unit increase in Q causes revenue to rise by P, i.e., MR = P.
MR = P is only true for firms in competitive markets.

38. Profit Maximization What Q maximizes the firm’s profit?
If increase Q by one unit, revenue rises by MR, cost rises by MC.
If MR > MC, then increase Q to raise profit.
If MR < MC, then reduce Q to raise profit.

39. Profit Maximization Profit = MR – MC
(continued from earlier exercise) Q TR TC
Profit MR MC
Profit = MR – MC
At any Q with MR > MC, increasing Q raises profit. $0 45 33 23 15 9 $5 5 7 1
–$5
$10 12 10 8 6 $4 –2 2 4 $6 1 10 10 2 20
At any Q with MR < MC, reducing Q raises profit. 10
(The table on this slide is similar to Table 2 in the textbook.)
For most students, seeing the complete table all at once is too much information. So, the table is animated as follows:
Initially, the only columns displayed are the ones students saw at the end of the exercise in Active Learning 1: Q, TR, and MR.
Then, TC appears, followed by MC. It might be useful to remind students of the relationship between MC and TC.
Then, the Profit column appears. Students should be able to see that, at each value of Q, profit equals TR minus TC.
The last column to appear is the change in profit.
When the table is complete, we use it to show
it is profitable to increase production whenever MR > MC, such as at Q = 0 , 1, or 2.
it is profitable to reduce production whenever MC > MR, such as at Q = 5. 3 30 10 4 40 10 5 50

40. MC and the Firm’s Supply Decision
Rule: MR = MC at the profit-maximizing Q.
At Qa, MC < MR.
So, increase Q to raise profit.
At Qb, MC > MR.
So, reduce Q to raise profit.
At Q1, MC = MR.
Changing Q would lower profit. Q
Costs MC Qb P1 MR Qa Q1
This slide is similar to Figure 1 in the chapter. I’ve omitted the AVC and ATC curves (which appear in Figure 1 in the chapter) because they are not needed at this point.

41. MC and the Firm’s Supply Decision
If price rises to P2,
then the profit-maximizing quantity rises to Q2.
The MC curve determines the firm’s Q at any price.
Hence,
Costs MC P2
MR2 Q2 P1 MR Q1
the MC curve is the firm’s supply curve. Q

42. Market Structure Problems
Assume the cost function: TC = Q Q2 and Price is $10 per unit for a firm in the competitive market. Calculate the profit maximizing output (Q) and economic profit.

43. Market Structure Problems
Assume the cost function: TC = Q Q2 and Price is $10 per unit for a firm in the competitive market.
Calculate the profit maximizing output (Q) and economic profit.
Solution:
MC = dTC /dQ = Q
In a perfectly competitive market, profit maximizing output is at where MR = P = MC
10 = Q
Therefore, Q = 400
Economic Profit = TR –TC = 10(400) – ( (400) (4002)) =$600

44. When would the firms Shutdown, Exit or Enter?
Shutdown: A short-run decision not to produce anything because of market conditions.
Exit: A long-run decision to leave the market.
A firm that shuts down temporarily must still pay its fixed costs. A firm that exits the market does not have to pay any costs at all, fixed or variable.

45. A Firm’s Short-Run Decision to Shut Down
If firm shuts down temporarily,
revenue falls by TR
costs fall by VC
So, the firm should shut down if TR < VC.
Divide both sides by Q: TR/Q < VC/Q
So we can write the firm’s decision as:
The “cost” of shutting down is TR, the revenue the firm loses if it shuts down.
The “benefit” of shutting down is VC, because the firm doesn’t have to pay its variable costs if it shuts down. (It still must pay its FC, though.)
If the benefit of shutting down exceeds the cost, it’s worthwhile for the firm to shut down.
Shut down if P < AVC

46. A Competitive Firm’s SR Supply Curve
The firm’s SR supply curve is the portion of its MC curve above AVC. Q
Costs
AVC
If P > AVC, then firm produces Q where P = MC. MC
ATC
In edit mode, it looks like the text boxes are on top of each other. But in presentation mode, the text boxes display only one at a time.
If P < AVC, then firm shuts down (produces Q = 0).

47. A Firm’s Long-Run Decision to Exit
If firm exits the market,
revenue falls by TR
costs fall by TC
So, the firm should exit if TR < TC.
Divide both sides by Q to rewrite the firm’s decision as:
The “cost” of exiting is TR, the revenue the firm loses if it leaves the market.
The “benefit” of exiting is TC, because the firm no longer pays its costs if it leaves the market.
If the benefit of existing is greater than the cost, then it’s worthwhile for the firm to exit.
Exit if P < ATC

48. A New Firm’s Decision to Enter the Market
In the long run, a new firm will enter the market if it is profitable to do so: if TR > TC.
Divide both sides by Q to express the firm’s entry decision as:
Enter if P > ATC
Similarly, a prospective entrant compares the benefits of entering the market (TR) with the costs (TC), and enters if the benefits exceed the costs.

49. Identifying a firm’s profit or Loss
A competitive firm
Determine if this firm’s total has profit/Loss?
Identify the area on the graph that represents the firm’s profit or Loss. Q
Costs, P MC
ATC
P = $10 MR 50 $6
Rather than tell students that profit equals (P – ATC) x Q, this exercise requires students to figure it out for themselves.
If this exercise is too easy for your students, you can replace it with lecture slides that appear at the end of this file. 49

50. Answers profit Q 50 A competitive firm Costs, P
profit per unit = P – ATC = $10 – 6 = $4 MC
ATC
P = $10 MR 50
profit $6
The height of the rectangle is P – ATC, profit per unit.
The width of the rectangle is Q, the number of units.
The area of the rectangle
= height x width
= (profit per unit) x (number of units)
= total profit.
Total profit = (P – ATC) x Q = $4 x 50 = $200 50

51. Identifying a firm’s profit or loss.
A competitive firm
Determine if this firm has total profit or loss.
Identify the area on the graph that represents the firm’s profit or loss. Q
Costs, P MC
ATC $5 30
Students that didn’t figure out the answer to the previous exercise should be able to get this one.
If this exercise is too easy for your students, you can replace it with lecture slides that appear at the end of this file.
P = $3 MR 51

52. Answers $5 loss P = $3 MR Q 30 A competitive firm Costs, P MC
Total loss = (ATC – P) x Q = $2 x 30 = $60
ATC $5 30
loss
loss per unit = $2
The height of the rectangle is ATC – P, loss per unit.
The width of the rectangle is Q, the number of units.
The area of the rectangle
= height x width
= (loss per unit) x (number of units)
= total loss. MR
P = $3 52

53. Demand Curve for Individual firm’s product
In a competitive market, the market demand curve slopes downward.
but the demand curve for any individual firm’s product is horizontal at the market price.
The firm can increase Q without lowering P,
so MR = P for the competitive firm.
A competitive firm’s demand curve P Q D
A competitive firm is a price-taker, can sell as much as it wants at the market price.
In effect, the competitive firm sells a product for which there are many perfect substitutes, so demand for its product is perfectly elastic; if it raises its price above the market price, demand for its product falls to zero.
The relationship between P and MR is what distinguishes a competitive firm from a monopoly firm, in terms of both firm behavior and welfare implications.
Price line represents the level of demand for the firm’s product

54. Market Structure Problems
Consider a firm which has a horizontal demand curve for its products. The firms Total Cost is given by the function: TVC = 150Q – 20Q2 +Q3. Below what price should the firm shut down operation?

55. Market Structure Problems
In the competitive market, the firm shut down only when P<AVC.
The firm continue to operate until:
P = AVC
In competitive market, P =MC
MC =dTVC / dQ = Q +3Q2
AVC = TVC /Q = (150Q – 20Q2 +Q3) / Q = Q +Q2
Equating, both equations:
MC = AVC or Q +3Q2 = Q +Q2
Or, 2Q2 – 20Q = 0 or 2Q (Q – 10) = 0
Or, Q = 0 and Q = 10
Substituting Q = 10 into marginal cost, P = MC = 150 – 40(10) + 3 (100) = $50
Similarly, substituting Q = 0 in the marginal cost, P = $150
Therefore, if the price falls below $50, the firm shuts down.

56. Firms behaviour in the Long Run-Profit Condition
In the LR, the number of firms can change due to entry & exit.
If existing firms earn positive economic profit,
New firms enter.
SR market supply curve shifts right.
P falls, reducing firms’ profits.
Entry stops when firms’ economic profits have been driven to zero.

57. Firms behaviour in the Long Run-Loss Condition
In the LR, the number of firms can change due to entry & exit.
If existing firms incur losses,
Some will exit the market.
SR market supply curve shifts left.
P rises, reducing remaining firms’ losses.
Exit stops when firms’ economic losses have been driven to zero.

58. SR & LR Effects of an Increase in Demand
A firm begins in long-run eq’m…
…but then an increase in demand raises P,…
…leading to SR profits for the firm.
…driving profits to zero and restoring long-run eq’m.
Over time, profits induce entry, shifting S to the right, reducing P…
One firm
Market Q P
(market) Q P
(firm) S1 MC
ATC S2
Profit D2 B P2 P2 Q2 D1 A C P1
long-run
supply P1
This slide replicates Figure 8 from the textbook. In edit mode, the text boxes in the top part of the slide appear to be on top of each other. But in slide-show mode, the text boxes display one at a time.
If students did not previously understand why the LR market supply curve is horizontal, this slide may help. Q1 Q3

59. Why Do Firms Stay in Business if Profit = 0?
Recall, economic profit is revenue minus all costs – including implicit costs, like the opportunity cost of the owner’s time and money.
In the zero-profit equilibrium, firms earn enough revenue to cover these costs.
Students often wonder why firms bother to stay in business if they make zero profit. The textbook gives a nice discussion of this, briefly summarized on this slide.

60. Distinction between The SR and LR Market Supply Curves
Example: identical firms.
At each P, market Qs = x (one firm’s Qs)
AVC
One firm Q P
(firm)
Market Q P
(market) MC S P3 P3 30
30,000 P2 P2 20
20,000 P1
“Identical” means all firms have the same cost curves.
Note: P1 is minimum AVC. At any price below P1, each firm will shut down, and market quantity supplied will equal zero.
Hence, the market supply curve begins at price = P1 and Q = 10,000. P1 10
10,000

61. The LR Market Supply Curve
In the long run, the typical firm earns zero profit.
The LR market supply curve is horizontal at P = minimum ATC.
One firm Q P
(firm)
Market Q P
(market) MC
LRATC
P = min. ATC
long-run
supply
That the LR market supply curve is horizontal at P = min ATC will become more clear shortly, when students see the SR and LR effects of an increase in demand.

62. The Zero-Profit Condition
Long-run equilibrium: The process of entry or exit is complete – remaining firms earn zero economic profit.
Zero economic profit occurs when P = ATC.
Since firms produce where P = MR = MC, the zero-profit condition is P = MC = ATC.
Recall that MC intersects ATC at minimum ATC.
Hence, in the long run, P = minimum ATC.

63. The Irrelevance of Sunk Costs
Sunk cost: a cost that has already been committed and cannot be recovered
Sunk costs should be irrelevant to decisions; you must pay them regardless of your choice.
FC is a sunk cost: The firm must pay its fixed costs whether it produces or shuts down.
So, FC should not matter in the decision to shut down.

64. Thank you