1. Firm Costs, Revenues, and Profits
UNIT 7:
Firm Costs, Revenues, and Profits

2. Key Topics Cost concepts Revenue concepts Profit concepts
Cash and Non Cash
Variable and Fixed
Total: TFC, TVC, TC
Average: AFC, AVC, ATC, AVC & AP
Marginal: MC, MC & MP
Revenue concepts
Total
Marginal
Profit concepts
Profit maximizing output
Firm & market supply

3. Key Topics - continued 4. SR production 5. LR production
Profits in P, ATC graph
Shut down condition (loss min.)
Firm & industry supply curves
5. LR production
Isocost lines & LR cost min. (Ch. 6 Appendix)
Returns to scale and LRAC
Equilibrium

4. Profit Overview (recall)
Profit = TR – TC
TR depends on P of output, Q of output
TC depends on P of inputs, Q of inputs, productivity of inputs, production technology used

5. Recent Examples of Firm ‘Cost’ ConcernsGM
Spent $5 billion to  costs of producing Saturn cars
Labor costs per car for GM were 2x Toyota’s
United, Delta, & other airlines
- Southwest’s costs often 50% less
Sears, K-Mart, Target
- Trying to compete with Walmart on basis of costs
Georgia Pacific
Started using ‘thinner’ saws
Less saw dust
800 more rail cars of lumber per year

6. Cost Concepts
Cash and Non Cash
Fixed and Variable
Total, Average, and Marginal

7. Opportunity Cost Examples
Activity
Opportunity Cost
Operate own business
Lost wages and interest
Own and farm land
Lost rent and interest
Buy and operate equipment
Lost interest and rent

8. Total Fixed vs. Total Variable Costs
TFC = total fixed costs
= costs that have to be paid even if output = 0
= costs that do NOT vary with changes in output
= ‘overhead’ and ‘sunk’ costs
TVC = total variable costs
= costs that DO vary with changes in output
= 0 if output = 0
TC = total costs
= TFC + TVC

9. Average Costs AFC = fixed costs per unit of output = TFC/q
AVC = variable costs per unit of output
= TVC/q
ATC = total costs per unit of output
= TC/q = AFC + AVC

10. Marginal Cost MC = additional cost per unit of additional output =
= slope of TC and slope of TVC curves

11. MC, AVC, and ATC Relationships
If MC > AVC  AVC is increasing
If MC < AVC  AVC is declining
If MC > ATC  ATC is increasing
If MC < ATC  ATC is declining

12. Product and Cost Relationships
Assume variable input = labor
MP = ΔQ/ΔL AP =
TVC = W ∙ L
MC =
note: MC Δ is opposite of MP Δ
AVC =
note: AVC Δ is opposite of AP Δ

13. A ‘Janitor’ Production Example
Assume the only variable input a janitorial service firm uses to clean offices is workers who are paid a wage, w, of $8 an hour. Each worker can clean four offices in an hour. Use math to determine the variable cost, the average variable cost, and the marginal cost of cleaning one more office.

14. w = $8 Assume: q = TP = 4L L TP AP MP TVC AVC MC 1 4 8 2 16 3 12 24 321 4 8 2 16 3 12 24 32
NOTE: AVC = TVC/q = w/AP
MC = ΔTVC/Δq = w/MP

15. Another Cost of Production Example
Assume a production process has the following costs:
TFC = 120
TVC = .1q2
MC = .2q

16. Complete the following table:Q
TFC
TVC TC
AFC
AVC
ATC MC 20 40 60 80
100
Can you graph the cost functions (q on horizontal axis)?

17. Total Costs of Production
TFC = AFC x q
= (fixed cost per unit of output) (units of output)
TVC = AVC x q
= (variable cost per unit of output) (units of output)
TC = ATC x q
= (total cost per unit of output) (units of output)

18. TFC in AFC graph
AFC = TFC/q  TFC = AFC x q $
AFC1
TFC
AFC q q1

19. TVC in AVC graph
AVC = TVC/q  TVC = AVC x q $
AVC
AVC1
TVC q q1

20. TC in ATC graph
ATC = TC/q  TC = ATC x q $
ATC
ATC1 TC q q1

21. Revenue Concepts TR = total revenue = gross income = total $ sales
= PxQ = (price of output) (units of output)
= AR x Q = (revenue per unit of output) (units of output)
AR = average revenue
= revenue per unit of output
= TR/Q
MR = marginal revenue
= additional revenue per unit of additional output
= ΔTR/ΔQ

22. General Types of Firms (based on the D for their product)
Perfectly Competitive
D curve for their product is flat
P is constant ( can sell any Q at given P determined by S&D)
AR = MR = P (all constant)
TR = P x Q ( linear, upward sloping given P is constant)
Imperfectly Competitive
D curve for their product is downward sloping
P depends on Q sold ( must lower P to sell more Q)
AR = P (= firm D curve)
TR = PxQ (nonlinear, inverted U shape given P is not constant)
MR = slope of TR (decreases with ↑Q, also goes from >0 to <0)

23. General Graphs of Revenue Concepts
Perfectly Competitive Firm
Imperfectly Competitive Firm $ $
PR=AR=MR
P=AR MR Q Q $ $ TR TR Q Q

24. Specific Firm Revenue Examples
Perfectly Competitive Firm
Imperfectly Competitive Firm
P = AR = 10
P = AR = 44 – Q
TR = PQ = 10Q
TR = PQ = 44Q – Q2
MR = 10
MR = 44 – 2Q

25. TR in P graph (competitive firm)
TR = P x q $ P P TR q q1

26. Revenue-Cost Concepts
Profit = TR – TC
Operating profit = TR - TVC

27. Comparing Costs and Revenues to Maximize Profit
The profit-maximizing level of output for all firms is the output level where MR = MC.
In perfect competition, MR = P, therefore, the firm will produce up to the point where the price of its output is just equal to short-run marginal cost.
The key idea here is that firms will produce as long as marginal revenue exceeds marginal cost.

28. General Graph of Perfectly Competitive Firm Profit Max$ MC MR Q $ TR TC Q

29. Perfectly Competitive Firm Profit Max (Example)
P = MR = 10
MC = .2Q
TR = 10Q
TC = Q2
Π Max Q 
MR = MC
 10 = .2Q
 Q = 50
Max π = TR-TC (at Q = 50)
= 10(50) – [ (50)2]
= 500 – 120 – 250
= 130

30. General Graph of Imperfectly Competitive Firm Profit Max$ MC MR Q $ TR TC Q

31. Imperfectly Competitive Firm Profit Max (example)
P = 44-Q
MR = 44-2Q
TR = 44Q-Q2
MC = .2Q
TC = Q2
Π Max Q 
MR=MC
 44-2Q = .2Q
 2.2Q = 44
 Q = 20
Max π = TR-TC (at Q = 20)
= [44(20)-(20)2] – [ (20)2]
= [480] – [160]
= 320

32. Fixed Costs and Profit Max
True or False?
Fixed costs do not affect the profit-maximizing level of output?
True.
Only, marginal costs (changes in variable costs) determine profit-maximizing level of output. Recall, profit-max output rule is to produce where MR = MC.

33. Q. Should a firm ‘shut down’ in SR?
Profit if ‘produce’
= TR – TVC – TFC
Profit if ‘don’t produce’ or ‘shut down’
= -TFC
 Shut down if
TR – TVC – TFC < -TFC
TR – TVC < 0
TR < TVC

34. Perfectly Competitive Firm & Market Supply
Firm S = MC curve above AVC
 (P=MR) > AVC
Market S = sum of individual firm supplies

35. Graph of SR Shut Down Point$
Short-run
Supply curve MC
ATC
AVC
Market price
Shut-down point Q

36. SR Profit Scenarios
Produce, π > 0
Produce, π < 0 (loss less than – TFC)
Don’t produce, π = -TFC

37. SR vs LR Production if q = f(K,L)
SR: K is fixed
 only decision is q which determines L
LR: K is NOT fixed
 decisions =
1) q and
2) what combination of K & L to use to
produce q
Recall, π = TR – TC
 to max π of producing given q, need to min. TC

38. Budget Line
= maximum combinations of 2 goods that can be bought given one’s income
= combinations of 2 goods whose cost equals one’s income

39. Isocost Line
= maximum combinations of 2 inputs that can be purchased given a production ‘budget’ (cost level)
= combinations of 2 inputs that are equal in cost

40. Isocost Line Equation TC1 = rK + wL rK = TC1 – wL K = TC1/r – w/r L
Note: ¯slope = ‘inverse’ input price ratio
= ΔK / ΔL
= rate at which capital can be exchanged
for 1 unit of labor, while holding costs
constant

41. Equation of TC1 = 10,000 (r = 100, w = 10)

42. Isocost Line (specific example)
TC1 = 10,000
r = 100  max K = 10,000/100 = 100
w = 10  max L = 10,000/10 = 1000 K
100
TC1 = 10,000
 K = L L
1000

43. Increasing Isocost K
TC3 > TC2 > TC1 L
TC1
TC2
TC3

44. Changing Input Prices K
TC1
TC1 r w L L

45. Different Ways (costs) of Producing q1K 1 2 q1 3
TC3
TC2
TC1 L

46. Cost Min Way of Producing q1K
K* & L* are cost-min. combinations
Min cost of producing q1 = TC1 K* 1 2 q1 3
TC3
TC2
TC1 L L*

47. Cost Minimization
- Slope of isoquant = - slope of isocost line

48. Average Cost and OutputSR
Avg cost will eventually increase due to law of diminish MP ( MC will start to  and eventually pull avg cost up)
LR economics of scale
a) If increasing  LR AC will  with  q
b) If constant  LR AC does not change with  q
c) If decreasing  LR AC will  if  q

49. LR Equilibrium  P of output = min LR AC
LR Disequilibrium
P > min LR AC (from profits)
Firms will enter
 mkt S   P
P < min LR AC (firm losses)
Firms will exit
 mkt S   P