UNIT 7:

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

2. Key Topics • Cost 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 • 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’ Concerns • GM • 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

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 ofadditional 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. Assume: q = TP = 4L w = $8 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: 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

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 = 120 + .1Q2 Π Max Q  MR = MC  10 = .2Q  Q = 50 Max π = TR-TC (at Q = 50) = 10(50) – [120 + .1(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 = 120 + .1Q2 Π Max Q  MR=MC  44-2Q = .2Q  2.2Q = 44  Q = 20 • Max π = TR-TC (at Q = 20) = [44(20)-(20)2] – [120 + .1(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 $ MC Short-run Supply curve 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 = 100 - .1L 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 q1 K 1 2 q1 3 TC3 TC2 TC1 L

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

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

48. Average Cost and Output • SR 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