1. Production. Costs Problem 6 on p.194. OutputFCVCTCAFCAVCATCMC 010,000--- 100200 125 300133.3 400150 500200 600250

2. Production. Costs Problem 6 on p.194. OutputFCVCTCAFCAVCATCMC 010,000--- 10010,000200 10,000125 30010,000133.3 40010,000150 50010,000200 60010,000250

3. Production. Costs Problem 6 on p.194. OutputFCVCTCAFCAVCATCMC 010,000--- 10010,00020,000200 10,000125 30010,000133.3 40010,000150 50010,000200 60010,000250

4. Production. Costs Problem 6 on p.194. OutputFCVCTCAFCAVCATCMC 010,000--- 10010,00020,000200 10,00025,000125 30010,00040,000133.3 40010,00060,000150 50010,000100,000200 60010,000150,000250

5. Production. Costs Problem 6 on p.194. OutputFCVCTCAFCAVCATCMC 010,000--- 10010,000 20,000200 10,00015,00025,000125 30010,00030,00040,000133.3 40010,00050,00060,000150 50010,00090,000100,000200 60010,000140,000150,000250

6. Production. Costs Problem 6 on p.194. OutputFCVCTCAFCAVCATCMC 010,0000--- 10010,000 20,000200 10,00015,00025,000125 30010,00030,00040,000133.3 40010,00050,00060,000150 50010,00090,000100,000200 60010,000140,000150,000250

7. Production. Costs Problem 6 on p.194. OutputFCVCTCAFCAVCATCMC 010,0000 --- 10010,000 20,000200 10,00015,00025,000125 30010,00030,00040,000133.3 40010,00050,00060,000150 50010,00090,000100,000200 60010,000140,000150,000250

8. Production. Costs Problem 6 on p.194. OutputFCVCTCAFCAVCATCMC 010,0000 --- 10010,000 20,000100200 10,00015,00025,00050125 30010,00030,00040,00033.3133.3 40010,00050,00060,00025150 50010,00090,000100,00020200 60010,000140,000150,00016.7250

9. Production. Costs Problem 6 on p.194. OutputFCVCTCAFCAVCATCMC 010,0000 --- 10010,000 20,000100 200 10,00015,00025,0005075125 30010,00030,00040,00033.3100133.3 40010,00050,00060,00025125150 50010,00090,000100,00020180200 60010,000140,000150,00016.7233.3250

10. Production. Costs Problem 6 on p.194. OutputFCVCTCAFCAVCATCMC 010,0000 --- 10010,000 20,000100 200 10,00015,00025,0005075125 30010,00030,00040,00033.3100133.3 40010,00050,00060,00025125150 50010,00090,000100,00020180200 60010,000140,000150,00016.7233.3250 MC = cost of making an extra unit

11. Production. Costs Problem 6 on p.194. OutputFCVCTCAFCAVCATCMC 010,0000 --- 10010,000 20,000100 200 10,00015,00025,0005075125 30010,00030,00040,00033.3100133.3 40010,00050,00060,00025125150 50010,00090,000100,00020180200 60010,000140,000150,00016.7233.3250

12. Production. Costs Problem 6 on p.194. OutputFCVCTCAFCAVCATCMC 010,0000 --- 10010,000 20,000100 200 10,00015,00025,0005075125 30010,00030,00040,00033.3100133.3 40010,00050,00060,00025125150 50010,00090,000100,00020180200 60010,000140,000150,00016.7233.3250

13. Production. Costs Problem 6 on p.194. OutputFCVCTCAFCAVCATCMC 010,0000 --- 10010,000 20,000100 200100 20010,00015,00025,0005075125 30010,00030,00040,00033.3100133.3 40010,00050,00060,00025125150 50010,00090,000100,00020180200 60010,000140,000150,00016.7233.3250

14. Production. Costs Problem 6 on p.194. OutputFCVCTCAFCAVCATCMC 010,0000 --- 10010,000 20,000100 200100 20010,00015,00025,000507512550 30010,00030,00040,00033.3100133.3 40010,00050,00060,00025125150 50010,00090,000100,00020180200 60010,000140,000150,00016.7233.3250

15. Production. Costs Problem 6 on p.194. OutputFCVCTCAFCAVCATCMC 010,0000 --- 10010,000 20,000100 200100 20010,00015,00025,000507512550 30010,00030,00040,00033.3100133.3150 40010,00050,00060,00025125150200 50010,00090,000100,00020180200400 60010,000140,000150,00016.7233.3250500

16. If cost is given as a function of Q, then For example: TC = 10,000 + 200 Q + 150 Q 2 MC = ?

17. Profit is believed to be the ultimate goal of any firm. If the production unit described in the problem above can sell as many units as it wants for P=$360, what is the best quantity to produce (and sell)?

18. OutputFCVCTCAFCAVCATCMC 010,0000 --- 10010,000 20,000100 200100 20010,00015,00025,000507512550 30010,00030,00040,00033.3100133.3150 40010,00050,00060,00025125150200 50010,00090,000100,00020180200400 60010,000140,000150,00016.7233.3250500 Profit is believed to be the ultimate goal of any firm. If the production unit described in the problem above can sell as many units as it wants for P=$360, what is the best quantity to produce (and sell)?

19. OutputFCVCTC 010,0000 10010,000 20,000 20010,00015,00025,000 30010,00030,00040,000 40010,00050,00060,000 50010,00090,000100,000 60010,000140,000150,000 Doing it the “aggregate” way, by actually calculating the profit:

20. OutputFCVCTCTR 010,0000 10010,000 20,000 20010,00015,00025,000 30010,00030,00040,000 40010,00050,00060,000 50010,00090,000100,000 60010,000140,000150,000 Doing it the “aggregate” way, by actually calculating the profit: P=$360

21. OutputFCVCTCTR 010,0000 0 10010,000 20,00036,000 20010,00015,00025,00072,000 30010,00030,00040,000108,000 40010,00050,00060,000144,000 50010,00090,000100,000180,000 60010,000140,000150,000216,000 Doing it the “aggregate” way, by actually calculating the profit: P=$360

22. OutputFCVCTCTRProfit 010,0000 0 10010,000 20,00036,000 20010,00015,00025,00072,000 30010,00030,00040,000108,000 40010,00050,00060,000144,000 50010,00090,000100,000180,000 60010,000140,000150,000216,000 Doing it the “aggregate” way, by actually calculating the profit: P=$360

23. OutputFCVCTCTRProfit 010,0000 0–10,000 10010,000 20,00036,00016,000 20010,00015,00025,00072,00047,000 30010,00030,00040,000108,00068,000 40010,00050,00060,000144,00084,000 50010,00090,000100,000180,00080,000 60010,000140,000150,000216,00066,000 Doing it the “aggregate” way, by actually calculating the profit: P=$360

24. OutputFCVCTCTRProfit 010,0000 0–10,000 10010,000 20,00036,00016,000 20010,00015,00025,00072,00047,000 30010,00030,00040,000108,00068,000 40010,00050,00060,000144,00084,000 50010,00090,000100,000180,00080,000 60010,000140,000150,000216,00066,000 Doing it the “aggregate” way, by actually calculating the profit: P=$360

25. Alternative: The Marginal Approach The firm should produce only units that are worth producing, that is, those for which the selling price exceeds the cost of making them. OutputFCVCTCAFCAVCATCMC 010,0000 --- 10010,000 20,000100 200100 20010,00015,00025,000507512550 30010,00030,00040,00033.3100133.3150 40010,00050,00060,00025125150200 50010,00090,000100,00020180200400 60010,000140,000150,00016.7233.3250500 < 360 > 360

26. Principle (Marginal approach to profit maximization): If data is provided in discrete (tabular) form, then profit is maximized by producing all the units for which and stopping right before the unit for which

27. Principle (Marginal approach to profit maximization): If data is provided in discrete (tabular) form, then profit is maximized by producing all the units for which MR > MC and stopping right before the unit for which MR < MC In our case, price of output stays constant throughout therefore MR = P (an extra unit increases TR by the amount it sells for) If costs are continuous functions of Q OUTPUT, then profit is maximized where

28. Principle (Marginal approach to profit maximization): If data is provided in discrete (tabular) form, then profit is maximized by producing all the units for which MR > MC and stopping right before the unit for which MR < MC In our case, price of output stays constant throughout therefore MR = P (an extra unit increases TR by the amount it sells for) If costs are continuous functions of Q OUTPUT, then profit is maximized where MR=MC

29. What if FC is $100,000 instead of $10,000? How does the profit maximization point change? OutputFCVCTCTRProfit 010,0000 0–10,000 10010,000 20,00036,00016,000 20010,00015,00025,00072,00047,000 30010,00030,00040,000108,00068,000 40010,00050,00060,000144,00084,000 50010,00090,000100,000180,00080,000 60010,000140,000150,000216,00066,000

30. What if FC is $100,000 instead of $10,000? How does the profit maximization point change? OutputFCVCTCTRProfit 0100,000010,0000–10,000 100100,00010,00020,00036,00016,000 200100,00015,00025,00072,00047,000 300100,00030,00040,000108,00068,000 400100,00050,00060,000144,00084,000 500100,00090,000100,000180,00080,000 600100,000140,000150,000216,00066,000

31. What if FC is $100,000 instead of $10,000? How does the profit maximization point change? OutputFCVCTCTRProfit 0100,0000 0–10,000 100100,00010,000110,00036,00016,000 200100,00015,000115,00072,00047,000 300100,00030,000130,000108,00068,000 400100,00050,000150,000144,00084,000 500100,00090,000190,000180,00080,000 600100,000140,000240,000216,00066,000

32. What if FC is $100,000 instead of $10,000? How does the profit maximization point change? OutputFCVCTCTRProfit 0100,0000 0–100,000 100100,00010,000110,00036,000–74,000 200100,00015,000115,00072,000–43,000 300100,00030,000130,000108,000–22,000 400100,00050,000150,000144,000–6,000 500100,00090,000190,000180,000–10,000 600100,000140,000240,000216,000–24,000

33. What if FC is $100,000 instead of $10,000? How does the profit maximization point change? OutputFCVCTCTRProfit 0100,0000 0–100,000 100100,00010,000110,00036,000–74,000 200100,00015,000115,00072,000–43,000 300100,00030,000130,000108,000–22,000 400100,00050,000150,000144,000–6,000 500100,00090,000190,000180,000–10,000 600100,000140,000240,000216,000–24,000

34. Fixed cost does not affect the firm’s optimal short- term output decision and can be ignored while deciding how much to produce today. Principle: Consistently low profits may induce the firm to close down eventually (in the long run) but not any sooner than your fixed inputs become variable ( your building lease expires, your equipment wears out and new equipment needs to be purchased, you are facing the decision of whether or not to take out a new loan, etc.)

35. Sometimes, it is more convenient to formulate a problem not through costs as a function of output but through output (product) as a function of inputs used. Problem 2 on p.194. “Diminishing returns” – what are they? In the short run, every company has some inputs fixed and some variable. As the variable input is added, every extra unit of that input increases the total output by a certain amount; this additional amount is called “marginal product”. The term, diminishing returns, refers to the situation when the marginal product of the variable input starts to decrease (even though the total output may still keep going up!)

36. Total output, or Total Product, TP Amount of input used Marginal product, MP Range of diminishing returns

37. KLQMP K 0200 1 50 220150 320300 420400 520450 620475 Calculating the marginal product (of capital) for the data in Problem 2:

38. KLQMP K 0200--- 12050 220150 320300 420400 520450 620475 Calculating the marginal product (of capital) for the data in Problem 2:

39. KLQMP K 0200--- 12050 220150100 320300150 420400100 52045050 62047525 Calculating the marginal product (of capital) for the data in Problem 2:

40. In other words, we know we are in the range of diminishing returns when the marginal product of the variable input starts falling, or, the rate of increase in total output slows down. (Ex: An extra worker is not as useful as the one before him) Implications for the marginal cost relationship: Worker #10 costs $8/hr, makes 10 units. MC unit =

41. In other words, we know we are in the range of diminishing returns when the marginal product of the variable input starts falling, or, the rate of increase in total output slows down. (Ex: An extra worker is not as useful as the one before him) Implications for the marginal cost relationship: Worker #10 costs $8/hr, makes 10 units. MC unit = $0.80 Worker #11 costs $8/hr, makes …

42. In other words, we know we are in the range of diminishing returns when the marginal product of the variable input starts falling, or, the rate of increase in total output slows down. (Ex: An extra worker is not as useful as the one before him) Implications for the marginal cost relationship: Worker #10 costs $8/hr, makes 10 units. MC unit = $0.80 Worker #11 costs $8/hr, makes 8 units. MC unit =

43. In other words, we know we are in the range of diminishing returns when the marginal product of the variable input starts falling, or, the rate of increase in total output slows down. (Ex: An extra worker is not as useful as the one before him) Implications for the marginal cost relationship: Worker #10 costs $8/hr, makes 10 units. MC unit = $0.80 Worker #11 costs $8/hr, makes 8 units. MC unit = $1

44. In other words, we know we are in the range of diminishing returns when the marginal product of the variable input starts falling, or, the rate of increase in total output slows down. (Ex: An extra worker is not as useful as the one before him) Implications for the marginal cost relationship: Worker #10 costs $8/hr, makes 10 units. MC unit = $0.80 Worker #11 costs $8/hr, makes 8 units. MC unit = $1 In the range of diminishing returns, MP of input is falling and MC of output is increasing

45. Marginal cost, MC Amount of output Amount of input used Marginal product, MP This amount of output corresponds to this amount of input

46. When MP of input is decreasing, MC of output is increasing and vice versa. Therefore the range of diminishing returns can be identified by looking at either of the two graphs. (Diminishing marginal returns set in at the max of the MP graph, or at the min of the MC graph)

47. Back to problem 2, p.194. To find the profit maximizing amount of input (part d), we will once again use the marginal approach, which compares the marginal benefit from a change to the marginal cost of than change. More specifically, we compare VMP K, the value of marginal product of capital, to the price of capital, or the “rental rate”, r. KLQMP K VMP K r 0200--- 12050 220150100 320300150 420400100 52045050 62047525

48. Back to problem 2, p.194. To find the profit maximizing amount of input (part d), we will once again use the marginal approach, which compares the marginal benefit from a change to the marginal cost of than change. More specifically, we compare VMP K, the value of marginal product of capital, to the price of capital, or the “rental rate”, r. KLQMP K VMP K r 0200--- 12050 100 220150100200 320300150300 420400100200 52045050100 6204752550

49. Back to problem 2, p.194. To find the profit maximizing amount of input (part d), we will once again use the marginal approach, which compares the marginal benefit from a change to the marginal cost of than change. More specifically, we compare VMP K, the value of marginal product of capital, to the price of capital, or the “rental rate”, r. KLQMP K VMP K r 0200--- 12050 10075 22015010020075 32030015030075 42040010020075 5204505010075 620475255075 > > > > > < STOP

50. Back to problem 2, p.194. To find the profit maximizing amount of input (part d), we will once again use the marginal approach, which compares the marginal benefit from a change to the marginal cost of than change. More specifically, we compare VMP K, the value of marginal product of capital, to the price of capital, or the “rental rate”, r. KLQMP K VMP K r 0200--- 12050 10075 22015010020075 32030015030075 42040010020075 5204505010075 620475255075 > > > > > < STOP

51. Why would we ever want to be in the range of diminishing returns? Consider the simplest case when the price of output doesn’t depend on how much we produce. Until we get to the DMR range, every next worker is more valuable than the previous one, therefore we should keep hiring them. Only after we get to the DMR range and the MP starts falling, we should consider stopping. Therefore, the profit maximizing point is always in the diminishing marginal returns range! Surprised?

52. Cost minimization (Another important aspect of being efficient.) Suppose that, contrary to the statement of the last problem, we ARE ABLE to change not just the amount of capital but the amount of labor as well. (Recall the distinction between the long run and the short run.) Given that extra degree of freedom, can we do better? (In other words, is there a better way to allocate our budget to achieve our production goals?)

53. In order not to get lost in the multiple possible (K, L, Q) combinations, it is useful to have some of them fixed and focus on the question of interest. In our case, we can either: Fix the total budget spent on inputs and see if we can increase the total output; or, Fix the target output and see if we can reduce the total cost by spending our money differently.

54. Think of the following analogy: Sam needs his 240 mg of caffeine a day or he will fall asleep while driving, and something bad will happen. He can get his caffeine fix from several options listed below: OptionCaffeine, mg Bottled Frappucino, 9.5oz80 Coca-Cola, 12oz 40 Mountain Dew, 12oz60 Which one should he choose?

55. Think of the following analogy: Sam needs his 240 mg of caffeine a day or he will fall asleep while driving, and something bad will happen. He can get his caffeine fix from several options listed below: OptionCaffeine, mgCost of ‘input’ Bottled Frappucino, 9.5oz80 Coca-Cola, 12oz 40 Mountain Dew, 12oz60

56. Think of the following analogy: Sam needs his 240 mg of caffeine a day or he will fall asleep while driving, and something bad will happen. He can get his caffeine fix from several options listed below: OptionCaffeine, mgCost of ‘input’ Bottled Frappucino, 9.5oz80$2.00 Coca-Cola, 12oz 40$0.80 Mountain Dew, 12oz60$1.00

57. Think of the following analogy: Sam needs his 240 mg of caffeine a day or he will fall asleep while driving, and something bad will happen. He can get his caffeine fix from several options listed below: OptionCaffeine, mgCost of ‘input’Mg/$ Bottled Frappucino, 9.5oz80$2.00 Coca-Cola, 12oz 40$0.80 Mountain Dew, 12oz60$1.00

58. Think of the following analogy: Sam needs his 240 mg of caffeine a day or he will fall asleep while driving, and something bad will happen. He can get his caffeine fix from several options listed below: OptionCaffeine, mgCost of ‘input’Mg/$ Bottled Frappucino, 9.5oz80$2.0040 Coca-Cola, 12oz 40$0.8050 Mountain Dew, 12oz60$1.0060

59. Think of the following analogy: Sam needs his 240 mg of caffeine a day or he will fall asleep while driving, and something bad will happen. He can get his caffeine fix from several options listed below: OptionCaffeine, mgCost of ‘input’Mg/$ Bottled Frappucino, 9.5oz80$2.0040 Coca-Cola, 12oz 40$0.8050 Mountain Dew, 12oz60$1.0060

60. Next, think of caffeine as Sam’s ‘target output’ (what he is trying to achieve) and drinks as his inputs, which can to a certain extent be substituted for each other. The same principle holds for any production unit that is trying to allocate its resources wisely: In order to achieve the most at the lowest cost possible, a firm should go with the option with the highest MP input /P input ratio. Note that following this principle will make the firm better off regardless of the demand it is facing!

61. If then - reduce the amount of capital; - increase the amount of labor. If then - reduce the amount of labor; - increase the amount of capital. If then inputs are used in the right proportion. No need to change anything. As you do that, - MP L will decrease; - MP C will increase; - the LHS will get smaller, - the RHS bigger