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# Cost curves

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• 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.
• Thinking at the margin helps not only Jack, but all managers in the real world, who make business decisions every day by comparing marginal costs with marginal benefits.
• In the next chapter, we will learn more about how firms choose Q to maximize their profits.
• If you did Active Learning 1 and created a class-generated list of General Motors’ costs, you might return to that list and ask students which of the costs on their list are fixed and which are variable.
• Point out that the TC curve is parallel to the VC curve but is higher by the amount FC.
• Most students quickly 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.
• Many students have heard the terms “cost per unit” or “unit cost” in other business courses. ATC means the same thing.
• In this example, the efficient scale is Q=5, where ATC = \$76.
At any Q below or above 5, ATC &gt; \$76.
• 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.
• ### Cost curves

1. 1. Bellringer Mankiw Chapter 13 Costs 1. Calculate the TC, FC, VC, AFC, AVC, ATC, MC 2. on the back of the page graph in red MC, blue ATC, green AVC, black AFC
2. 2. Hot dogs per hour FC VC 0 \$3 \$0 Total Cost AFC AVC ATC MC Hot dogs per hour FC VC ------ 0 \$3 \$0 1 \$0.30 1 \$0.30 2 \$0.80 2 \$0.80 3 \$1.50 3 \$1.50 4 \$2.40 4 \$2.40 5 \$3.50 5 \$3.50 6 \$4.80 6 \$4.80 7 \$6.30 7 \$6.30 8 \$8.00 8 \$8.00 9 \$9.90 9 \$9.90 10 \$12.00 10 \$12.00 Total Cost AFC AVC ATC MC ------
3. 3. 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 5
4. 4. Example 1: Farmer Jack’s Production Function Q (no. of (bushels workers) of wheat) 3,000 Quantity of output L 2,500 0 0 1 1000 2 1800 3 2400 500 4 2800 0 5 3000 THE COSTS OF PRODUCTION 2,000 1,500 1,000 0 1 2 3 4 5 No. of workers 6
5. 5. 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 ∆Q Marginal product of labor (MPL) = ∆L THE COSTS OF PRODUCTION 7
6. 6. EXAMPLE 1: Total & Marginal Product L Q (no. of (bushels workers) of wheat) ∆L = 1 ∆L = 1 ∆L = 1 ∆L = 1 ∆L = 1 0 0 1 1000 2 1800 3 2400 4 2800 5 3000 THE COSTS OF PRODUCTION MPL ∆Q = 1000 1000 ∆Q = 800 800 ∆Q = 600 600 ∆Q = 400 400 ∆Q = 200 200 8
7. 7. EXAMPLE 1: MPL = Slope of Prod Function Q (no. of (bushels MPL workers) of wheat) 0 1 2 3 4 5 0 1000 1800 2400 2800 3000 1000 800 600 400 200 THE COSTS OF PRODUCTION 3,000 MPL Quantity of output L equals the slope of the 2,500 production function. 2,000 Notice that MPL 1,500 diminishes as L increases. 1,000 This explains why 500 the production function gets flatter 0 as L0increases. 3 1 2 4 5 No. of workers 9
8. 8. 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 10
9. 9. 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 11
10. 10. 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…. THE COSTS OF PRODUCTION 12
11. 11. EXAMPLE 1: Farmer Jack’s Costs L Q Cost of (no. of (bushels land workers) of wheat) Cost of labor Total Cost 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 13
12. 12. EXAMPLE 1: Farmer Jack’s Total Cost Curve 0 \$12,000 Total Cost \$1,000 1000 \$3,000 1800 \$5,000 2400 \$7,000 2800 \$9,000 3000 \$10,000 Total cost Q (bushels of wheat) \$11,000 THE COSTS OF PRODUCTION \$8,000 \$6,000 \$4,000 \$2,000 \$0 0 1000 2000 3000 Quantity of wheat 14
13. 13. Marginal Cost  Marginal Cost (MC) is the increase in Total Cost from producing one more unit: ∆TC MC = ∆Q THE COSTS OF PRODUCTION 15
14. 14. EXAMPLE 1: Total and Marginal Cost Q Total (bushels Cost of wheat) ∆Q = 1000 ∆Q = 800 ∆Q = 600 ∆Q = 400 ∆Q = 200 0 \$1,000 1000 \$3,000 1800 \$5,000 2400 \$7,000 2800 \$9,000 3000 \$11,000 THE COSTS OF PRODUCTION Marginal Cost (MC) ∆TC = \$2000 \$2.00 ∆TC = \$2000 \$2.50 ∆TC = \$2000 \$3.33 ∆TC = \$2000 \$5.00 ∆TC = \$2000 \$10.00 16
15. 15. EXAMPLE 1: The Marginal Cost Curve 0 TC MC \$1,000 1000 \$3,000 1800 \$5,000 2400 \$7,000 2800 \$9,000 3000 \$11,000 \$2.00 \$2.50 \$3.33 \$10 Marginal Cost (\$) Q (bushels of wheat) \$12 \$8 MC usually rises as Q rises, as in this example. \$6 \$4 \$2 \$5.00 \$10.00 THE COSTS OF PRODUCTION \$0 0 1,000 2,000 3,000 Q 17
16. 16. 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 18
17. 17. 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 19
18. 18. EXAMPLE 2  Our second example is more general, applies to any type of firm producing any good with any types of inputs. THE COSTS OF PRODUCTION 20
19. 19. EXAMPLE 2: Costs Q FC VC \$800 \$700 TC FC VC \$0 \$100 1 100 70 170 \$500 2 100 120 220 3 100 160 260 4 100 210 310 5 100 280 380 6 100 380 480 7 100 520 620 TC \$600 Costs 0 \$100 \$400 \$300 \$200 \$100 \$0 0 1 2 3 4 5 6 7 Q THE COSTS OF PRODUCTION 21
20. 20. EXAMPLE 2: Marginal Cost TC 0 \$100 1 170 2 220 3 260 4 310 5 380 6 480 7 620 MC \$70 50 40 50 70 100 140 \$200 Recall, Marginal Cost (MC) is \$175change in total cost from the producing one more unit: \$150 ∆TC MC = ∆Q \$100 Usually, MC rises as Q rises, due \$75 to diminishing marginal product. Costs Q \$125 \$50 Sometimes (as here), MC falls \$25 before rising. \$0 (In other examples, MC may be 7 0 1 2 3 4 5 6 constant.) Q THE COSTS OF PRODUCTION 22
21. 21. EXAMPLE 2: Average Fixed Cost Q FC 0 \$100 \$200 Average fixed cost (AFC) is fixed cost divided by the \$175 quantity of output: \$150 AFC n/a 100 \$100 2 100 50 3 100 33.33 4 100 25 5 100 20 6 100 16.67 7 100 14.29 Costs 1 AFC \$125 = FC/Q \$100 Notice that AFC falls as Q rises: \$75 The firm is spreading its fixed \$50 costs over a larger and larger \$25 number of units. \$0 0 1 2 3 4 5 6 7 Q THE COSTS OF PRODUCTION 23
22. 22. EXAMPLE 2: Average Variable Cost Q VC \$200 Average variable cost (AVC) is variable cost divided by the \$175 quantity of output: \$150 AVC \$0 n/a 1 70 \$70 2 120 60 3 160 53.33 4 210 52.50 5 280 56.00 6 380 63.33 7 520 74.29 Costs 0 THE COSTS OF PRODUCTION AVC \$125 = VC/Q \$100 As Q rises, AVC may fall initially. \$75 In most cases, AVC will \$50 eventually rise as output rises. \$25 \$0 0 1 2 3 4 Q 5 6 7 24
23. 23. EXAMPLE 2: Average Total Cost Q TC 0 \$100 ATC AFC AVC n/a n/a n/a 1 170 \$170 \$100 \$70 2 220 110 50 60 3 260 86.67 33.33 53.33 4 310 77.50 25 52.50 5 380 76 20 56.00 6 480 80 16.67 63.33 7 620 88.57 14.29 Average total cost (ATC) equals total cost divided by the quantity of output: 74.29 THE COSTS OF PRODUCTION ATC = TC/Q Also, ATC = AFC + AVC 25
24. 24. EXAMPLE 2: Average Total Cost TC 0 \$100 1 170 \$200 ATC Usually, as in this example, \$175 the ATC curve is U-shaped. n/a \$150 \$170 110 Costs Q \$125 2 220 3 260 86.67 4 310 77.50 \$50 5 380 76 \$25 6 480 80 \$0 7 620 88.57 THE COSTS OF PRODUCTION \$100 \$75 0 1 2 3 4 5 6 7 Q 26
25. 25. EXAMPLE 2: Why ATC Is Usually U-Shaped As Q rises: \$200 Initially, falling AFC pulls ATC down. \$175 Costs Eventually, rising AVC pulls ATC up. \$150 Efficient scale: The quantity that minimizes ATC. \$125 \$100 \$75 \$50 \$25 \$0 0 1 2 3 4 5 6 7 Q THE COSTS OF PRODUCTION 27
26. 26. EXAMPLE 2: The Various Cost Curves Together \$200 \$175 Costs ATC AVC AFC MC \$150 \$125 \$100 \$75 \$50 Check mark? Bowed up L shape Smile Bowed down L shape \$25 \$0 0 1 2 3 4 5 6 7 Q THE COSTS OF PRODUCTION 28
27. 27. EXAMPLE 2: ATC and MC When MC < ATC, ATC MC \$200 ATC is falling. \$175 \$150 ATC is rising. \$125 The MC curve crosses the ATC curve at the ATC curve’s minimum. Costs When MC > ATC, \$100 \$75 \$50 \$25 \$0 0 1 2 3 4 5 6 7 Q THE COSTS OF PRODUCTION 29
28. 28. Cost Round up  If MC is higher than AVC, does MC increase or decrease?  Why does the AFC curve slope down forever as a firm produces more?  Which curve looks like a check mark?  Which curve has the most extreme upward slope?  Which is the only average curve that decreases over time?  Which curve is the above the other average curves?
29. 29. Costs assignment 1 2