Theory of Cost.pptx managerial economics basics and matrix

For MBA student Managerial economics course

1. Chapter 3: Theory of Cost Managerial Economics

2. Concept of Cost Cost is defined as those expenses faced by a business in the process of supplying goods and services to consumers.

3. Types of Costs Explicit cost (EC) is the direct monetary expenditure or out-of-pocket expenses paid for the firm’s resources, such as material, wages, interest on loans, rent etc. Implicit cost (IC) is the indirect nonmonetary cost that can only be estimated by the opportunity cost which is the loss of earnings due to lost opportunities. Therefore: Economic profit =TR- EC – IC; Accounting profit = TR-EC A sunk cost is a cost that an entity has incurred, and which it can no longer recover. It is type of fixed cost that can’t be recouped or which is lost forever once paid. Thus, it should not be considered when making the decision to continue investing in an ongoing project.

4. Fixed costs are those, which are fixed in volume for a certain given output. It does not vary with the variation in the output. Cost of managerial and administrative staff, Depreciation of machinery Maintenance of land etc. can be example of fixed costs. Variable costs are those, which vary with the variation in the total output. Variable costs include cost of raw materials, direct labor charges, etc. Total Cost (TC) represents the value of the total resources requirements for the production of goods and services.

5. Average Costs (AC) = TC/Q, Q is the total output. Marginal Costs (MC) is the addition to the total cost on account of producing and additional unit of the product or, marginal cost is the cost of marginal unit produced. MC= ∆ TC/ ∆ Q= ∆ TVC/ ∆ Q ; TC = TVC + TFC = E MC+TFC, TVC= E MC Short Run Costs: Some inputs are fixed in short run. Fixed costs are costs associated with such fixed inputs must be paid regardless of the level of output produced. Long run cost : the long run simply refers to a period of time during which all inputs can be varied.

6. Total Cost Curve in the Short Run

7. Total cost curve The total-fixed-cost curve is horizontal at $6,000, indicating that TFC is constant for all levels of output. TVC starts at the origin , because the firm incurs no variable costs if production is zero ; TVC rises as output increases, because to produce more the firm must use more resources, thereby increasing cost. Total cost curve lies above the TVC curve by an amount exactly equal to $6,000 ( TFC ) at each output level. Consequently, TC and TVC are parallel and have identical shapes .

8. Average and Marginal cost schedules

9. Short Run Average and Marginal Cost Curves SMC first declines, reaches a minimum at Q 1, and rises thereafter. AVC first declines, reaches a minimum at Q 2 ( SMC = AVC) , and rises thereafter. ATC first declines, reaches a minimum at Q 3 ( SMC = ATC) , and rises thereafter. AFC declines continuously.

10. Short Run Average and Marginal Cost Curves SMC lies below both AVC and ATC over the range for which these curves decline; SMC lies above them when they are rising. If SMC is below AVC, each additional unit of output adds less to cost than the AVC of that unit. Thus AVC must decline over this range. When SMC is above AVC , each additional unit of output adds more to cost than AVC . In this case, AVC must rise. So when SMC is less than AVC , AVC is falling; when SMC is greater than AVC , AVC is rising.

11. It refers to mathematical relation between cost of a product and the various determinants of cost. C=f(q) Where: C= cost of production Q= quantity of output f= functional r/ship The basic principle of the cost behavior is that the total cost increases with the increase in output. Cost Function

12. SHORT-RUN COSTS AND PRODUCTION If 4 units of labor are employed, the firm can produce (a maximum of) 100 units; if 6 units of labor are employed, the firm’s maximum output is 200 units; and so on. (Remember, the production function assumes technical efficiency.) If the price of a unit of labor services ( w )= $1,000  Wage rate Hence TVC= w X L If 3 units of capital in the short run ( K=3) and that capital costs $2,000 per unit to employ. Thus the TFC =r X K =$2,000X3=$6,000 Where r is the price of a unit of capital services. Therefore TC = wL + rK

13. Average, Marginal Cost and Production Q= 25 X 4, AVC=TVC/Q=(1000 X 4)/(25 X 4)=(w X L)/(AP X L)= 40=w/AP MP is the additional labor employed to increase production in 100-unit intervals.

14. Graph of AVC, SMC, AP, and MP Assume the wage rate is $21. From 0 to 500 units of Labor, MP > AP and AP is rising. But, SMC & AVC falling b/c of inverse r/ship SMC=w/MP, AVC=w/AP AP = Q/L ,Q=6.5X500=3,250 MP reaches maximum and MC reaches minimum at 3,250 units of output. MC=w/MP=21/9, AVC=3.23=w/AP=21/65.

15. Production and Cost curves When MP (AP) is increasing, MC (AVC) is decreasing. When MP (AP) is decreasing, MC (AVC) is increasing. When MP = AP at maximum AP , MC = AVC at minimum AVC In short run, the effect of the law of diminishing marginal product on the marginal cost of production. MP generally rises at first, then diminishes b/c capital is fixed. As MP begins to fall, MC begins to rise. In previous Figure, MP begins to fall beyond 500 units of labor (beyond point A in Panel A). MC begins to rise beyond 3,250 units of output (beyond point a in Panel B). In the range between 500 and 800 units of labor.

16. Production and Cost curves MP is falling, but while MP still lies above AP, AP continues to rise up to point C , where MP = AP . At point C , AP reaches its maximum value at 800 units of labor. When 800 units of labor are employed, 5,600 units of output are produced (5,600 = AP X L = 7 X 800). Thus, at 5,600 units of output, MC =AVC= $3, SMC = w / MP = $21/7 = $3, AVC = w / AP = $21/7 = $3 So, at 5,600 units of output, AVC reaches its minimum and is equal to MC.

17. Production and Cost curves If labor usage increases beyond 800 units. MP is below AP, and AP continues to decrease but never becomes negative. MP will eventually become negative. Manager who wishes to minimize costs would never hire an amount of labor that would have a negative marginal product . If MP is negative, the manager could increase output by decreasing labor usage, and this would also decrease the firm’s expenditure on labor. At 1,100 units of labor, AP is 6, and output is 6,600 units (= AP X L = 6 X 1,100). MC= $5.25 and AVC = $3.50 when 6,600 units are produced. SMC = w / MP and AVC = w / AP

18. Long-run average and Cost curve A curve that defines the minimum average cost of producing alternative levels of output, allowing for optimal selection of both fixed and variable factors of production.

19. Economies of Scale Economies of scale: Exist when long-run average costs decline as output is increased. Diseconomies of scale: Exist when long-run average costs rise as output is increased. Constant returns to scale: Exist when long-run average costs remain constant as output is increased.

20. The relationship between increased per-worker productivity and reduced per worker cost at fixed labor prices associated with an increase in output and experience is called the learning curve effect. The learning curve effect measures an increase in per-worker productivity associated with an improvement in labor skills from on the job experience. It can be achieved by employee training and off-site continuing education programs, the adoption of new production, organizational and managerial techniques, the replacement of higher cost with lower cost materials, new product design, and so on. LEARNING CURVE EFFECT

21. Empirical Production Function is the mathematical form of the production function to be estimated. Cubic empirical specification for a short-run production function is derived from a long-run cubic production function Cubic form of the long-run production function is expressed as: Holding capital constant at K units (K =K ), the short-run cubic production function is Empirical estimates of production and costs

22. Short-run Cubic Production Function The level of labor usage beyond which marginal product begins to fall, and diminishing returns set in, is L m = − B /3A  Differentiation of MP. When MP= AP and average product is at its maximum L a = − B /2A  Differentiation of AP or Equating as AP=MP

23. Estimation of production functions Linear Production Function: Q=F(K,L)= aK + bL Q=F(K,L)=4K + L  Capital is always 4 times as productive as labor. F(5,2)= 4(5) + 1(2)=22 MP k =a, MP L =b  Possible to verify by derivative The marginal product of an input is simply the coefficient of the input in the linear production function. Thus, the marginal product of an input is independent of the quantity of the input used. Linear production functions do not obey the law of diminishing marginal product.

24. Estimation of production functions Examples of production functions power function : exponential for one input Q = aL b if b > 1, MP increasing  = 3x 2 if b = 1, MP constant = 3x if b < 1, MP decreasing = 3x 1/2

25. Estimation of production functions: Example

26. Problems 1. For each of the following situations, determine whether the manager is concerned with a short-run or a long-run production decision. Explain briefly in each case. a. A petroleum drilling supervisor on an offshore drilling platform decides to add an extra six-hour shift each day to keep the drill rig running 24 hours per day. b . The vice president of offshore petroleum drilling operations in the Gulf of Mexico chooses to deploy three more offshore drilling platforms in the Gulf. c . A manufacturing engineer plans the production schedule for the month. d . After studying a demographic report on future increases in birthrates, a hospital administrator decides to add a new pediatric wing to the hospital.

27. Problems During a year of operation, a firm collects $175,000 in revenue and spends $80,000 on raw materials, labor expense, utilities, and rent. The owners of the firm have provided $500,000 of their own money to the firm instead of investing the money and earning a 14 percent annual rate of return. a. The explicit costs of the firm are $___ . The implicit costs are $___ . Total economic cost is $___. b. The firm earns economic profit of $___. c. The firm’s accounting profit is $___. d. If the owners could earn 20 percent annually on the money they have invested in the firm, the economic profit of the firm would be___.

28. Problems

29. 10. Assume average variable cost is constant over a range of output. What is marginal cost over this range? What is happening to average total cost over this range? 11. Suppose that a firm is currently employing 20 workers, the only variable input, at a wage rate of $60. The average product of labor is 30, the last worker added 12 units to total output, and total fixed cost is $3,600. a. What is marginal cost? b. What is average variable cost? c . How much output is being produced? d . What is average total cost? e . Is average variable cost increasing, constant, or decreasing? What about average total cost?

30. Solution for Q-11: Given: L= 20 workers, Wage rate= 60, Average product of Labor=30. Last worker added 12 units to total output, TFC= $3,600. MC= ∆TC/∆Q=60/12=5 AVC= TVC/Q=WL/Q= 60X20/APLXL= 1200/600=2 Q=APL X L= 30 X 20=600 ATC=AVC + AFC= 2 + 3600/600 =8 ATC (8)>MC (5) >AVC (2). Thus, AVC is increasing but ATC is decreasing.

31. 12. The cost function for Managerial Enterprises is given by C ( Q ) = 20 + 3 Q 2 . Determine the marginal cost, average fixed cost, average variable cost, and average total cost when Q = 10. Answer: Using the formula for marginal cost (here a = c = 0), we know that MC = 6 Q. Thus, the marginal cost when Q = 10 is $60. To find the various average costs, we must first calculate total costs. The total cost of producing 10 units of output is C (10) = 20 +3(10) 2 = $320 Fixed costs are those costs that do not vary with output; thus fixed costs are $20. Variable costs are the costs that vary with output, namely VC ( Q ) = 3 Q 2 . Thus, VC (10) = 3(10) 2 = $300. It follows that the average fixed cost of producing 10 units is $2, the average variable cost is $30, and the average total cost is $32.

32. Problem : A firm’s total cost function is Required: Suppose that the firm produces 10 units of output. Calculate TFC, TVC, ATC, AFC, AVC, and MC. The Cost Function (Example)

33. LONG-RUN COSTS AND OUTPUT DECISIONS In the Long-run production – all inputs are variable If all inputs of a firm change - the scale of the firm changes Firms increase size of the firm or scale of production by changing the fixed inputs of short run production – in order to increase output Long-run cost behavior of a firm is derived from – short run costs of separate production plants In order to discuss about long run We look at firms in three short-run circumstances: firms earning economic profits, firms suffering economic losses but continuing to operate to reduce or minimize those losses, and firms that decide to shut down and bear losses just equal to fixed costs.

34. Short-run Conditions and Long-run Directions ABC Car Wash Weekly Costs TOTAL FIXED COSTS (TFC) TOTAL VARIABLE COSTS (TVC) (800 WASHES) TOTAL COSTS (TC = TFC + TVC) $ 3,600 1. Normal return to investors $ 1,000 1. 2. Labor Materials $ 1,000 600 Total revenue (TR) at P = $5 (800 x $5) $ 4,000 2. Other fixed costs (maintenance contract, insurance, etc.) 1,000 $ 1,600 Profit (TR - TC) $ 400 $ 2,000 LONG-RUN COSTS AND OUTPUT DECISIONS

35. Producing at a Loss to offset Fixed Costs: The ABC Car wash A firm will operate if total revenue covers total variable cost CASE 1: SHUT DOWN CASE 2: OPERATE AT PRICE = $3 Total Revenue (q = 0) $ Total Revenue ($3 x 800) $ 2,400 Fixed costs Variable costs Total costs + $ $ 2,000 2,000 Fixed costs Variable costs Total costs + $ $ 2,000 1,600 3,600 Profit/loss (TR - TC) - $ 2,000 Operating profit/loss (TR - TVC) $ 800 Total profit/loss (TR - TC) - $ 1,200 If revenues exceed variable costs, operating profit is positive and can be used to offset fixed costs and reduce losses, and it will pay the firm to keep operating. If revenues are smaller than variable costs, the firm suffers operating losses that push total losses above fixed costs . In this case, the firm can minimize its losses by shutting down . Short-run Conditions and Long-run Directions

36. Shutting Down to Minimize Loss A Firm Will Shut Down If Total Revenue Is Less Than Total Variable Cost CASE 1: SHUT DOWN CASE 2: OPERATE AT PRICE = $1.50 Total Revenue (q = 0) $ Total revenue ($1.50 x 800) $ 1,200 Fixed costs Variable costs Total costs + $ $ 2,000 2,000 Fixed costs Variable costs Total costs + $ $ 2,000 1,600 3,600 Profit/loss (TR - TC): - $ 2,000 Operating profit/loss (TR - TVC) - $ 400 Total profit/loss (TR - TC) - $ 2,400 Any time that price (average revenue) is below the minimum point on the average variable cost curve, total revenue will be less than total variable cost, and operating profit will be negative—that is, there will be a loss on operation. In other words, when price is below all points on the average variable cost curve, the firm will suffer operating losses at any possible output level the firm could choose. When this is the case, the firm will stop producing and bear losses equal to fixed costs. This is why the bottom of the average variable cost curve is called the shut-down point. At all prices above it, the marginal cost curve shows the profit-maximizing level of output. At all prices below it, optimal short-run output is zero. Short-run Conditions and Long-run Directions

37. The short-run supply curve of a competitive firm is that portion of its marginal cost curve that lies above its average variable cost curve As long as price (which is equal to average revenue per unit) is sufficient to cover average variable costs, the firm stands to gain by operating instead of shutting down. Shut-down point The lowest point on the average variable cost curve. When price falls below the minimum point on AVC, total revenue is insufficient to cover variable costs and the firm will shut down and bear losses equal to fixed costs. Short-run Conditions and Long-run Directions

38. The Industry Supply Curve in the Short Run Is the Horizontal Sum of the Marginal Cost Curves (above AVC) of All the Firms in an Industry short-run industry supply curve The sum of the marginal cost curves (above AVC ) of all the firms in an industry. Short-run Conditions and Long-run Directions

39. LONG-RUN DIRECTIONS Profits, Losses, and Perfectly Competitive Firm Decisions in the Long and Short Run SHORT-RUN CONDITION SHORT-RUN DECISION LONG-RUN DECISION Profits TR > TC P = MC: operate Expand: new firms enter Losses 1. With operating profit P = MC: operate Contract: firms exit (TR  TVC) (losses < fixed costs) 2. With operating losses Shut down: Contract: firms exit (TR < TVC) losses = fixed costs