Cost function.ppt
- 1. Theory of Costs • Cost : is the monetary value of inputs used in the production of an item. Two types of cost of a product • Social cost: is the cost of producing an item to the society • Private cost: is the cost of producing an item to the individual producer. 1
- 2. Private cost of production can be measured in two ways Economic cost & accounting cost A. Economic cost: the cost of all inputs used to produce the item. • Economic cost = Explicit costs + Implicit cost – Explicit costs – costs paid in cash – Implicit cost – imputed cost of self-owned or self employed resources based on their opportunity costs. 2
- 3. Implicit Vs Explicit Costs – Opportunity cost principle - the economic cost of an input used in a production process is the value of output sacrificed elsewhere The opportunity cost of an input is the value of forgone income in best alternative employment B. Accounting cost: refers to the cost of purchased inputs only It is the explicit cost of production only 3
- 4. Cost Concepts (Short-run cost of production) 1. Total Fixed Cost (TFC) 2. Total Variable Cost (TVC) 3. Total Cost (TC = TVC+TFC) 4. Average Fixed Cost (AFC = TFC/Q) 5. Average Variable Cost (AVC = TVC/Q) 6. Average Total Cost (AC = AFC+AVC) 7. Marginal Cost (MC= ∆TVC/∆Q 4
- 5. Cost concept … • Total fixed cost (TFC) or fixed cost (FC) refers to those costs that do not vary as the firm changes its output level – Examples: the payment or rent for land, buildings and machinery, Depreciation, Interest, Taxes (property), Insurance – The fixed cost is independent of the level of output produced. – Graphically, it is depicted as a horizontal line 5
- 6. • Total variable cost (TVC) or Variable cost (VC) refers to the cost that changes as the amount of output produced is changed – Examples - purchases of raw materials, payments to workers, electricity bills, fuel and power costs – Total variable cost increases as the amount of output increases • If no output is produced, then total variable cost is zero; the larger the output, the greater the total variable cost 6
- 7. • Total cost (TC) is the sum of total fixed cost and total variable cost, i.e., TC = TFC + TVC • As the level of output increases, total cost of the firm also increases. • Marginal cost (MC) is the additional cost incurred from producing an additional unit of output: MC = TC/Q or MC = TVC/Q 7
- 8. Selected attributes • MC is generally increasing. • MC crosses ATC and AVC at their minimum point. • If MC is below the average cost, Average cost will be decreasing. • If MC is above the average cost, Average cost will be increasing. 8
- 9. Total Costs of Production Units of output Total Fixed Cost Total Variable Cost Total Cost Marginal Cost Average Cost Q TFC TVC TC MC AC 0 100 0 100 - - 1 100 30 130 30 130 2 100 50 150 20 75 3 100 60 160 10 53.3 4 100 65 165 5 41.25 5 100 75 175 10 35 6 100 95 195 20 32.5 7 100 125 225 30 32.14 8 100 165 265 40 33.12 9 100 215 315 50 35 10 100 275 375 60 37.5 9
- 10. Q 0 TFC (Total Fixed Cost) TC TVC TFC TVC (Total Variable Cost) TC (Total Cost) “TOTAL” COST CURVES 10
- 11. Q 0 AFC (Average Fixed Cost) AFC AFC = TFC/Q As more output is produced, the Average Fixed Cost decreases. 11
- 12. Q 0 TV C AVC TVC (Total Variable Cost) q1 The Average Variable Cost at a point on the TVC curve is measured by the slope of the line from the origin to that point. AVC=TVC/Q Minimum AVC 12
- 14. Q 0 AVC AVC (Average Variable Cost) q1 The Average Variable Cost is U shaped. First it decreases, reaches a minimum and then increases. Minimum AVC 14
- 15. 15 In summary, AVC, ATC and MC curves are all U-shaped due to the law of variable proportions. The simplest total cost function which would incorporate the law of variable proportions is the cubic polynomial of the following form. 3 2 3 2 1 Q b Q b Q b bo TC Where Q- is the level of output and b0, b1, b2 &b3 – are none zero constants. From this type of total cost function, bo- represents the TFC, and AFC = Q b0 3 3 2 2 1 Q b Q b Q b - represents TVC and 2 3 2 1 3 3 2 2 1 Q b Q b b Q Q b Q b Q b AVC ATC = AFC + AVC 2 3 2 1 0 Q b Q b b Q b
- 16. Q 0 MC AVC AVC (Average Variable Cost) q1 The Marginal Cost curve passes through the minimum point of the AVC curve. It is also U-shaped. First it decreases, reaches a minimum and then increases. Minimum AVC MC (Marginal Cost) 16
- 17. Q 0 MC AC AVC AFC AVC q1 MC AFC AC The “PER UNIT” COST CURVES 17
- 18. 18 Finally, the MC curve passes through the minimum point of both ATC and AVC curves. This can be shown by using calculus. Suppose the TC = f (Q) Slope of But f (Q) is MC and Q1 (or dQ/dQ) =1 ) ( )) ( ( Q f dQ Q f d MC Q Q f Q TC AC ) ( 2 ) ( . )) ( ( (Q)) (f d Q Q f Q Q Q f dQ d AC Q Q Q f Q MC Q AC ) ( 2 f(Q) - MC.Q
- 19. 19 Thus, slope of Slope AC = AC Q Q f where AC MC Q ) ( , 1 Now, i) when MC<AC, the slope of AC is negative, i.e. AC curve is decreasing (initial stage of production) ii) When MC >AC, the slope of AC is positive, i.e. the AC curve is increasing (after optimal combination of fixed and variable inputs. iii) When MC = AC, the slope of AC is zero, i.e. the AC curve is at its minimum point. The relationship between AVC and MC can be shown in a similar fashion.
- 20. Table 5.4 Average Cost of Production (Q) (TC) (AC) 0 100 - 1 130 130.00 2 150 75.00 3 160 53.33 4 165 41.25 5 175 35.00 6 195 32.50 7 225 32.14 8 265 33.13 9 315 35.00 10 375 37.50 20
- 21. Total Product (Q) Total Variable Cost (TVC) Average Variable Cost (AVC) 0 0 - 1 30 30.0 2 50 25.0 3 60 20.0 4 65 16.3 5 75 15.0 6 95 15.8 7 125 17.9 8 165 20.6 9 215 23.9 10 275 27.5 Table 5.5 Average Variable Costs of Production 21
- 22. The Link between Production and Cost Maximum MP Maximum AP Minimum AVC Minimum MC Unit product Unit cost AP MP MC AVC Labor Quantity 22
- 23. 23 Thus, TVC = WL AVC = Q TVC = Q WL = W. L Q 1 But, L Q represents APL Therefore, AVC = W. APL 1 Hence, AVC and APL are inversely related.Similarly, MCand MPL, MC = dQ dTC = dQ dTVC (Remember that MC = dQ dTC MC = dQ L W d ) . ( MC = W. dQ dL ………………………… (because w is constant) MC = W. dQ dL MC = W. dL dQ 1 MC = W. MPL 1 ……………………………………………… (Because dL dQ = MPL) Hence, MC and MPL have also an inverse relation.
- 24. Summary of production and cost There is an inverse relationship between AP and AVC There is an inverse relationship between MP and MC Whenever MP is above AP ,the MC is below AVC Whenever MP is below AP ,the MC is above AVC Whenever MP is equal to AP ,the MC is equal to AVC i.e MP = AP when AP is maximum, MC = AVC, when AVC is minimum 24
- 25. Cost Curves in the Long Run • In the long run, the amount of all factors of production can be varied so that there are no fixed costs. • The time period corresponding to the long run will be such a condition that the producers can make all the necessary changes in the size of the plant. • Fixed cost will be variable in the long run decision of production • When we say that fixed costs vary with the size of the plant, we mean that all costs behave in the same way as all other components of the variable costs. 25
- 26. The Long run average cost curves • The long- run average cost curve is an ‘envelope’ of all the short run ATC curves corresponding to all the different levels of factors of production that are fixed in the short- run. • The LRAC curve is given by the point of tangency to all the short-run curves representing all the alternative plant sizes that a firm could be able to build in the long-run. • To know it more look at the following graph. 26
- 27. LA C SAC 1 Q 0 COST SAC 2 LONG-RUN AVERAGE COST CURVE SAC 3 SAC 4 SAC 5 SAC 6 27
- 28. 28 Why is the LAC U-shaped? The LAC curve is U-shaped due to the laws of returns to scale(i.e increasing & decreasing returns to scale) that is, as output expands from a very low levels increasing returns to scale prevails (i.e., output rises proportionally more than inputs), & so the cost per-unit of output falls As output continues expand, the forces of decreasing returns to scale eventually begin to overtake the forces of increasing returns to scale & the LAC begins to rise In general, the reason for the U-shaped ness of the LAC curve are the existence of increasing returns to scale at initial stage of expansion decreasing returns to scale at a later stage of expansion.
- 29. 29 QO C (Increasing returns to scale Decreasing returns to scale C0 constant returns to scale Fig the LAC curve is U-shaped due to the combined effects of increasing, constant and decreasing returns. Q
- 30. 30 LMC LAC SMC2 SAC2 SMC3 Q3 Q2 Q1 C Fig Long run marginal cost curve; it is derived from the short run marginal cost curves by connecting the points of intersection of the vertical lines drawn from the point of tangency of SAC curves with the LAC curves with and the corresponding SMC curves SMC1 SAC1 SAC3 Q
- 31. 31 Dynamic changes in costs: the learning curve Reason why a large firm may have a lower long-run average cost than a small firm: increasing returns to scale in production it is tempting to conclude that firms which enjoy lower average cost over time are growing firms with increasing returns to scale but this need not be true In long-run, average cost may decline over time because workers and managers absorb new technological information as they become more experienced at their job That is, as workers get experience their efficiency increases which then reduces the average and marginal costs of producing a unit of product A firm’s learns’ over time as cumulative output increases. Managers can use this learning process to help plan production and forecast future costs.
- 32. 32 A Number of labor required to produce one unit Fig Learning Curve: shows that at the firm’s cumulative out put increases(as the firm gets experienced),the amount of inputs(such as labor)required to produce one unit of out put decreases. Learning curve Cumulative out put
- 33. 33 Learning vs Economies of scale A firm’s average cost of production can decline overtime because of growth of sales (output) when increasing returns to scale prevails in the firm (a move from A to B on curve AC,), or it can decline because there is a learning curve ( a move from A on AC, to C on AC2) Thus, increasing returns to scale reduces average cost of production with increase in output, where as learning shifts the average cost curve down ward. Cost per unit of out put Economies of scale Learning AC1 AC2 Out put A C B