Production costs. Microéconomie, chapter 7. Solvay Business School Université Libre de Bruxelles
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1 Production costs Microéconomie, chapter 7 1
2 Points to be addressed What costs to take into account? Short run costs Long run costs Short and long run cost curves Returns to scale and economies of scale 2
3 Introduction Technology and input prices determines the production costs for the firm Economic efficiency requires to produce at a minimum cost at each level of output 3
4 What costs to take into account? Rentals of office space, machinery are obvious costs for the firm What if the firm owns already these inputs and needs not renting them? Then the unearned income from not renting them to others are costs for the firm (opportunity cost) 4
5 What costs to take into account? Opportunity cost Unearned income from the most profitable alternative uses of the firm s assets It is an implict cost that must be taken into account 5
6 Opportunity cost Example The firm owns its office space Does this firm not incur any cost for the use of office space? Yes, the firm could have rented the office space it owns to receive some income 6
7 What costs to take into account? Sunk costs Any past spending that cannt be recovered They do not influence the production decisions of the firm and need not be taken into account 7
8 Sunk costs Example The firm seeks to rent some office space It has already made a downpayment of for the purchase of an office building The sale price is 5,5 millions ( 5 millions are still to be paid) Before the settlement, the firm finds another building equally convenient for 4,25 millions Which building should the firm buy? 8
9 Sunk costs Example The firm should buy the second building The downpayment of is a sunk cost that has no influenec of the decision What the firm must consider is to spend 4,25 millions more, or to spend 5 millions more 9
10 What costs to take into account? Some costs change with the output level, others are constant Total cost is composed of: 1. Fixed costs Independent of the output level 2. Variable costs Depend on the output level 10
11 Fixed and variable costs Total output depends on fixed inputs and variable inputs Total cost consists of fixed costs (from fixed inputs) and variable costs (from variable inputs) 11
12 Fixed costs and variable costs Which costs are fixed and which variable depends on the time horizon In the short run, most costs are fixed In the long run, all costs are variable 12
13 Fixed costs and sunk costs Fixed and sunk costs are often confounded Fixed cost: Cost independent of the level of output, to be paid only if production takes place Sunk cost: Cost independent of the level of output, paid even if production does not take place 13
14 Average and marginal costs Marginal cost (MgC): It is the additional cost from producing one more unit of output Fixed costs do not influence the marginal cost: MgC = ΔC Δq = ΔVC Δq 14
15 Average and marginal costs Average cost (AC) It is the total cost per unit of output AC = C q = VC q + FC q 15
16 Short run marginal cost If labor is the only variable input in the short run and wage is w, then VC = wl MgC = w ΔL Δq = w 1 MgP L The MgC increases as the MgP of labor decreases 16
17 Short run cost curves q F(K,L) In the short run capital is fixed L 17
18 Short run cost curves q f (L) In the short run capital is fixed L 18
19 Short run cost curves q,l f 1 (q) f (L) The inverse of the short run production function gives the short run cost function L,q 19
20 Short run cost curves L f 1 (q) The inverse of the short run production function gives the short run cost function q 20
21 Short run cost curves cost w f 1 (q) The inverse of the short run production function gives the short run cost function q 21
22 Short run cost curves cost VC The total cost curve includes the fixed costs FC q 22
23 Short run cost curves cost VC When AC>MgC the AC decreases MgC AC q q 23
24 Short run cost curves cost VC AC MgC When AC<MgC the AC increases q q 24
25 Short run cost curves cost VC MgC When AC>MgC the AC attains its minimum AC q* q 25
26 Short run cost curves When MgC < AC, then AC decreases When MgC > AC, then AC increases When MgC = AC, then AC attains its minimum 26
27 Short run cost curves cost AVC AC MgC q q* q output 27
28 Short run and long run In the short run some costs are fixed, e.g. from the use of capital In the long run there is no fixed costs Both capital and labor are variable inputs 28
29 Cost minimization The firm chooses the combination of inputs that allows to produced any given level of output at the minimum cost Assume Two inputs: labor (L) and capital (K) Price of labor : the wage w Price of capital r = depreciation rate + interest rate r = rental cost (they coincide if capital markets are competitive) 29
30 Cost minimization The isocost line It contains all the combinations of L and K with the same cost C = wl + rk There is one for each possible level of cost C The slope -(w/r) is the rate at which labor can be replaced by capital without changing the cost 30
31 Cost minimization capital K 2 K 1 A Output Q 1 can be obtained through K 2,L 2 or K 3,L 3 but at a higher cost than the minimum throuhg K 1,L 1 on the isocost line C 1 K 3 Q 1 L 2 L 1 C 0 C 1 C 2 labor L 3 31
32 Inputs substitution When the wage w changes, the slope -(w/r) of the isocost lines changes too In particular, a more expensive labor is replaced by more capital 32
33 Inputs substitution capital If labor costs increase, the slope of the isocost line increases K 2 B The new combination of inputs uses less labor and more capital K 1 A Q 1 C 2 C 1 L 2 L 1 labor 33
34 Cost minimization The minimization of costs is characterized by the tangency of the isocot line and the isoquant TRMS = ΔK ΔL = - MgP L MgP K slope of the isocost lines = - w r MgP L MgP K = w r when the cost is minimized 34
35 Cost minimization MgP L w = MgP K r At the combination of inputs that minimizes costs, one additional euro in capital is as productive as one additional euro in labor 35
36 Cost minimization Example: let w = 10, r = 2, and MgP L = MgP K. Is the firm minimizing costs? One less unit of labor decreases q in MgP L units, and decreases costs in 10 One more unit of capital increases q in PMg K units and increases costs in 2 Since MgP L = MgP K output does not change but costs decreases in 8 = 10-2 The firm has incentives to replace labor with capital Decreasing labor increases MgP L Increasing capital decreases MgP K The firm will replace labor with capital until: MgP L w = MgP K r 36
37 Cost minimization For any given input prices w and r, for each level of output q the re is an isocost line that minimizes costs The expansion path draws the bundles of inputs the minimize costs at each level of output 37
38 The expansion path capital r= 20 and w= 10 the expansion path gives the bundles of inputs that produce each q at a minimum cost given the input prices B C Expansion path A 200 Units 300 Units labor 38
39 The expansion path The expansion path determines the long run total cost curve: For any given w and r, the tangency of an isocost and an isoquant gives the minimum cost of producing the output of the isoquant The total cost curve graphs the combinations of output and cost thus obtained 39
40 Long run cost curves Long run average cost 1. With increasing returns to scale: As inputs double, output more than doubles Average cost decreases 3. With decreasing returns to scale: As inputs double, output less than doubles Average cost increases 40
41 Long run cost curves If returns to scale are first increasing and then decreasing, then the average cost curve AC is U -shaped The shape in U is a consequence of the returns to scale of all factors and not of decreasing marginal returns as in the short run 41
42 Long run cost curves When AC decreases, MgC < AC When AC increases, MgC > AC therefore, the long run MgC curve is U- shaped too when returns to scale are first increasing and then decreasing MgC = AC at the minimum of AC 42
43 Long run cost curves cost MgC AC A output 43
44 Long run cost curves When the proportions of inputs change with the level of output, the expansion path is not a straight line We cannot rely on the returns to scale to obtain the form of the cost curves We have to use the notion of economies of scale 44
45 Economies of scale Average cots AC decreases first as output increases because 1. Workers specialize 2. Production is organized more efficiently 3. The firm can obtain better prices for inputs 45
46 Economies of scale Average cost AC eventually increases becases 1. The organization of production can become very complex 2. A strong demand for inputs will increase their prices 46
47 Economies of scale There can be Economies of scale As output doubles, cost les than doubles Diseconomies of scale As output doubles, cost more than doubles 47
48 Constant economies of scale cost 3000 F Total cost 2000 E 1000 D output 48
49 Economies of scale cost 3000 F Total cost 2000 E Economies of scale 1000 D output 49
50 Economies of scale cost Diseconomies of scale 3000 F Proportional cost 2000 E Economies of scale 1000 D output 50
51 Economies of scale The economies of scale are measured by the elasticity E C of cost with respect to output E C is the increase (in percentage terms) in the cost induced by an increase of output of 1% = MgC AC 51
52 Economies of scale if E C = 1, then MgC = AC Costs are proportional to output No economies or diseconomies of scale: constant economies of scale E C < 1 when MgC < AC Economies of scale MgC and AC are decreasing E C > 1 when MgC > AC Diseconomies of scale MgC and AC are increasing 52
53 Economies of scale A U-shaped long run AC curve represents Economies of scale at low levels of output Diseconomies of scale at high levels of output 53
54 Long run cost curves cost MgC AC A output 54
55 Long run cost curves capital E C In the long run output can increase from Q 1 to Q 2 with a smaller increase in the cost than in the short run A Long run expansion path K 2 K 1 P Short run Expansion path Q 2 Q 1 L 1 L 2 B L 3 D F labor 55
56 Long and short run cost curves cost Mg 1C AC 1 q output 56
57 Long and short run cost curves cost Mg 1C MgC 2 AC 1 AC 2 q output 57
58 Long and short run cost curves cost MgC 1 MgC 2 MgC 3 AC 1 AC 2 AC 3 AC LT q q* q output 58
59 Long and short run cost curves In the long run the firm can change K The long run AC curve is the lower envelope to all short run AC curves It gives the minimum average cost of producing each level of output 59
60 Long and short run cost curves In the long run the firm chooses the size (K) that minimizes AC for the chosen level of output The long run AC curve shows Economies of scale at low levels of output Diseconomies of scale at high levels of output The long run MgC curve satisfies MgC<AC when long run AC decreases satisfies MgC>AC when long run AC increases satisfies MgC=AC at the minimum long run AC 60
61 Long and short run cost curves cost MgC LT MgC 1 MgC 2 MgC 3 AC 1 AC 2 AC 3 AC LT q q* q output 61
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