Production Microéconomie, chapter 6 1
List of subjets Production technology Production with a single input (labor) Isoquants Production with two inputs (labor and capital) Returns to scale 2
The production decision of the firm 1. It depends on the available technology How can inputs be transformed into outputs inputs: labor, capital, raw materials outputs: cars, furniture, books Different bundles or inputs deliver different amounts of outputs 3
The production decision of the firm 2. It depends also on the production costs The firm takes into account the prices of capital, labor, and other inputs The firm will produce, whatever she chooses, at a minimum cost given technology and the inputs prices If capital is much more expensive than labor, the firm can choose to produce the chosen level of output with more labor and less capital. 4
The production decision of the firm 3. The firm maximizes profits Given the minimum cost of producing any given level of output, the firm chooses the level of output that maximizes profits 5
The technology of production The production function: Gives the maximum output (q) the can be produced with each bundle of inputs Describes what is technologically feasible using inputs efficiently We will consider two inputs only: labor (L) and capital (K) 6
The technology of production The production function with two inputs: q = F(K,L) The level of output (q) depends on the amount of capital (K) and labor (L) used 7
The technology of production Short run and long run Adjusting the level of some inputs takes longer the for other inputs The firm must consider both which inputs to adjust and over what time horizon It needs to distinguish between short run and long run 8
The technology of production Short run At least one input is a fixed input Long run Horizon beyond which no input is fixed, all inputs are variable inputs 9
Production with one input In the short run only one input can be adjusted say capital is fixed and labor is variable Output can be increased increasing labor only 10
Production with one input L K q 0 10 0 1 10 10 2 10 30 3 10 60 4 10 80 5 10 95 6 10 108 7 10 112 Without labor output is zero The first units of labor are increasingly productive Additional units of labor are less and less productive 11
Production with one input The average productivity of labor measures the contribution, on average, of each unit of labor to producing output PM L = output labor = q L 12
Production with one input The marginal productivity of labor measures the contribution of an additional unit of labor to the production of output PMg L = Δoutput Δlabor = Δq ΔL 13
Production with one input L K q q/l dq/dl 0 10 0 - - 1 10 10 10 10 2 10 30 15 20 3 10 60 20 30 4 10 80 20 20 5 10 95 19 15 6 10 108 18 13 7 10 112 16 4 14
Production with one input output 112 D 80 C Total output 60 B 30 A 0 1 2 3 4 5 6 7 8 9 10 labor 15
Production with one input output 112 D 80 C Total output 60 B Marginal productivity at B 30 A Average productivity at B 0 1 2 3 4 5 6 7 8 9 10 labor 16
Production with one input In the previous example, As labor increases beyond 3 units, output increases less and less At low levels of L additional units allow for a better use of installed capital and thus the marginal productivity of labor is increasing At high levels of L additional units prevent from an efficient use of instaled capital and thus the marginal productivity of labor is decreasing 17
Law of decreasing marginal returns As a factor increases, while others remain fixed, the corresponding increases in output become beyond some point smaller and smaller 18
Law of decreasing marginal returns It is a consequence of some inputs being fixed in the short run assumes a constant capital stock The productivity of labor increases with the stock of capital assumes constant technology Technical progress increases the output that can be obtained from each combination of inputs The productivity of labor increases with technical progress 19
Capital accumulation output 112 D D A higher capital stock increases the level of output at each level of labor C C Increase in the stock of capital B B A A 0 1 2 3 4 5 6 7 8 9 10 labor 20
Technical progress D output 112 C D Technical progress increases the marginal and average productivity of labor at every level C Technical progress 60 B B A A 0 1 2 3 4 5 6 7 8 9 10 labor 21
Productivity of labor Wages (i.e. living standards) and productivity are directly linked When firms maximize profits, inputs are remunerated by their marginal productivity Wages can increase only if labor productivity increases Labor productivity increases if 1. the stock of capital increases 2. there is technological progress 22
Productivity of labor 23
Productivity of labor 1. The increase in the stock of capital was the main source of the increase in labor productivity 2. The postwar rate of growth of labor productivity in Europe was higher than in the US since the rate of capital accumulation was also higher, due to the reconstruction effort 24
Production with two inputs In the long run firms can produce a given level of output with different combinations of labor and capital 25
Production with two inputs labor capital 1 2 3 4 5 1 20 40 55 65 75 2 40 60 75 85 90 3 55 75 90 100 105 4 65 85 100 110 115 5 75 90 105 115 120 26
Production with two inputs Isoquants link all the inputs combinations that allow to produce a given level of output 27
Isoquants capital 5 4 3 A Example: 55 units of output can be produced both with 3K and 1L (pt. A) or 1K and 3L (pt. D) 2 q 3 = 90 1 D q 2 = 75 q 1 = 55 1 2 3 4 5 labor 28
Decreasing returns capital 5 4 For a given level of capital, labor has decreasing returns (A, B, C) 3 A B C 2 1 q 1 = 55 q 2 = 75 q 3 = 90 1 2 3 4 5 labor 29
Production with two inputs Decreasing returns of labor with a constant capital: If capital stays constant at 3 and labor increases 0 to 1, 2, and 3, then output increases at a decreasing rate (55, 20, 15) 30
Decreasing returns capital 5 4 Capital has decreasing returns, for a given level of labor (C, D, E) 3 C 2 1 D E q 1 = 55 q 2 = 75 q 3 = 90 1 2 3 4 5 labor 31
Production with two inputs Decreasing returns of capital with a constant labor: If labor stays constant at 3 and labor increases 0 to 1, 2, and 3, then output increases at a decreasing rate (55, 20, 15) 32
Production with two inputs Inputs substitution Firms can choose the combination of inputs to produce any given level of output A decrease in one input requires and increase in the other input to keep output constant 33
Production with two inputs Inputs substitution The slope of each isoquant is the rate at which inputs can be substituted at a given level of output The (absolute value of the) slope is the marginal rate of technical substitution (MRTS) It is the increase in one input needed to compensate a decrease in one unit of the other input in order to keep output constant 34
Production with two inputs Marginal rate of technical substitution: TMST = variation of capital variation of labor = ΔK ΔL (q constant) 35
Marginal rate of technical substitution capital 5 4 2 The MRTS decreases along the isoquant 3 1 1 2 1 1 2/3 1 Q 1 =55 Q 2 =75 Q 3 =90 1 2 3 4 5 labor 36
Production with two inputs As labor substitutes capital Labor becomes relatively less productive Capital becomes relativively more productive Less capital is needed to substitute one unit of labor at constant output The slope of the isoquant becomes smaller (in absolute value) 37
MRTS and decreasing marginal returns In the example, increasing labor from 1 to 4 decreases the MRTS from 2 to 1/3 The decrease in the MRTS is a consequence of the decreasing marginal returns of inputs Why? 38
MRTS and decreasing marginal returns Assume labor increases and capital decreases so that output remains constant The change in output due to the change in labor is: MgP L ΔL 39
MRTS and decreasing marginal returns Assume labor increases and capital decreases so that output remains constant The change in output due to the change in capital is: MgP K ΔK 40
MRTS and decreasing marginal returns Since output does not change, both changes must compensate, i.e. MgP L ΔL + MgP K ΔK = 0 MgP L MgP K = ΔL ΔK = MRTS 41
Isoquants: special cases Tow special cases of inputs substitution 1. Perfect substitutes The MRTS is constant 42
Isoquants: special cases capital A B Perfect substitutes Capital and labor substitute each other always at the same rate C Q 1 Q 2 Q 3 labor 43
Isoquants: special cases 2. Perfect complements Inputs must be used in fixed proportions There is no possible substitution between inputs 44
Isoquants: special cases capital Perfect complements capital and labor must be used always in the same proportions C Q 3 B Q 2 K 1 Q 1 A labor L 1 45
Returns to scale Its the rate at which output increases as inputs increase by a common factor Returns to scale can be Increasing constant decreasing 46
Increasing returns to scale Output increases more than proportionally than inputs when mass production is more efficient (e.g. cars) when a single supplier is more efficient (utilities, natural monopolies) 47
Increasing returns to scale capital A Output levels of the isoquants increase quickly 4 2 10 30 20 5 10 labor 48
Constant returns to scale Output increases in the same proportion than inputs 49
Constant returns to scale capital A 6 30 4 2 20 Output levels of the isoquants increase at a regular pace 10 5 10 15 labor 50
Decreasing returns to scale Output increases less than proportionally than inputs Efficiency decreases with the output level 51
Decreasing returns to scale capital A 4 20 Output levels of the isoquants increase slowly 2 10 10 5 labor 52