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Microeconomics: Production Theory and Technical Constraints

This text explores producer theory in microeconomics, focusing on the model that explains and predicts producer behavior. It covers technical constraints, production functions, average and marginal products, laws of production, and the concept of technical substitution.

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Microeconomics: Production Theory and Technical Constraints

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  1. UNIVERSIDAD COMPLUTENSE DE MADRIDDepartamento de Fundamentos del Análisis Económico I Microeconomics: Production Rafael Salas 2nd term 2014-2015

  2. Objective Producer theory: to build a model to explain and predict producer behavior. Producer face an economic problem: to use inputs to obtain output, we are interested in how they solve the problem.

  3. Model We typically assume firms maximize profits or minimize costs subject to some constraints Constraints: 1. Technical constraints: “The state of the arts” are measurable by the production function 2. Economic constraints: limited resources; prices of inputs and output. Monetary costs and opportunity costs 3. Institutional constraints: the market the firm is in; specific legal aspects like taxes, subsidies, etc.

  4. Technical restrictions 1. Production function Firms transform inputs (or factors) into output or (products). Production functions represent the technical relationship between input and outputs. It represent the technology. It incorporates all production processes (methods) that are technically efficient (see below) Inputs and output are physical variables (Tons, etc.) and flows variable (in a year, in a month)

  5. Technical restrictions 1. Production process (method, technique) It is a combination of inputs required to attain a certain level of output. A production process “A” is technically efficient relative to another process “B”, if A uses less units of at least one input and no more from other input as compared with process B to produce a given level of output. Production functions only consider technically efficient production processes.

  6. Examples • To produce x=1, wehavethreeprocesses P1 uses L=2 and K=3 P2 uses L=3 and K=2 P3 uses L=1 and K=4 • To produce x=1, wehavetwoprocesses A uses L=2 and K=3 B uses L=3 and K=3 • To produce x=1, wehavetwoprocesses C uses L=2 and K=3 D uses L=1 and K=4

  7. Technical restrictions Assumption: output and inputs are perfect divisible Production functions are represented by a function of inputs q=F(L,K,E,…) It indicates the maximum quantity of output attainable for all possible combinations of inputs (because it incorporates only technically efficient processes) It describes the laws of production (see later on)

  8. Productionfunctions • It can be represented by a map of isoquants • An isoquant includes all the technically efficient methods (or all the combinations of inputs) for producing a given level of output • Examples: draw isoquants for q=40 from • q=10L+20K • q=LK It implies some input substitutability (see below)

  9. Short-run and Long-runproduction • Different properties according we are in: • The short-run: some input are fixed • Long-run: all inputs are variable

  10. Short-run production • Assume two inputs capital and labor. • Capital is typically fixed • We ask about how output changes as labor varies. • We draw a two-dimensional graph between output and labor, for a given level of capital.

  11. Average and Marginal Products • Average product (productivity) APL= q/L • Marginal product (productivity) MPL= dq/dL Graphically: • Average product is the slope of the slope running from the origin to the corresponding point in the production function • Marginal product is the slope of the production function

  12. Table 6.1 L K q q/L dq/dL 0 10 0 1 10 10 2 10 30 3 10 60 4 10 80 5 10 95 6 10 108 7 10 112 8 10 112 9 10 108 10 10 100

  13. GraphfromTable 6.1

  14. Average and Marginal Products L K q q/L dq/dL 0 10 0 - - 1 10 10 10 10 2 10 30 15 20 3 10 60 4 10 80 5 10 95 6 10 108 7 10 112 8 10 112 9 10 108 10 10 100

  15. Average and Marginal Products 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 8 10 112 14 0 9 10 108 12 -4 10 10 100 10 -8

  16. GraphfromTable 6.1

  17. Laws of production in the short-run • Law of diminishing marginal returns states that: in all productive activities, adding more of the variable factor, while holding all other constant, will at some point decrease the marginal productivity (as in the example above, from x=3 onwards)

  18. Long-run production • Assume two inputs capital and labor. • Capital is also variable • We ask about how output changes when both inputs vary. • We draw a two-dimensional graph between capital and labor, and output is drawn as a set of isoquants (contour lines)

  19. Long-run production • Isoquants are decreasing if they incorporates only technically efficient production processes • We get different shapes of isoquants (and therefore of production functions) depending on the degree of substitutability of factors. The degree of substitutability is linked with the curvature of the isoquants…

  20. Marginal Rate of Technical Substitution (MRTS) • One way to describe the degree of substitutability is by defining the MRTS: • MRTS=-dK/dL=MPL/MPK • MRTS means the number of K needed to be reduced if 1 unit of labor is increased to keep output constant • Apart from the extreme cases (perfect substitutes and complements), isoquants and downward sloping and strictly convex. It means decreasing MRTS as labor increases (capital becomes relatively more productive as more labor replaces capital to keep output constant)

  21. Different productionfunctions • We get different shapes of isoquants (and therefore of production functions) depending on the degree of substitutability of factors: • Linear isoquants (perfect substitutes) • Smooth strictly-convex isoquants • Right-angle isoquants (fixed-proportions production). No substitutability. Just one process. They have different properties. Draw them graphically

  22. Laws of production in the long-run • The laws of returns to scale: what would it happen to output if all factorsare changed by the same proportion. 3 cases: • Increasing Returns to scale (output increases more than proportionally) • Constant Returns to Scale (output increases proportionally) • Decreasing Returns to Scale scale (output increases less than proportionally) • Draw them graphically

  23. Exercises • 3, 4, 5 of page 219 of the textbook • 8, 9 and 10 page 220 of the textbook

  24. UNIVERSIDAD COMPLUTENSE DE MADRIDDepartamento de Fundamentos del Análisis Económico I Microeconomics II: Production Rafael Salas 2nd term 2014-2015

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