THE DISCOVERY OF PRODUCTION AND ITS TECHNOLOGY CHAPTER 8

DISCOVERING PRODUCTION Primitive society Fruit and land Accidental discovery: jam Opportunity cost Cost of engaging in any activity Opportunity forgone - particular activity Normal profit Just sufficient to recover opportunity cost Extra-normal profit Return above normal profit 2

PRODUCTION FUNCTION AND TECHNOLOGY Technology Set of technological constraints On production Combine inputs into outputs 3

PRODUCTION FUNCTION AND TECHNOLOGY No free lunch assumption Production process Need inputs to produce outputs Non reversibility assumption Cannot run a production process in reverse Free disposability assumption Combination of inputs Certain output Or strictly less output 4

PRODUCTION FUNCTION AND TECHNOLOGY Additivity assumption Produce output x One combination of inputs Produce output y Another combination of inputs Feasible: produce x+y 5

PRODUCTION FUNCTION AND TECHNOLOGY Divisibility assumption Feasible input combination y Then, λy – feasible input combination 0≤ λ ≤ 1 6

PRODUCTION FUNCTION AND TECHNOLOGY Convexity assumption Production activity: y Output: z Particular amounts of inputs Production activity: w Output: z Different amounts of inputs Produce: at least z Mix activities y (λ time) and w(1- λ time) 7

PRODUCTION FUNCTION AND TECHNOLOGY Production function Maximum amount of output Given a certain level of inputs Output= f (input 1, input 2 ) Marginal product of input 1 the increase in output as a result of a marginal increase in input 1 holding input 2 constant diminishing 8

ISOQUANT Isoquant Set of bundles Given production function Produce same output Most efficiently

ISOQUANT 10 All combinations of inputs along the same isoquant yield the same output. Labor 0 Capital I 100 II 200 III

ISOQUANT Isoquants Never cross each other Farther from the origin greater outputs Slope Marginal rate of technical substitution 11

MARGINAL RATE OF TECHNICAL SUBSTITUTION 12 The absolute value of the isoquant’s slope measures the rate at which one input can be substituted for the other while keeping the output level constant. Labor ( x 1 ) 0 Capital ( x 2 ) 4 7 α β

MARGINAL RATE OF TECHNICAL SUBSTITUTION Marginal rate of technical substitution (MRTS) Rate of substitution One input for another Constant output 13

THE PRODUCTION FUNCTION 14 The level of output is a function of the levels of capital and labor used. Capital ( x 2 ) 2 1 Labor ( x 1 ) 0 36 W W Output ( y ) 4 y1y1 y2y2

MARGINAL RATE OF TECHNICAL SUBSTITUTION Marginal product of input x 2 at point α MRTS of x 2 for x 1 at point α 15

DESCRIBING TECHNOLOGIES Returns to scale – ratio of Change in output Proportionate change in all inputs Constant returns to scale All inputs - increase by λ Output - increases by λ 16

DESCRIBING TECHNOLOGIES Increasing returns to scale All inputs - increase by λ Output - increases by more than λ Decreasing returns to scale All inputs - increase by λ Output - increases by less than λ Elasticity of substitution Substitute one input for another Given level of output 17

RETURNS TO SCALE 18 Constant returns to scale. Doubling the levels of labor (from 3 to 6) and capital (from 2 to 4) also doubles the level of output (from 4 to 8) Labor ( x 1 ) 0 Capital ( x 2 ) C A 8 B D p1p1 p2p2 (a) Increasing returns to scale. Doubling the levels of both inputs more than doubles the output level Labor ( x 1 ) 0 Capital ( x 2 ) A 10 B p1p1 (b) Decreasing returns to scale. Doubling the levels of both inputs less than doubles the output level Labor ( x 1 ) 0 Capital ( x 2 ) A 6 B p1p1 (c)

TIME CONSTRAINTS Immediate run Period of time Cannot vary inputs Fixed factor of production Cannot be adjusted Given period of time Variable factor of production Can be adjusted 19

TIME CONSTRAINTS Short run Time period At least one factor of production – fixed Long run Time period All factors of production – variable 20

TIME CONSTRAINTS Long-run production function All inputs – variable Short-run production function Some inputs – variable Capital – fixed Labor – variable 21

FIGURE 8.5 Short-run production function 22 With the level of capital fixed at x 2, the output level is a function solely of the level of labor. Capital ( x 2 ) Labor ( x 1 ) 0 C B x2x2

TIME CONSTRAINTS Total product curve Amount of output Add more and more units of variable input Hold one input constant Output – as we add more variable input First: increase at increasing rate After a point: Increase at decreasing rate Later: decrease 23

FIGURE 8.6 Short-run production function in labor-output space 24 The level of the fixed input, capital, is suppressed. Labor 0 Output 8 30 D G 10 E 1 A

TIME CONSTRAINTS Decreasing returns to factor Rate of output growth: decreasing Increase one input Other inputs – constant Marginal product curve Marginal product Factor of production 25

FIGURE 8.7 Marginal product 26 The slope of the short-run production function measures the change in the output level resulting from the introduction of 1 additional unit of the variable input - labor. Labor ( x 1 ) 0 Marginal product e d

THE PRODUCTION FUNCTION Cobb-Douglas production function Q=AK α L β A – positive constant 0<α<1; 0<β<1 K – amount of capital L – amount of labor Q – output 27

THE PRODUCTION FUNCTION Returns to scale = (α+β) For λ K and λL: Q’= A(λK) α (λL) β =λ α+β Q If α+β=1 Linearly homogeneous Constant returns to scale Q=AK α L 1-α If α+β>1 Increasing returns to scale If α+β<1 Decreasing returns to scale 28

THE PRODUCTION FUNCTION MRTS: dQ=0 Elasticity of substitution 29

THE PRODUCTION FUNCTION Q=AK α L β ; α+β=1 30

THE PRODUCTION FUNCTION Q=AK α L β ; α+β=1 Share of capital in output: K∙MPK/Q=α Share of labor in output: L∙MPL/Q=1-α Elasticity of output 31