Chapter Six Firms and Production Topics The Ownership

Chapter Six Firms and Production

Topics § The Ownership and Management of Firms. § Production. § Short-Run Production: One Variable and One Fixed Input. § Long-Run Production: Two Variable Inputs. § Returns to Scale. § Productivity and Technical Change. © 2009 Pearson Addison-Wesley. All rights reserved. 2

What is a firm? § Firm - an organization that converts inputs such as labor, materials, energy, and capital into outputs, the goods and services that it sells. w Sole proprietorships are firms owned and run by a single individual. w Partnerships are businesses jointly owned and controlled by two or more people. w Corporations are owned by shareholders in proportion to the numbers of shares of stock they hold. © 2009 Pearson Addison-Wesley. All rights reserved. 3

What Owners Want? § Main assumption: firm’s owners try to maximize profit! § Profit (p) - the difference between revenues, R, and costs, C: p = R – C © 2009 Pearson Addison-Wesley. All rights reserved. 4

What are the categories of inputs? § Capital (K) - long-lived inputs. w land, buildings (factories, stores), and equipment (machines, trucks) § Labor (L) - human services w managers, skilled workers (architects, economists, engineers, plumbers), and less-skilled workers (custodians, construction laborers, assembly-line workers) § Materials (M) - raw goods (oil, water, wheat) and processed products (aluminum, plastic, paper, steel) © 2009 Pearson Addison-Wesley. All rights reserved. 5

How firms combine the inputs? § Production function - the relationship between the quantities of inputs used and the maximum quantity of output that can be produced, given current knowledge about technology and organization © 2009 Pearson Addison-Wesley. All rights reserved. 6

Production Function q = f(L, K) Inputs (L, K) Output q § Formally, q = f(L, K) w where q units of output are produced using L units of labor services and K units of capital (the number of conveyor belts). © 2009 Pearson Addison-Wesley. All rights reserved. 7

Time and the Variability of Inputs § Short run - a period of time so brief that at least one factor of production cannot be varied practically w Fixed input - a factor of production that cannot be varied practically in the short run. w Variable input - a factor of production whose quantity can be changed readily by the firm during the relevant time period § Long run - a lengthy enough period of time that all inputs can be varied © 2009 Pearson Addison-Wesley. All rights reserved. 8

Short-Run Production § In the short run, the firm’s production function is q = f(L, K) w where q is output, L is workers, and K is the fixed number of units of capital. © 2009 Pearson Addison-Wesley. All rights reserved. 9

Table 6. 1 Total Product, Marginal Product, and Average Product of Labor with Fixed Capital © 2009 Pearson Addison-Wesley. All rights reserved. 10

Marginal Product of Labor § Marginal product of labor (MPL ) - the change in total output, Dq, resulting from using an extra unit of labor, DL, holding other factors constant: © 2009 Pearson Addison-Wesley. All rights reserved. 11

Average Product of Labor § Average product of labor (APL ) - the ratio of output, q, to the number of workers, L, used to produce that output: © 2009 Pearson Addison-Wesley. All rights reserved. 12

Total Product of Labor § Total product of labor- the amount of output (or total product) that can be produced by a given amount of labor © 2009 Pearson Addison-Wesley. All rights reserved. 13

Diminishing Marginal Returns sets in! Output, q, Units per day (a) C 110 90 B 56 0 A 4 6 11 L, Workers per day (b) APL, MPL Figure 6. 1 Production Relationships with Variable Labor a 20 b 15 Average product, AP L Marginal product, MP L c 0 4 6 11 L, Workers per day © 2009 Pearson Addison-Wesley. All rights reserved. 14

Law of Diminishing Marginal Returns If a firm keeps increasing an input, holding all other inputs and technology constant, the corresponding increases in output will become smaller eventually. w That is, if only one input is increased, the marginal product of that input will diminish eventually. © 2009 Pearson Addison-Wesley. All rights reserved. 15

Isoquants § Isoquant - a curve that shows the efficient combinations of labor and capital that can produce a single (iso) level of output (quantity). § Equation for an Isoquant: q = f (L, K). © 2009 Pearson Addison-Wesley. All rights reserved. 16

Table 6. 2 Output Produced with Two Variable Inputs © 2009 Pearson Addison-Wesley. All rights reserved. 17

K, Units of capital per day Figure 6. 2 Family of Isoquants a 6 b 3 2 c e f q = 35 d 1 q = 24 q = 14 0 1 2 3 © 2009 Pearson Addison-Wesley. All rights reserved. 6 L, Workers per day 18

Properties of Isoquants. 1. The farther an isoquant is from the origin, the greater the level of output. 2. Isoquants do not cross. 3. Isoquants slope downward © 2009 Pearson Addison-Wesley. All rights reserved. 19

Figure 6. 3 a, b Substitutability of Inputs © 2009 Pearson Addison-Wesley. All rights reserved. 20

Figure 6. 3 c Substitutability of Inputs © 2009 Pearson Addison-Wesley. All rights reserved. 21

Application A Semiconductor Integrated Circuit Isoquant © 2009 Pearson Addison-Wesley. All rights reserved. 22

Marginal Rate of Technical Substitution § marginal rate of technical substitution (MRTS) - the number of extra units of one input needed to replace one unit of another input that enables a firm to keep the amount of output it produces constant Slope of Isoquant! © 2009 Pearson Addison-Wesley. All rights reserved. 23

Figure 6. 4 How the Marginal Rate of Technical Substitution Varies Along an Isoquant K, Units of capital per d ay MRTS in a Printing and Pu blishing U. S. Firm a 16 D K = – 6 b 10 DL = 1 – 3 c 1 – 2 1 7 5 4 d e – 1 q = 10 1 2 3 4 5 6 7 8 9 10 L, Workers per d ay © 2009 Pearson Addison-Wesley. All rights reserved. 24

Substitutability of Inputs and Marginal Products. § Along an Isoquant Dq = 0, or: Extra units of labor Extra units of capital (MPL x ΔL) + (MPK x ΔK) = 0. Increase in q per extra unit of labor w or Increase in q per extra unit of capital MPL DL =MPK DK © 2009 Pearson Addison-Wesley. All rights reserved. = MRTS 25

Solved Problem 6. 1 § Does the marginal rate of technical substitution vary along the isoquant for the firm that produced potato salad using Idaho and Maine potatoes? What is the MRTS at each point along the isoquant? © 2009 Pearson Addison-Wesley. All rights reserved. 26

Returns to Scale § Constant returns to scale (CRS) - property of a production function whereby when all inputs are increased by a certain percentage, output increases by that same percentage. f(2 L, 2 K) = 2 f(L, K). © 2009 Pearson Addison-Wesley. All rights reserved. 27

Returns to Scale (cont). § Increasing returns to scale (IRS) - property of a production function whereby output rises more than in proportion to an equal increase in all inputs f(2 L, 2 K) > 2 f(L, K). © 2009 Pearson Addison-Wesley. All rights reserved. 28

Returns to Scale (cont). § Decreasing returns to scale (DRS) - property of a production function whereby output increases less than in proportion to an equal percentage increase in all inputs f(2 L, 2 K) < 2 f(L, K). © 2009 Pearson Addison-Wesley. All rights reserved. 29

The Cobb-Douglas Production Function § It one is the most popular estimated functions. q = ALa. Kb © 2009 Pearson Addison-Wesley. All rights reserved. 30

Solved Problem 6. 2 § Under what conditions does a Cobb. Douglas production function exhibit decreasing, constant, or increasing returns to scale? © 2009 Pearson Addison-Wesley. All rights reserved. 31

Application: Returns to Scale in U. S. Manufacturing © 2009 Pearson Addison-Wesley. All rights reserved. 32

Application: Returns to Scale in U. S. Manufacturing © 2009 Pearson Addison-Wesley. All rights reserved. 33

Application: Returns to Scale in U. S. Manufacturing © 2009 Pearson Addison-Wesley. All rights reserved. 34

Figure 6. 5 Varying Scale Economies © 2009 Pearson Addison-Wesley. All rights reserved. 35

Table 6. 3 Annual Percentage Rates © 2009 Pearson Addison-Wesley. All rights reserved. 36

Innovations § Technical progress - an advance in knowledge that allows more output to be produced with the same level of inputs © 2009 Pearson Addison-Wesley. All rights reserved. 37