Chapter 6 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.

The Ownership and Management of Firms Firm - an organization that converts inputs such as labor, materials, energy, and capital into outputs, the goods and services that it sells.

Private, Public, and Nonprofit Firms (For-profit) Private sector – firms owned by individuals or other nongovernmental entities and whose owners try to earn a profit. Public sector – firms and organizations that are owned by governments or government agencies. Nonprofit or not-for-profit sector – organizations neither government-owned nor intended to earn a profit.

Ownership of For-Profit Firms Sole proprietorships are firms owned and run by a single individual. General partnerships (partnerships) are businesses jointly owned and controlled by two or more people. Corporations are owned by shareholders in proportion to the numbers of shares of stock they hold. Owners have limited liability - Personal assets of corporate owners cannot be taken to pay a corporation’s debts even if it goes into bankruptcy.

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

What Owners Want? (cont.) To maximize profit a firm must produce as efficiently as possible. A firm engages in efficient production (achieves technological efficiency) if it cannot produce its current level of output with fewer inputs, given existing knowledge about technology and the organization of production.

Production A firm uses a technology or production process to transform inputs or factors of production into outputs. Capital (K) - long-lived inputs. land, buildings (factories, stores), and equipment (machines, trucks). Labor (L) - human services. 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).

Production Function 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.

Production Function (cont.) q = f(L, K) Inputs (L, K) Output q Formally, q = f(L, K) where q units of output are produced using L units of labor services and K units of capital (the number of conveyor belts).

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. Fixed input - a factor of production that cannot be varied practically in the short run. 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.

Short-Run Production In the short run, the firm’s production function is q = f(L, K) where q is output, L is workers, and K is the fixed number of units of capital.

Table 6.1 Total Product, Marginal Product, and Average Product of Labor with Fixed Capital

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.

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:

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:

Figure 6.1 Production Relationships with Variable Labor 110 Output, q, Units per day 90 B 56 A Diminishing Marginal Returns sets in! 4 6 11 L, Workers per day (b) L a MP 20 , L AP b 15 Average product, APL Marginal product, MPL c 4 6 11 L, Workers per day

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. That is, if only one input is increased, the marginal product of that input will diminish eventually.

Long-Run Production In the long run both labor and capital are variable inputs. It is possible to substitute one input for the other while holding output constant.

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).

Table 6.2 Output Produced with Two Variable Inputs

Figure 6.2 Family of Isoquants , Units of capital per d K b 3 e c f 2 q = 35 d 1 q = 24 q = 14 1 2 3 6 L , W o r k ers per d a y

Properties of Isoquants The farther an isoquant is from the origin, the greater the level of output. Isoquants do not cross. Isoquants slope downward

Figure 6.3(a) and (b) Substitutability of Inputs

Figure 6.3(c) Substitutability of Inputs

Application: A Semiconductor Integrated Circuit Isoquant

Substituting Inputs 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!

Figure 6.4 How the Marginal Rate of Technical Substitution Varies Along an Isoquant TS in a P r inting and Pu b lishing U . S . Fi r m y a a 16 , Units of capital per d D K = –6 b 10 D L = 1 K –3 1 c 7 –2 d 1 5 e –1 4 1 q = 10 1 2 3 4 5 6 7 8 9 10 L , W o r k ers per d a y

Substitutability of Inputs and Marginal Products Along an isoquant Dq = 0, or: (MPL x ΔL) + (MPK x ΔK) = 0. or Extra units of labor Extra units of capital Increase in q per extra unit of labor Increase in q per extra unit of capital MPL DL - = - = MRTS MPK DK

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?

Returns to Scale How much does output change if a firm increases all its inputs proportionately?

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(2L, 2K) = 2f(L, K).

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(2L, 2K) > 2f(L, K).

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(2L, 2K) < 2f(L, K).

The Cobb-Douglas Production Function It is one the most widely estimated production functions. q = ALaKb g=a+b determines the returns to scale.

Solved Problem 6.2 Under what conditions does a Cobb-Douglas production function (Equation 6.4, q = ALaKb) exhibit decreasing, constant, or increasing returns to scale?

Application: Returns to Scale in U.S. Manufacturing

Application: Returns to Scale in U.S. Manufacturing

Application: Returns to Scale in U.S. Manufacturing

Figure 6.5 Varying Scale Economies

Productivity and Technical Change Productivity may differ across firms – produce different amounts of output with a given amount of inputs. After a technical or managerial innovation, a firm can produce more today from a given amount of inputs than it could in the past.

Innovations Technical progress - an advance in knowledge that allows more output to be produced with the same level of inputs. Better management or organization of the production process similarly allows the firm to produce more output from given levels of inputs.

Innovations (cont.) Neutral technical change – a firm can produce more output using the same ratio of inputs.

Table 6.3 Annual Percentage Rates of Neutral Productivity Growth for Computer and Related Capital Goods