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Production ECO61 Microeconomic Analysis Udayan Roy Fall 2008 What is a firm? A firm is an organization that converts inputs such as labor, materials, energy, and capital into outputs, the goods and services that it sells. Sole proprietorships are firms owned and run by a single individual.

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production

Production

ECO61 Microeconomic Analysis

Udayan Roy

Fall 2008

what is a firm
What is a firm?
  • A firm isan organization that converts inputs such as labor, materials, energy, and capital into outputs, the goods and services that it sells.
    • Sole proprietorshipsare firms owned and run by a single individual.
    • Partnershipsare businesses jointly owned and controlled by two or more people.
    • Corporationsare owned by shareholders in proportion to the numbers of shares of stock they hold.
what owners want
What Owners Want?
  • Main assumption: firm’s owners try to maximize profit
  • Profit (p) isthe difference between revenues, R, and costs, C:

p = R– C

what are the categories of inputs
What are the categories of inputs?
  • 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)
how firms combine the inputs
How firms combine the inputs?
  • Production function is 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
Production Function

Production

Function

q = f(L, K)

  • Formally,

q = f(L, K)

    • where qunits of output are produced using Lunits of labor services and K units of capital (the number of conveyor belts).

Inputs

(L, K)

Output

q

the production function may be an algebraic formula
The production function may be an algebraic formula

Just plug in numbers for L and K to get Q.

marginal product 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
  • Average product of labor (APL) - the ratio of output, Q, to the number of workers, L, used to produce that output:
production with two variable inputs
Production with Two Variable Inputs
  • When a firm has more than one variable input it can produce a given amount of output with many different combinations of inputs
    • E.g., by substituting K for L

7-11

isoquants
Isoquants
  • An isoquant identifies all input combinations (bundles) that efficiently produce a given level of output
    • Note the close similarity to indifference curves
    • Can think of isoquants as contour lines for the “hill” created by the production function

7-12

family of isoquants

q

= 35

q

= 24

q

= 14

Family of Isoquants

y

a

a

6

, Units of capital per d

The production function above yields the isoquants on the left.

K

b

3

f

c

e

2

d

1

0

1

2

3

6

L

,

W

o

r

k

ers per d

a

y

properties of isoquants
Properties of Isoquants
  • Isoquants are thin
  • Do not slope upward
  • Two isoquants do not cross
  • Higher-output isoquants lie farther from the origin

7-15

substitution between inputs
Substitution Between Inputs
  • Rate that one input can be substituted for another is an important factor for managers in choosing best mix of inputs
  • Shape of isoquant captures information about input substitution
    • Points on an isoquant have same output but different input mix
    • Rate of substitution for labor with capital is equal to negative the slope

7-18

marginal rate of technical substitution
Marginal Rate of Technical Substitution
  • Marginal Rate of Technical Substitution for labor with capital (MRTSLK): the amount of capital needed to replace labor while keeping output unchanged, per unit of replaced labor
    • Let K be the amount of capital that can replace L units of labor in a way such that total output ― Q = F(L,K) ― is unchanged.
    • Then, MRTSLK = - K / L, and
    • K / L is the slope of the isoquant at the pre-change inputs bundle.
    • Therefore, MRTSLK = - slope of the isoquant
marginal rate of technical substitution19
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!

how the marginal rate of technical substitution varies along an isoquant

D

K

= –6

D

L

= 1

q

= 10

How the Marginal Rate of Technical Substitution Varies Along an Isoquant

M

R

TS

in a P

r

inting and Pu

b

lishing

U

.

S

.

Fi

r

m

y

a

a

16

, Units of capital per d

b

10

K

–3

c

1

7

d

–2

1

5

e

–1

4

1

0

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
Substitutability of Inputs and Marginal Products.
  • Along an isoquant output doesn’t change (Dq= 0), or:

(MPLx ΔL) + (MPKx 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

mrts and marginal product
MRTS and Marginal Product
  • Recall the relationship between MRS and marginal utility
  • Parallel relationship exists between MRTS and marginal product
  • The more productive labor is relative to capital, the more capital we must add to make up for any reduction in labor; the larger the MRTS

7-24

figure 7 13 declining mrts
Figure 7.13: Declining MRTS
  • We often assume that MRTSLK decreases as we increase L and decrease K
  • Why is this a reasonable assumption?

7-25

extreme production technologies
Extreme Production Technologies
  • Two inputs are perfect substitutes if their functions are identical
    • Firm is able to exchange one for another at a fixed rate
    • Each isoquant is a straight line, constant MRTS
  • Two inputs are perfect complements when
    • They must be used in fixed proportions
    • Isoquants are L-shaped

7-26

returns to scale30
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(2L, 2K) = 2f(L, K).

returns to scale cont
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(2L, 2K) > 2f(L, K).

returns to scale cont32
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(2L, 2K) < 2f(L, K).

productivity differences and technological change
Productivity Differences and Technological Change
  • A firm is more productive or has higher productivity when it can produce more output use the same amount of inputs
    • Its production function shifts upward at each combination of inputs
    • May be either general change in productivity of specifically linked to use of one input
  • Productivity improvement that leaves MRTS unchanged is factor-neutral

7-34

the cobb douglas production function
The Cobb-Douglas Production Function
  • It one is the most popular estimated functions.

q = ALaKb

cobb douglas production function
Cobb-Douglas Production Function
  • A shows firm’s general productivity level
  • a and b affect relative productivities of labor and capital
  • Substitution between inputs:

7-36