chapter 5 - fin 321

the marginal rate of technical substitution is equal to the ratio of marginal products

-MPL/MPK = change in K / change in L

the law of diminishing marginal returns determines the shape of the marginal product of labor curves

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

Properties of Isoquants

-the farther an isoquant from the origin, the greater is the level of output -do not corsss -slope downward

Varying Returns to Scale

Many production functions have increasing returns to scale for small amounts of output, constant returns for moderate amounts of output, and decreasing returns for large amounts of output.

average product of labor

Q/L ratio of output to the amount of labor used to produce that output

if inputs can be substituted imperfectly, isoquants are

convex to the origin

a production function shows only ________________ because it gives the maximum output

efficient production processes

if inputs are perfect substitutes

isoquants are straight lines

capital (K)

land, buildings, equipment

the average product curve reaches its peak where the

marginal product and average product are equal

the production function summarizes ways

maximum quantity of output can be produced with different combinations of inputs, given current knowledge about technology and organization

organizational innovations (new way of organizing)

may also alter the production function and increase the amount of output produced by a given amount of inputs

Materials (M)

natural resources, raw materials, and processed products

technological progress is ----- if more output is produced using the same ratio of inputs

neutral

technological process is _______ if it is capital or labor saving

nonneutral

long run

period of time that all relevant inputs can be varied inputs are all variables

production function for a firm that uses only labor and capital:

q = f(L,K) q units of output L units of labor K units of capital

if inputs can be substituted at all, so inputs must be used in fixed proportions, isoquants are

right angles

if the marginal product curve is above the average product of curve, the average product must

rise with extra labor

Isoquants

shows the efficient combinations of labor and capital that can produce the same (iso) level of output (quantity)

labor (L)

skilled and less-skilled workers

If the firm continues to grow, the owner starts having difficulty managing everyone,

so the firm suffers from decreasing returns to scale.

When a firm is small, increasing labor and capital allows for gains from cooperation between workers and greater

specialization of workers and equipment, so there are increasing returns to scale

in the context of a production process with only capital and labor as inputs, we assume

that capital is fixed and labor is variable

constant return to scale (CRS)

doubling inputs exactly doubles the output f(2L,2K) = 2f(L,K) = 2q

increasing returns to scale (IRS)

doubling inputs more than doubles the output. f(2L, 2K) > 2f(L,K) = 2q

the total production function

A numerical or mathematical expression of a relationship between inputs and outputs. It shows units of total product as a function of units of inputs.

short run:

a period of time where at least one factor of production cannot be varied. inputs can be fixed or variables

output

a service such as an automobile tune-up by a mechanic, or a physical product such as a computer chip or a potato chip

inputs (KLM)

capital labor materials

marginal product of labor (MPL)

change in quantity / change in labor change in total output resulting from using an extra unit of labor, holding other factors (capital constant)

process innovation

changes the production function: more output to be produced with the same level of inputs (technological progress)

decreasing returns to scare (DRS)

decreasing returns to scale if doubling inputs less than doubles output f(2L,2K) < 2f(L,K) = 2q

if the marginal product is below the average product, the the average product must

fall with extra labor

marginal rate of technical substitution (MRTS)

how many units of capital the firm can replace with an extra unit of labor when holding output constajt -slope of the isoquant change in K/ change in L

the 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

production function

inputs -> production function -> output

a firm uses a technology or production process to transform

inputs or factors of production into outputs

in the long run, labor L and capital K are variable

the firm can substitute one input for another while continuing to produce the same level of output

As the firm grows, returns to scale are eventually exhausted. There are no more returns to specialization, so

the production process has constant returns to scale.