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.
