Chapter 9ProductionChapter OutlineThe Production
FunctionProduction In The Short RunProduction In The Long
RunReturns To Scale9-2Figure 9.2: The Production Function
9-3Production function: the relationship that describes how inputs
like capital and labor are transformed into output.athematicall!"Q#
F $K" L%& #CapitalL # Labor'(ol(ing state of technolog!The
Production Function time Long run: the shortest period of time
re)uired to alter the amounts of all inputs used in a production
process. Q# F $K" L%" L * & are variableShort run: the longest
period of time during which at least one of the inputs used in a
production process cannot be (aried. Q# F $L%" K is +,ed but Lis
(ariable.Variable input: an input that can be (aried in the short
run -L.Fixed input: an input that cannot (ar! in the short
run-&.9-4Figure 9.3: A Specifc Short-un Production Function
9-5Short/run Production FunctionThree properties01.It passes
through the origin2.Initiall! the addition of (ariable inputs
augments output an increasing rate3.be!ond some point additional
units of the (ariable input gi(e rise to smaller and smaller
increments in output. Assume: K= K0 = 1Figure 9.!: Another Short-un
Production Function9-6Short-run Production FunctionLaw of
diminishing returns: if other inputs are +,ed" the increase in
output from an increase in the (ariable input must e(entuall!
decline.Figure 9.": The #$ect o% Technological Progre&& in
Food Production9-7Increase in technological
progress(1808)(2008)Figure 9.': The (arginal Product o% a )aria*le
+nput 9-8Short-run Production FunctionTotal product curve: a cur(e
showing the amount of output as a function of the amount of
(ariable input $4%.Marginal product: change in total product due to
a 1/unit change in the (ariable input0 PL # 5TPL65L# 5465LAverage
product: total output di(ided b! the )uantit! of the (ariable
input0 7PL #TPL6L# 46L,or-ed Out Pro*lem .a%ter Slide
/"012ue&tion: Suppose that at a +rm8s current le(el of
production the marginal product of capital is e)ual to 19 units"
while the marginal rate of technical substitution between capital
and labor is 2. :i(en this" we know the marginal product of labor
must be03e407.ero" and the a(erage and marginal product
intersect.3e40 ake sure the a(erage product peaks at the output
where the ra! from the origin is tangent to the total product cur(e
and where the marginal product passes through it. The marginal
product must peak at the output where the in?ectionpoint is on the
total product cur(e" and the marginal product reaches >ero when
the total product peaks. Peak of 7PL$should be here%9-13so!uant"
the set of all input combinations that !ield a gi(en le(el of
output.Marginal rate of technical substitution #M$TS%: the rate at
which one input can be e,changed for another without altering the
total level of output.Production +n The :ong un,or-ed
Pro*lem2ue&tion0 7 dail! production function for calculators is
4 # 12L2/ L3. Show all !our work for the following )uestions. a%
@hat is the marginal product e)uation for laborAb% @hat is the 7PL
functionA3e40a%d46dL # PL# 2BL / 3L2b% 46L# 7PL# $12L2 C L3%6L #
12L C L2Figure 9.D0 Part of an Iso)uant ap for the Production
Function9-15Figure 9.;: Part o% an +&o
