Lesson 1.3 - Production Theory (Chp 5) Flashcards
what’s the terms managers use to find the optimal way to produce?
production process
what does the production process explain
how scarce resources (inputs) are used to produce a good or service (output); shows max product output achieved from any specific set of inputs; shows tech available and constraints faced by managers
how does efficiently using inputs affect a firm?
minimizes costs and leads to maximizing profits
simplest case of the production process
one input is fixed, the other is variable
production function formula
Q = f(X1, X2)
what do we assume in the long run for the production function
all inputs are variable
what does Average product tell us?
output per worker; how many units of output on average each worker is responsible for making
formula for AP
AP = Q / X1 holding X2 constant
what does marginal product tell us
good measure of the efficiency of each worker; the incremental change in output created by a small change in use of the input; increase in output resulting from the last worker hired
formula for MP
MP = dQ/dX1 holding X2 constant if labour can be varied continuously or change in Q / change in L if labour is discrete; OR Q(L) - Q(L-1) for year 2 where L is year 2 and L-1 is year 1
explain MP and AP curves
eventually both reach a maximum and decrease as more labour is employed
what are the common units in the production function
labour is variable and X1 and capital is fixed and is X2
where does MP = AP
where AP is maximized, where slope of AP = 0
where is MP maximized with respect to AP
MP is maximized before AP
explain law of diminishing returns
if we keep adding increments of labour, eventually the incremental gains (i.e., the change in output for the change in labour used or the MP) get smaller, and eventually the extra labour is counterproductive
What happens to production function and the variables in the long run
both labour and capital are variable, for both variables we can find MP and AP
how do we graph the production function where 2 variables are variable?
quantity of variable x1 used on one axis and quantity of variable x2 used on the second axis. isoquants are drawn on the graph
explain an isoquant
a curve that shows all of the possible (efficient) input bundles capable of producing a given level of output
what does it mean when an isoquant is farther from the origin?
higher level of output it represents
what does each isoquant represent?
an infinite number of possible input combinations, given a continuous production function
shape of isoquants
downward and increasing slope
when are isoquants right angles
when production process uses inputs in fixed proportions, then no substitution is possible, perfect complements
when are isoquants straight lines drawn from one axis to the other?
if inputs are perfectly substitutable
what must managers operate within with isoquants?
since isoquants could bend back on themselves, managers must operate on the segments for which each input has a positive MP
what does a positive slope for an isoquant mean?
increases in both capital and labour are required to maintain a specific output rate
explain ridge lines
the lines that profit-maximizing firms operate within, because outside them, MPs of inputs are negative and isoquant slope is positive
shape of ridge lines
2 lines curving outwards towards each other from the origin with labour and capital as the axis
what is MRTS and definition
marginal rate of technical substitution (MRTS) shows the rate at which a firm can substitute one input for another while holding output constant
MRTS formula
-dX2 / dX1 with Q held constant = -MP1 / MP2 = -1*slope of isoquant
what does an MRTS of 0.58 mean when MRTS = -dX2/dX1 = -MP1 / MP2
could subsitute 0.58 pounds of x2 for one pound of x1 and get the same output
total outlay M formula
M = Price of L * L + price of K * K
what does the isocost curve show?
It shows all of the possible bundles of K and L that can be purchased for a total outlay of M, given PK and PL
what is the isocost curve formula?
total outlay M formula solved for K
what is the slope of the isocost curve?
-Price of L / Price of K
how to maximize output with isocost curve and isoquants?
maximize output at a given cost by selecting combination of inputs that is determine by the point where the isocost curve is tangent to the highest valued isoquant possible
formula for maximum output
MP L / PL = MP K / P KOR marginal product per dollar spent should be the same for all inputs
explain corner solution for isoquant/isocurve
optimal input bundle with just one input deployed; if no tangency was possible between isocost curve and isoquants, they just touch
explain increasing returns to scale
doubling both inputs more than double the output
explain decreasing returns to scale
doubling both inputs leads to less than a doubling of output
explain constant returns to scale
doubling both inputs leads to double the output
explain output elasticity
the percentage change in output resulting from a one percent increase in all inputs or resulting from a 1% increase in a single input (in cobb-douglas function) OR % change in output divided by an equal percentage change in all inputs = change in Q/Q /change in input/input
what can we use the output elasticity to determine
if there is increasing/decreasing/constant returns to scale
what is a Cobb Douglas Production function
Q = aL^bK^c
how to find partial output elasticity with respect to labour
dQ/dL * (L/Q) = b
how to find partial output elasticity with respect to capital
dQ/dK * (K/Q) = c
increasing/decreasing/constant returns to scale with output elasticity
if b + c > 1, increasing returns to scale;
if b + c = 1, constant;
if b + c < 1, decreasing
formula for estimating production function
log Q = log a + b log L + c log K
what happens if MRTS is large?
isoquant is steep, it takes a lot of X2 to substitute one unit of x1
what happens if MRTS is small
isoquant is flat, it takes little of X2 to substitute for 1 unit of x1
what happens if MRTS is constant
isoquant is straight and X1 and X2 are perfect substitutes
what happens if MRTS is undefined
isoquant is right angle and X1 and X2 are perfect complements and no substitution possible
4 sources of increasing returns to scale
1) Indivisibilities: some tech can only be implemented at a large scale of production
2) Subdivision of task: larger scale allows increased division of tasks and increased specialization
3) Probabilistic efficiencies: law of large numbers may reduce risk as scale increases
4) Geometric relationships: doubling size of box multiplies surface area by 4 times but increases volume by 8 times (storage, transport devices)
2 sources of decreasing returns to scale
1) Coordination inefficiencies: larger organizations are more difficult to manage
2) Incentive problems: designing efficient compensation systems in large organizations is difficult
formula relating price of output to price of input **
MP U * P of output = MP U
formula for MRTS of hay for grain
MRTS = change in grain / change in hay
what does the production process include and 4 examples
all activities associated with providing goods and services like employment practices, acquisition of capital resources, production distribution, managing intellectual resources
what does a production function show?
shows the maximum amount that can be produced per time period with the best available technology from any given combination of inputs.
how can a production function be represented?
table, graph, equation
what happens to AP if MP > AP
AP must be increasing
what happens to AP if MP < AP
AP must be decreasing
where is the economic region of production located?
inside ridge lines
graph of isocost curve?
downward straight line, y axis is K (M/Pk), x axis is L (M/PL)
how is AP of labour geometrically represented?
slope of total product curve with respect to labour
Hedge Fun is a landscaping firm that specializes in topiary. Last year, the firm had 30 employees and served 120 customers. This year, it had 35 employees and served 135 customers. The average product of labor is at a maximum when the number of customers
less than 120; AP maximized when MP = AP
