Chapter 10 - Production Flashcards
Production (definition)
Any activity that creates present or future utility/ a process that transforms inputs into outputs
Production Function (definition)
Relationship by which inputs are combined to produce outputs
Q = F (K,L)
Factors of Production (CELL)
They are the inputs in a production function.
Capital
Enterprise
Land
Labour
(Common to add factors such as Knowledge, Technology, Organisation and Energy)
Short Run (definition)
Longest period of time during which at least one of the inputs used in a production process can be varied.
Long Run (definition)
Shortest period of time required to alter the amounts of all inputs used in a production process
Variable Input
an input that can be varied in the short run
Fixed Input
an input that cannot be varied in the short run
SR production function w/ curvilinear shape
1) Passes through origin = meaning that if no variable input is used output will be 0
2) Initially addition of variable inputs augments output at an increasing rate
3) after a certain quantity there are diminishing returns
Law of Diminishing Returns (LDR)
If other inputs are fixed the increase in output from an increase in the variable input must eventually decline
Malthus Population Growth (generalise what it’s about)
Population growth = geometric growth
Production growth = arithmetic growth
LDR suggests no matter how much labour, fertiliser, water and capital equipment land input fixed at low level increase in other inputs would quickly cease to have any affect on total output
However Malthus failed to anticipate growth in agricultural technology (Boserup Theory)
- ourstripped the effect of a fixed supply of land
- BUT there is also rapid population growth which will peak at 1970 (after which it will decline)
Total Product Curve
SR production function = showing the amount of output as a function of the amount of variable output
Marginal Product
∆Q/∆L
Change in total output due to a unit change in the variable input
Geometrically MP at any point is simply the slope of TPC at that point
Will employ till the point MP=0
Average Product
Q/L
Total output divided by the quantity of the variable input
When Variable Input = Labour, AP also known as Labour Productivity
Geometrically AP is the slope of the line joining the origin to the corresponding point on TPC
Relationship between Average-Marginal (MP and AP curves)
When MP curve > AP curve then AP must be rising
When MP curve < AP curve then AP curve must be falling
Intersection of MP and AP at AP’s Max Value!
Rule for efficient allocation (to do with MP…)
Allocate next unit of input to the production activity where MP is highest
Interior solution (efficient allocation)
MP of variable input, when all of it’s placed in one activity, is lower than MP of 1st unit of input in other activity
output-maximisation = distribute the input across the 2 activities, MP same in both
Corner solution (efficient allocation)
when MP of input is always higher in one activity than in the other
output maximisation = concentrate all input in the activity where it is more productive
Production in the LR
ALL INPUTS ARE VARIABLE
Isoquant (definition)
set of all input combinations that yield a given level of output
Isoquant Map - provides a concise representation of a production process
- shifting NE = increasing output
- Input bundle on isoquant yields more output than below
- number assigned to isoquant = output level (which is determined by production function)
Marginal Rate of Technical Substitution (MRTS)
The rate at which one input can be exchanged for another without changing the total level of output
Absolute value of the slope of the isoquant =
|∆K/∆L|
- diminishes with downward movements along an isoquant
- holding output constant, the less we have of one input the more we must add of the other input to compensate for a 1-unit reduction
Relationship between MRTS and MP
MRTS is simply the ratio of MP(L) and MP(K)
MP(K) - MP of capital at A and reduction of output due to loss of ∆K =
MP(K)∆K
MP(L) - MP of labour at A and gain in output of extra ∆L
= MP(K)∆L
Loss of ∆K offset by Gain in ∆L
MP(L)/MP(K) = ∆K/∆L
Increasing Returns to Scale (definition)
A proportional increase in every input yields a more than proportional increase in output
F(cK,cL) > cF (K,L)
Constant Returns to Scale (definition)
A proportional increase in every input yields an equal proportional increase in output
F(cK,cL) = cF(K,L)
Decreasing Returns to Scale (definition)
A proportional increase in every input yields a less than proportional increase in output
(constant and decreasing RTS often enable many sellers to coexist within the same narrowly defined markets)
F(cK, cL) < cF(K,L)
Leontief (fixed proportions) Production Function
Q = min (aK, bL)
- Q is either equal to aK or bL depending on whichever one is smaller
- Isoquant Map looks similar to perfect complements
- K and L are used most efficiently when aK = bL
- Locus point when K = bL/a
- MRTS in Leontief will be infinite on the vertical arm of the isoquant
- hero on the horizontal and undefined at the cusp
Total Differential
dz = dz/dx (dx) + dz/dy (dy)
The total change in Z equals the change in Z due to the change in X plus the change in Z due to the change in Y
Product Rule
dy/dx = u’ (v) + v’ (u)
Difference between LDR and decreasing RTS
LDR = when ONE input varies while others are held fixed
Decreasing RTS = when all inputs are varied by a given proportion
Quotient Rule
f(x)/g(x) = g(x) f’(x) - f(x) g’(x)/ (g(x))^2
Saddle Points
d^2z/dx^2 * d^2/dy^2 < d^2z/dydx * d^2z/ dxdy
Integration by Parts
{u(x)v’(x) dx = u(x)v(x) - {u’(x)v(x) dx
Total differential with error (football pitch example)
body + yodx+dxdy
error = dxdy
∆ in area = body+yodx
If MP is decreasing then AP must also be decreasing… explain.
False.
If MP is decreasing that means the contribution to output of an additional unit of input is becoming smaller.
Although it can still exceed AP
Example if AP = 10 and MP decreases from 12 to 11, MP is still > AP therefore AP would still increase!
This is dependent if MP is lower or higher than AP, if it is still higher then AP will continue to increase!
