Chapter 10 - Production

Question 1

Production (definition)

Answer 1

Any activity that creates present or future utility/ a process that transforms inputs into outputs

Question 2

Production Function (definition)

Answer 2

Relationship by which inputs are combined to produce outputs

Q = F (K,L)

Question 3

Factors of Production (CELL)

Answer 3

They are the inputs in a production function.

Capital
Enterprise
Land
Labour

(Common to add factors such as Knowledge, Technology, Organisation and Energy)

Question 4

Short Run (definition)

Answer 4

Longest period of time during which at least one of the inputs used in a production process can be varied.

Question 5

Long Run (definition)

Answer 5

Shortest period of time required to alter the amounts of all inputs used in a production process

Question 6

Variable Input

Answer 6

an input that can be varied in the short run

Question 7

Fixed Input

Answer 7

an input that cannot be varied in the short run

Question 8

SR production function w/ curvilinear shape

Answer 8

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

Question 9

Law of Diminishing Returns (LDR)

Answer 9

If other inputs are fixed the increase in output from an increase in the variable input must eventually decline

Question 10

Malthus Population Growth (generalise what it’s about)

Answer 10

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)

Question 11

Total Product Curve

Answer 11

SR production function = showing the amount of output as a function of the amount of variable output

Question 12

Marginal Product

Answer 12

∆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

Question 13

Average Product

Answer 13

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

Question 14

Relationship between Average-Marginal (MP and AP curves)

Answer 14

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!

Question 15

Rule for efficient allocation (to do with MP…)

Answer 15

Allocate next unit of input to the production activity where MP is highest

Question 16

Interior solution (efficient allocation)

Answer 16

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

Question 17

Corner solution (efficient allocation)

Answer 17

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

Question 18

Production in the LR

Answer 18

ALL INPUTS ARE VARIABLE

Question 19

Isoquant (definition)

Answer 19

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)

Question 20

Marginal Rate of Technical Substitution (MRTS)

Answer 20

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

Question 21

Relationship between MRTS and MP

Answer 21

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

Question 22

Increasing Returns to Scale (definition)

Answer 22

A proportional increase in every input yields a more than proportional increase in output

F(cK,cL) > cF (K,L)

Question 23

Constant Returns to Scale (definition)

Answer 23

A proportional increase in every input yields an equal proportional increase in output

F(cK,cL) = cF(K,L)

Question 24

Decreasing Returns to Scale (definition)

Answer 24

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)

Question 25

Leontief (fixed proportions) Production Function

Answer 25

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

Question 26

Total Differential

Answer 26

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

Question 27

Product Rule

Answer 27

dy/dx = u’ (v) + v’ (u)

Question 28

Difference between LDR and decreasing RTS

Answer 28

LDR = when ONE input varies while others are held fixed

Decreasing RTS = when all inputs are varied by a given proportion

Question 29

Quotient Rule

Answer 29

f(x)/g(x) = g(x) f’(x) - f(x) g’(x)/ (g(x))^2

Question 30

Saddle Points

Answer 30

d^2z/dx^2 * d^2/dy^2 < d^2z/dydx * d^2z/ dxdy

Question 31

Integration by Parts

Answer 31

{u(x)v’(x) dx = u(x)v(x) - {u’(x)v(x) dx

Question 32

Total differential with error (football pitch example)

Answer 32

body + yodx+dxdy

error = dxdy

∆ in area = body+yodx

Question 33

If MP is decreasing then AP must also be decreasing… explain.

Answer 33

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!