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Uni Y1 S1 - Principles Of Microeconomics ECON1022 > Topic 01- Technology > Flashcards

Topic 01- Technology Flashcards

1
Q

a- What is a function?

A

Something that transforms input into output

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2
Q

What is a production function?

A

Way to describe technology- tells us how many units of output (production) can be produced at most for a given amount of input (FOP)

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3
Q

What does the following notation mean:
K
L
q
f

A

K- capital
L- labour
q- quantity
f- production function

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4
Q

How do you denote a production function and what does it mean?

A

q = f(K,L)

The maximum amount of output (q) that can be produced by inputs/factors of production (K and L)

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5
Q

When do you typically have a fixed factor?

A

In the short run

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6
Q

What occurs in the short run as a result of the fixed factor?

A

Law of diminishing marginal returns

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7
Q

Define marginal product of labour and marginal product of capital

A

Extra product generated by 1 extra unit of labour keeping all other factors (FOP) constant

Extra product generated by 1 extra unit of capital keeping all other factors (FOP) constant

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8
Q

How do you denote marginal product of labour?

A

MPL (but small capital L bottom right)

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9
Q

How do you graphically show a basic production function?

A

Have labour (L) on the horizontal axis and quantity produced/output (q) on the vertical axis

Show a slow increase in quantity for the increase in labour but gradually show the graph becoming more steep until the graph reaches its steepest point- the graph then starts to become less steep until it reaches its maximum point after which point the function begins to decline (SEE IMAGE IN NOTES)

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10
Q

How is the marginal product of labour significant graphically?

A

It is the slope/gradient of the production function

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11
Q

What is important to remember about the word marginal?

A

It will represent the gradient of something else

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12
Q

How can you algebraically display marginal product of labour (MPL- small L)?

A

MPL (small L) = change in quantity/change in labour
… MPL = delta (triangle) quantity/delta labour

REMEMBER delta labour = 1 as seeing affect on quantity of increasing labour by 1 unit at a time

MPL = dq/dL = slope or gradient of the production function

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13
Q

How can you graphically display the marginal product of labour curve and how does it relate to the production function?

A

MPL (small L) curve increases fairly constantly until it reaches its peak (when the production function curve is steepest)
It then falls fairly constantly until 0 (x-axis) whilst remaining positive (showing that the production function continues to rise at a decreasing rate)
When the MPL curve intersects the x-axis the production reaches its maximum point which has a gradient of 0
The MPL curve then becomes negative at which point the production function begins to fall

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14
Q

b- Which 2 inputs/FOP are substitutes and give an example?

A

Capital (K) and labour (L)
E.g. 5 units of labour spray painting a car can be replaced by 5 machines

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15
Q

What is one way in which we can show how a firm can produce the same amount of quantity but using different amounts of labour and capital?

A

An isoquant (set of all combinations of inputs that lead to same level of output)- curve which literally means constant/same (iso) quantity (quant)
A firm can produce on the line using varying amounts of capital and labour
NOTE curve must be INWARDS facing and cannot be outwards facing in order to comply with diminishing returns to a fixed factor (further reasoning explained on another card)

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16
Q

Are capital and labour always substitutes?

A

No- as sometimes labour (workers) needs to operate capital (machinery) and … the same amount of quantity cannot be produced if there is a different number of labour to machinery- e.g. 5 trench diggers need 5 units of labour in order to operate … they are complimentary

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17
Q

What are the conditions/observations of isoquants?

A

1) Points on the same isoquant (curve) produce the same quantity- each isoquant shows a different quantity/output
2) Isoquants are thin- if thick then shows that higher capital and labour produces same quantity which isn’t true- SEE NOTES FOR IMAGE
3) Isoquants must slope downwards- if it is thin but it slopes upwards then it shows that a higher amount of labour and capital produces the same amount of quantity which isn’t true- SEE NOTES FOR IMAGE
4) The further Isoquants are to the north east, the higher quantity/output they produce- Isoquants to the top right have higher capital and labour … more output
5) 2 different Isoquants with different production levels cannot cross- the point of intersection would indicate that the same amount of capital and labour produces 2 different quantities which isn’t possible
6) Every point has an isoquant that goes through it BUT not all are drawn- there is an isoquant for every quantity producible

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18
Q

What is the technical term for when the gradient of the slope of an isoquant determines the substitutability of labour for capital and how is it denoted?

A

Marginal rate of technical substitution of labour for capital- MRTSLK(LK small)

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19
Q

What would you notice about the substitutability (if you had capital (K) on the vertical axis and labour (L) on the horizontal axis) with varying gradient slopes of an isoquant?

A

More vertical slope = if you’re initially producing a quantity on an isoquant with a fair bit of capital and fairly little labour (top left) then it will be possible to reduce capital by quite a large amount and only employ some workers to continue producing along the same isoquant and … the same quantity

More horizontal slope = if you’re initially producing a quantity on an isoquant with a fair bit of capital and fairly little labour (top left) then it will be possible to reduce capital by quite a small amount but you would need to employ many more workers to continue producing along the same isoquant and … the same quantity

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20
Q

How do you generally calculate the marginal rate of technical substitution of labour for capital (MRTSLK)- small LK?

A

Work out the gradient of the slope/isoquant SO THAT WE MAINTAIN THE SAME QUANTITY- I.e produce along the same isoquant
… MRTSLK (small LK) = change in capital K/ change in labour L- so that same quantity produced

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21
Q

In practice how would you go about calculating MRTSLK (small LK)?

A

1) Calculate change in K (capital) = MPK (small K) * –Change in K (negative as capital falls)
2) Calculate change in L (labour) = MPL (small L) * Change in L
3) Equate change in labour with change in capital as total change in production is 0- as on same isoquant producing same quantity- so change in labour should be equal to the change in capital (remember delta K and delta L will most likely not equal each other … they can be equated because of most likely differing values of MPK and MPL- overall the effect is the same as the quantity is constant hence why they are equal)
4) … –MPKchange in K = MPLchange in L
5) … by rearranging: change in K/change in L = –MPL/MPK … as MRTSLK = change in K/change in L, MRTSLK = –MPL/MPK
6) Lastly substitute your values for MPL and MPK into the formula created (remember the negative) and you will have a value for MRTSLK

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22
Q

Why must an isoquant bend inwards towards the origin (0)?

Doesn’t make sense

A

SEE WORD DOC PIC- see the MRTSLK (small LK) formula and the move along the isoquant to the right from A to B
To move from A to B, capital would fall and labour would increase in order to produce the same quantity along the isoquant. If labour was to increase then it is more likely that diminishing marginal returns to a fixed factor would occur and then the marginal product of labour (the quantity produced by each extra until of labour) would fall which is the numerator in the MRTSLK equation.

At the same time capital would fall and therefore it is less likely that diminishing marginal returns would occur and therefore the marginal product of capital (the quantity produced by each extra until of capital) would increase which is the denominator in the MRTSLK equation.

… as a whole the MRTSLK (small LK) becomes closer to 0 hence why it bends inwards towards the origin

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23
Q

What are the 3 main thought experiments we look at?

A

1) One fixed factor-> Law of diminishing marginal returns- short run
2) Substitutability- change 2 factors but in particular way so that quantity produced is the same and production continues to occur along the isoquant- increased one but compensated by decreasing the other
3) Returns to scale- long run- all factors/inputs variable

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24
Q

What is returns to scale?

A

Returns to scale- increase all factors (capital and labour both) by a factor greater than 1
All factors increased proportionally

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25
Q

What is increasing returns to scale?

A

When PRODUCT increases by a factor greater than the factor the inputs (capital and labour) increased by … product increased greater proportionally than capital and labour

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26
Q

What is constant returns to scale?

A

When PRODUCT increases by the same factor the inputs (capital and labour) increased by

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27
Q

What is decreasing returns to scale?

A

When PRODUCT increases by a factor less than the factor the inputs (capital and labour) increased by … product increased less proportionally than capital and labour

28
Q

What is the difference between marginal returns and returns to scale?

A

Marginal returns involves seeing the affect on quantity/output by manipulating the an input/FOP by 1 unit whilst keeping all other inputs/FOP constant e.g. fixing capital but changing labour- ALSO with marginal returns you always assume diminishing marginal returns to a fixed factor

Returns to scale is where both/all inputs are variable and both (capital and labour) are risen by the same factor to see the affect on quantity/output

29
Q

How can you show marginal returns and returns to scale together?

A

Using a Cobb-Douglas production function

30
Q

What is Cobb-Douglas?

A

A production function

31
Q

What does a Cobb-Douglas production function look like?

A

Has 3 dimensions
Labour (L) along the bottom (like where length would be)
Capital (K) where width would be
Quantity (q) where height would be
SEE WORD DOC IMAGE

32
Q

What are the curved lines in the Cobb-Douglas production function?

A

They are isoquants- makes sense when you visualise the digaram from a 2 dimensional point of view

33
Q

How does a Cobb-Douglas production function show marginal returns and returns to scale together?

A

1st instance: marginal returns:
SEE DIAGRAM ON NOTES- see first slice when capital (K) fixed at 20 and labour is increased, quantity rises at a decreasing rate (curve is concave) which shows decreasing marginal returns to a fixed factor (capital at 20)- SHOWS that marginal product of labour (MPL- small L- product produced by 1 extra unit of labour) eventually falls because of the fixed capital at 20

2nd instance: returns to scale:
When capital AND labour increase by the same amount/proportion together, quantity increases at an increasing rate (curve is convex). Quantity increases by a greater proportional rate than the increase in capital and labour hence why there are increasing returns to scale. The line becomes steeper and steeper.

34
Q

What are the assumptions made about firms?

A

1) They maximise economic profit … are profit maximisers (Profit (pi) = Revenue (R) – Costs (C))
2) Firm produces q units of a single good or service using only 2 inputs/FOP- firm operates using production function q = f (K,L)
3) Firm is perfectly competitive and is a price taker (market determines price of final good, rental price of capital and wage of labour)- has no influence over price- no market power

35
Q

How do you calculate profit?

A

Profit (pi) = Revenue (R) – Costs (C)
Profit (pi) = pq – (rK + wL)
… Profit (pi) = (price x quantity) – (rental price of capital + wage rate of labour)

36
Q

When do diminishing returns occur?

A

Occurs in the short run when at least 1 Factor of Production (FOP) is fixed

37
Q

How can you show diminishing returns using the production function?

A

Production function: q = f(K,L)

Assume one of the FOP (K- capital or L- labour) are fixed- can choose either and same result will be found

In this case we assume capital (K) is fixed (denoted by horizontal line on top of the K)- we then gradually increase labour and what you find that is that output or quantity (q) rises but at a decreasing rate until the increase is 0 (can be followed by a fall in quantity)

Here the marginal product of labour (MPL- small capital L on bottom right) shows the difference in output or quantity (q) by increasing labour by 1 unit … it shows that initially the difference rises, peaks and then falls eventually to 0 (and may even become negative if labour was to rise further)

38
Q

How do denote a fixed factor?

A

By putting a horizontal line on top of the letter the factor is denoted by e.g. a horizontal line on top of K to denote fixed capital and a horizontal line on top of L to denote fixed labour

39
Q

What does the marginal product of labour show?

A

Extra output/production/quantity generated by 1 extra unit of labour

40
Q

What does the marginal product of capital show?

A

Extra output/production/quantity generated by 1 extra unit of capital

41
Q

How do you denote the marginal product of labour?

A

MPL (small capital L on bottom right of P)

42
Q

How do you denote the marginal product of capital?

A

MPK (small capital K on bottom right of P)

43
Q

What is the law of diminishing marginal returns?

A

States that the marginal product of labour is eventually diminishing to 0

In other words the extra product generated by 1 extra unit of the variable input eventually falls to 0

44
Q

Explain how to display the MPL curve based on a production function

A

Don’t specifically annotate the vertical axis
Horizontal axis is labour (L)

MPL gradually increases until MPL reaches its maximum point (at this point the production function above is at its steepest point- increase in quantity is at its greatest as a result of labour increasing by 1 unit)
The the MPL starts to fall until it reaches 0 (at this point the production function above is at its maximum point- here quantity produced in the production function is at its maximum hence the MPL being at 0)
After this point the MPL becomes negative and in the production function above, quantity also begins to fall as labour increases
SEE IMAGES IN NOTES FOR CLARITY

45
Q

What part of the production function and MPL (small L) is of interest and why are the other parts not of interest?

A

In both the production function and the MPL curve it is the black line (middle part)

In the production function it is the between point when the production function is steepest and the maximum point of the production function

… in the MPL curve this is between the points when the MPL curve is at its maximum and when the MPL curve is 0

This is the main important bit because it’s where the law of diminishing marginal returns is mainly shown (SEE NOTES)

Also the part of the production function after its maximum point when quantity begins to fall as labour continues to rise (the point on the MPL curve after it reaches 0 and then becomes negative) is not of interest as here it is obvious that firms will not continue to employ more labour as it is leading to a fall in quantity

The part of the production function before the steepest point (the maximum point on the MPL) is not interesting either as firms are most likely going to employ more labour as doing so will show a proportionally greater increase in output

46
Q

When does the law of diminishing marginal returns occur?

A

In the short run when there is 1 fixed factor

47
Q

Define substitute goods

A

Substitute goods are two alternative goods that could be used for the same purpose
E.g. workers can paint a car and so can robots

48
Q

Define complement goods

A

Complementary goods are products which are bought and used together
E.g. diggers and the labour (workers) who operate them

49
Q

What is the potential issue that can arise by now having both inputs (labour and capital) both variable?

A

A potential issue could arise in how to graphically display 3 variables (2 inputs and 1 output)- output being quantity produced

50
Q

How are 2 variable inputs and an output shown graphically?

A

Using a level curve called an Isoquant

51
Q

What is an isoquant a type of?

A

An isoquant is a type of a level curve

52
Q

What needs to occur in order to produce at a different point on the same isoquant?

A

1 input must be substituted for another input

For example labour is increased then the amount of capital will need to be reduced to produce along the same isoquant (same quantity)

53
Q

How do you measure the slope of an isoquant?

A

Change in K / Change in L = Marginal rate of technical substitution (MRTS)

q is constant as working out substitutability along same isoquant

54
Q

Why is it important to measure the slope of an isoquant?

A

Affects substitutability- see notes

55
Q

How would you draw an isoquant?

A

Capital K on vertical y-axis
Labour L on horizontal x-axis

L shaped curve drawn at various places with quantity increasing in north-east direction

56
Q

How do denote (formula) a Cobb-Douglas production function?

A

(A)(K^a)(L^b)

Where parameter A is positive and where parameters a and b are positive and less than 1
K = capital
L = labour

57
Q

What is short run?

A

Where at least 1 factor of production is fixed (typically we assume that capital is fixed and labour is variable)
This is because changes to labour can be made at short notice- e.g. an email asking the entire workforce to come to work on Saturday

… if you can adjust capital then it is assumed that that is the long-run even if the actual time frame is only 2 weeks for example … important not to associate short and long run with time frames- it depends on context instead

58
Q

What is long-run?

A

Where all factors of production of a firm are variable (both labour and capital are variable)

If capital can be adjusted then it is assumed that that is the long run even if the actual time frame is only 2 weeks for example … important not to associate short and long run with time frames- it depends on context instead

59
Q

What do we assume is the objective of firms?

A

To maximise profit

60
Q

What do we assume are the constraints of firms?

A

1) Technology (affects production function q = f (K,L)
2) Prices that they face (price of good, rental price of capital, wage price of labour)- no influence over price

61
Q

How do you approach the objective which aims to predict how agents react to a changing environment?

A

1) Identify agents (firms, individuals, government etc) objectives (typically profit maximisation but also others e.g. well-being of consumer, sales maximisation etc)
2) Identify agents constraints (typically technology and price but also others)

The solve to maximise objectives subject to constraints

62
Q

What is the general objective of the firms problem and how is this applied?

A

To predict how agents (firms, individuals, governments etc) react to a changing environment

To see how agents (in this case firms) react to a change in the final price of the good, a change in the rental price of capital or a change in the wage rate of labour- how will this affect quantity produced, labour employed and capital employed

63
Q

Ultimately what will we derive to try to solve the firms problem?

A

We will derive the supply function

64
Q

Give a general outline of the steps to solve the firms problem

A

Problem involves finding 3 variables (q, L, K) which is complex
… we divide it down into 2 simpler steps

1) Cost minimisation- initially you assume that q is constant and focus on working out L and K

2) Profit maximisation- use K and L values found to work out optimal q

Process needs to be done twice for short run and long run

65
Q

What should you do if you feel lost about the various parts of solving the firms problem?

A

Visit the table at the end of topic 01 notes- SEE NOTES

Uni Y1 S1 - Principles Of Microeconomics ECON1022 (6 decks)

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