Topic 02- Firm

Question 1

What is the firms problem?

Answer 1

To find outputs and inputs which maximise objectives (typically profit but can be other things e.g. wellbeing, sales etc) but are subject to constraints e.g. technology, prices (final price of good, wage rate, rental price of capital etc)

Question 2

What is the difference between the short and long run?

Answer 2

Short run- all but one input/FOP is fixed- usually capital (K) is fixed and labour variable as changes to labour can be made quite quickly
Long run- all inputs/FOP are variable- capital is changed as well as labour

Question 3

In general how do you calculate cost in the short run and what is the short run cost function?

Answer 3

Cost (C) = rK (K upper bar as capital is fixed in short run) + wL
… cost is equal to the rental price of capital multiplied by the amount of capital + the wage rate of labour multiplied by the amount of labour

Cost function:
- expressed in monetary units e.g. $ or £
- function of q (… tells you how much it costs to produce a certain level of output)

Cost function … equals:
C(q) = rK (upper bar) + wL(q)
As production function is basically q = f (L) as K is constant … inverse is L(q)

Question 4

What does the short run cost mean?

Answer 4

C (q) = rK (upper bar as capital is fixed- horizontal line above K) + wL (q)
The q’s are important as the cost function depends only on q
rK (upper bar) is the Fixed cost (FC) which doesn’t depend on quantity BUT wL (q) is the Variable cost which does depend on quantity (VC (q))
… the 2 equations below are equal and the same:

C(q) = FC + VC(q)
C(q) = rK (upper bar) + wL (q)

Question 5

How would you show total cost more generally with respect to quantity and why?

Answer 5

C (q) = FC + VC (q)
Fixed cost is the same no matter the quantity hence why it’s value does not depend on quantity
Variable cost however does depend on the quantity produced

Question 6

What does the variable cost curve look like and why?

Answer 6

Variable cost = labour needed to produce a certain quantity q multiplied by the wage rate of labour
… VC (q) = wL (q)
The production function is denoted by q = f(K,L) but because K is fixed (K upper bar), the production function is equal to q = f(L) which is the inverse of the variable cost function … the variable cost curve is the inverse of the production function curve- the inverse of the production function is simply L(q) which multiplied by some constant w is equal to VC(q) hence the shape is the just the inverse (the normal cost function has the same shape as the variable cost curve because C(q) = rK (upper bar) + wL(q) and here the only difference is the addition of rK (upper bar) but in the short run this is constant/fixed anyway and doesn’t as quantity changes (ALSO KEY THING TO REMEMBER when you have something adding onto the graph it only causes it to shift upwards- think back to maths transformations e.g. +10 would cause a graph to shift up by 10 … the actual shape of the graph doesn’t change hence why both the VC (q) and C(q) curves have the same shape which are both the inverse of the production function)- ALSO … that is why the cost curve sits above the variable cost curve- the fixed cost is added on (rK upper bar) and … why the gap and the difference between the cost curve and variable cost curve is just the fixed cost

The production function moves to the right initially and then gradually increases and becomes steeper and then it slowly flattens and reaches a maximum (due to diminishing marginal returns)
The variable cost function moves upwards initially and then moves right and has a gradient of 0 and the continues to rise exponentially
(SEE NOTES IMAGES FOR BOTH)

Question 7

How would you show fixed cost on a diagram?

Answer 7

The difference between the cost curve and variable cost curve. Both the cost curve and variable cost curve have the same shape but have gap between them (the cost curve is greater/higher) and the gap is fixed cost
SEE NOTES FOR IMAGE

Question 8

What is the equation that comprises all the average costs and how do you know it’s correct?

Answer 8

Average cost = average fixed cost + average variable cost
AC (q) = AFC (q) + AVC (q)
this is because: Total cost = total fixed cost + total variable cost:
TC = FC + VC
If you divided the second equation by quantity you would get the first equation

Question 9

What is marginal cost?

Answer 9

Cost of producing 1 extra unit of output- it is also the slope/gradient of the cost function

Question 10

How does marginal cost reflect the slope of the cost function?

Answer 10

When marginal cost is positive, the cost function is increasing
When marginal cost is negative, the cost function is decreasing
When marginal cost equals 0, the cost function is at a maximum

Hence why the MC curve has the shape it does- it is falling initially until it reaches 0 (or a minimum point) and then begins to rise exponentially after this point reflecting the exponential rise in the cost function

Anything marginal has the same properties e.g. marginal product of labour and the basic production function

Question 11

How do calculate marginal cost?

Answer 11

Work out the gradient of the cost function
… change in cost (q)/change in quantity
Delta cost (q)/delta quantity

OR can be written as derivative of cost function …
C prime (apostrophe) (q) = dc(q)/dq

Question 12

What is the connection between the average cost curve and the marginal cost curve?

Answer 12

When marginal cost greater than average cost then average cost curve rises
When marginal cost smaller than average cost then average cost curve falls
When marginal cost equal to average cost then average cost does not change/stays constant- intersection of AC and MC curves occurs at the lowest point (minimum) of the AC curve
RELATIONSHIP seen when drawn together - SEE NOTES IMAGE

Question 13

How do you calculate profit?

Answer 13

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

pq = revenue
K- amount of capital
L- amount of labour

Question 14

What do you assume in the short run about a firm when solving its problem?

Answer 14

In the short run you assume capital is constant as it is a fixed factor and only labour is variable

Fixed capital denoted by K upper bar (K with horizontal line above it)- fixed number, not under your control, inherited from the past
… only L and q are variable (amount of labour and quantity produced)

Question 15

What do you assume in the long run about a firm when solving its problem?

Answer 15

All 3 unknown variables (K capital, L labour and q quantity produced) changeable/variable/unknown

Question 16

What is important to remember about short and long run?

Answer 16

Different for each type of firm- dependent on context

E.g. a shopkeepers long run may be 6 months whereas the long run for a nuclear power plant may be 10 years

Question 17

What is the formula for cost known as?

Answer 17

The cost function

Question 18

What is average cost and how do you calculate it?

Answer 18

Cost per unit
Basically average total cost

Cost divided by quantity or number of units

AC (q) = C(q)/q

Question 19

What is average fixed cost and how do you calculate it?

Answer 19

Fixed cost per unit

Fixed cost divided by the quantity/number of units

AFC (q) = FC/q

Note average fixed cost is a function of quantity even though fixed cost is not- this is because it is the fixed cost per unit and … has been divided by quantity/number of units

Question 20

What is average variable cost and how do you calculate it?

Answer 20

Variable cost per unit

Variable cost divided by the quantity/number of units

AVC (q) = VC (q)/q

Question 21

List all the unit costs

Answer 21

1) Average Cost (AC)
2) Average Fixed Cost (AFC)
3) Average Variable Cost (AVC)
4) Marginal Cost (MC)

Not really too important but marginal cost I believe is also a unit cost as it is to do with 1 unit

Question 22

What is the shape of the marginal cost (MC) curve and why?

Answer 22

U shaped (but sometimes drawn so that only half of U or right side of U drawn- minimum point on curve starts on the y-axis (unit cost) and x-axis quantity)

MC is eventually increasing because the cost function becomes steeper and steeper (see image of cost function alongside the variable cost function and the fixed cost in notes)- cost function rises exponentially as quantity continues to rise (due to the law of diminishing marginal returns- diminishing returns because of rising costs) … the cost of producing 1 extra unit of output increases at an increasing rate (exponentially)

… marginal cost (MC) rises due to diminishing marginal returns as diminishing returns mean that the cost of producing an extra unit of output must be rising hence why MC rises exponentially with the cost function C(q)

Question 23

What must you remember about fixed cost (FC) and average fixed cost (AFC (q))?

Answer 23

REMEMBER: AFC = FC/q
If fixed cost is greater than 0 then:
As q tends to 0, AFC tends to infinity as it’s getting bigger the smaller q is (think fractions and also to asymptotes and how dividing by 0 gives you a math error- calculator can’t show infinity if you divide by 0 by that’s what it tends to)

As q tends to infinity, AFC tends to 0 because the smaller the fraction will be when dividing by larger and larger denominators

Question 24

What is the shape of the unit cost functions?

Answer 24

MC is half U shaped- only slightly more than half of right side U is shown- falls to a minimum and then rises exponentially due to the cost function
AC is U shaped and intersects the MC curve when AC is smallest (at its minimum)
AVC is also U shaped liked the AC curve and is below the AC curve throughout
The AC curve and AVC curve never touch as the AFC is in between them always- they gap gets smaller and smaller as AFC becomes smaller and smaller as quantity rises but the 2 curves never touch
AVC also intercepts the MC curve when AVC is smallest (at its minimum) for the same reason as AC- variable cost includes marginal cost because it’s changing
SEE NOTES IMAGE

Question 25

Where can I see the calculation parts to topic 02?

Answer 25

SEE IMAGES ON NOTES

Question 26

How can you calculate the point at which the AC curve intersects the MC curve?

Answer 26

2 ways to calculate the point at which the AC curve intersects the MC curve:
1. Differentiate AC curve and equate to 0 and solve to find minimum value
2. It is the intersection of the AC and MC curve so equate together and solve to find 20- substitute back into MC or AC folder to find corresponding y-axis value (unit cost value)

Question 27

How many ways are there to calculate the point at which the AC curve intersects the MC curve?

Answer 27

2

Question 28

How many ways can you write/display profit (equations)?

Answer 28

8 ways

Question 29

How can you write/display profit (equations)?

Answer 29

1) Profi (pi) = Revenue - Costs
… can be broken down into:

2) Profit (pi) = pq - (rK (upper bar) + wL(q)) : standard equation

3) Profit (pi) = pq - C(q) : basically the upper equation simplified- remember C(q) = rK (upper bar) + wL(q)

4) Profit (pi) = q(p - AC (q)) : taken q out of brackets of upper equation- remember AC (q) is unit cost and … divided by q hence why multiplying it by q is equal to C(q)

5) Profit (pi) = pq - (FC + VC (q))- remember that C(q) is also equal to FC + VC (q) which is then further broken down into rK (upper bar in short run) + wL (q)

6) Profit (pi) = q(p - AVC (q)) - FC : here the minus in the above equation is multiplied out so that you get Profit (pi) = pq - VC (q) - FC : you then want to take q out of the first part of the equation only leaving FC as it is which gets you : q(p - AVC(q)) - FC

7) Profit (pi) = Operating profit - FC
…
8) Profit (pi) = q(Operating profit per unit) - FC

(For explanation of equations 7 and 8 see next flashcard- but important to know)

Question 30

What can you say about the following profit equation:

Profit (pi) = q(p - AVC (q)) - FC

Answer 30

Operating/operational profit (also known as quasi-profit, quasi rent or producer surplus in economics) is the equation above excluding the - FC bit …

Operating profit = q(p - AVC (q)) = pq - VC (q)
…
Operating profit per unit = p - AVC (q)
…
Profit (pi) = Operating profit - FC
…
Profit (pi) = q(Operating profit per unit) - FC

Question 31

Should you make a comparison of the operating profit definition in Economics and the operating profit definition in Accounting and Finance?

Answer 31

No keep both separate as have slightly different definitions

Question 32

What does operating profit mean in economics?

Answer 32

Profit from the operations of an agent (firm etc)
… it is 0 if you don’t produce anything

Question 33

What is larger operating profit or normal profit and why?

Answer 33

Operating profit as it ignores fixed cost (FC)

Operating profit only takes variable cost into account (it is revenue (pq) minus variable cost) whereas normal profit takes both variable and fixed cost into account hence why it is smaller

Question 34

How would you use the profit equations to graphically display important quantities (profit, cost, revenue, operating profit, fixed cost, variable cost)?

Answer 34

SEE NOTES IMAGES WHERE I HAVE BROKEN DOWN HOW YOU CAN APPLY YOUR KNOWLEDGE OF THE EQUATIONS TO A GRAPH
HONESTLY IT’S ACTUALLY VERY CLEVER AND YOU FIND THAT THE EQUATIONS AND GRAPHS ARE MORE CLOSELY LINKED THAN YOU THINK- YOU CAN MAKE CLEVER AND INTERESTING OBSERVATIONS

Question 35

When finding the optimal level of production, what questions/problems must you address?

Answer 35

1) Output decision- if you are going to produce then how much should this be
2) Shutdown decision- whether or not to produce at all or to simply shut down to avoid losses- might find that the proposed output decision might actually lead to more loss than not producing at all

Question 36

To answer the first question on output decision, what must you do to get a candidate for optimal production level?

Answer 36

You basically want to compare price (which is the revenue that you earn) and MC (cost incurred from selling an extra unit of output)

If the price increase (revenue increase) is greater than the marginal cost of producing an extra unit of output then it is worth increasing production by 1 unit as this will increase profit

If however the price increase (revenue increase) is smaller than the marginal cost of producing an extra unit of output then it might be more beneficial to decrease output as then the decrease in marginal cost for reducing output by 1 unit is greater than the fall in price (revenue) which will lead to greater profit

Basically what you’ve done is trialled a fairly low output level and a fairly high output level and basically found that neither are optimal so instead you produce at the point when P=MC as at this point a small change in production will change revenue and costs at the same rate and … this will not change profit

… the quantity that occurs when p = MC is a candidate for optimal production but not necessarily the most optimal point to produce at (SEE IMAGE ON NOTES FOR WHAT I’VE DESCRIBED IN THIS PARAGRAPH AND THE ONES ABOVE)

Question 37

When considering the shutdown decision, how many special prices do we need to consider and know?

Answer 37

2

Question 38

When considering the shutdown decision, what are the special prices that we need to consider and know?

Answer 38

1) Shutdown price
2) Break-even price

Question 39

When considering the shutdown decision, how do you denote the shutdown price?

Answer 39

Shutdown price denoted by small capital PSD

Question 40

When considering the shutdown decision, how do you denote the break-even price?

Answer 40

Break-even price denoted by small capital PBE

Question 41

When considering the shutdown decision, what is the shutdown price?

Answer 41

The minimum point on the average variable cost curve (move left from this point and the price identified is the PSD)

See image on notes

Question 42

When considering the shutdown decision, what is the break-even price?

Answer 42

The minimum point on the average cost curve (move left from this point and the price identified is the PBE)

See image on notes

Question 43

What should your shutdown decision be when the market given price is above the minimum point on the AC curve (above break-even price)?

Answer 43

You should produce here as your price is greater than your AC and you know that profit is found by:
Profit (pi) = pq - C(q) which is equal to the following when you take q out:
Profit (pi) = q(p - AC(q))

… because p is greater than AC then p - AC(q) is positive and q* is also positive and … 2 positives multiplied will also be positive hence why your profit is greater than 0
Also shutting down would mean that you produce 0 output and here your profit would be negative as your fixed costs would be taken away (have to be paid no matter production amount- sunk costs)

… by comparison it is better to produce when p is greater than AC to earn profit greater than 0 than to produce when quantity is equal to 0 as this gives negative profit of -FC

Question 44

How should you present your answer when the market given price is above the minimum point on the AC curve (break-even price)?

Answer 44

at q* p>AC
Profit (pi) = R - C
Profit (pi) = pq - C(q)
Profit (pi) = q(p - AC(q))

q>0 and p - AC(q)>0 …
Profit (pi) = q(p - AC(q)) > 0

when q=0, profit (pi) = -FC < 0

… greater profit earned when output decision is at q*

(See image in notes)

Question 45

What should your shutdown decision be when the market given price is below the minimum point in the AC curve (below break-even price) but above the minimum point on the AVC curve (above shutdown price)?

Answer 45

First if you use/look at the equation:
Profit (pi) = q(p - AC(q))
then you can see that p - AC is negative as AC is greater than p and … your profit earned from producing at q* is negative as a negative p - AC multiplied by a positive quantity will equal a negative
Also you know that producing 0 quantity will be equal to your fixed costs taken away … both producing at q* and producing 0 quantity give you a negative but now you need to determine the profit value which is less negative (I.e the lesser of 2 evils)

So now use a profit equation which includes AVC:
Profit (pi) = q(p - AVC(q)) - FC
now apply this equation to the question/graph- so p - AVC here is positive multiplied by a positive quantity q* gives you a positive from which fixed costs are taken away
Compare this to the shutdown decision (producing 0 output) which is equal to -FC … it is worth producing at q* as some positive minus FC will be greater than just minus FC on its own … the lesser of 2 evils is found by producing at q*

NOTE- when p is between min AC and min AVC (between break-even and shutdown points) then firm here is covering its average variable costs (cost of production per unit) and is also contributing towards its average fixed costs (sunk costs per unit) but isn’t covering average fixed costs entirely (remember vertical distance between AC and AVC is AFC) hence why loss is still made

Question 46

How should you present your answer when the market given price is below the minimum point on the AC curve (break-even price) but above the minimum point in the AVC curve (shutdown price)?

Answer 46

at q* AC>p>AVC
Profit (pi) = R - C
Profit (pi) = pq - C(q)
Profit (pi) = q(p - AC(q))

As AC>p and q>0, profit (pi) < 0
When q=0, profit (pi) = -FC < 0

Profit (pi) = pq - (FC + VC(q))
Profit (pi) = pq - VC(q) - FC
Profit (pi) = q(p - AVC(q)) - FC

as q>0 and p - AVC>0:
Profit (pi) = some positive value - FC < 0
When q=0, profit (pi) = -FC < 0

… although both profit values are negative, production at q* gives a greater profit figure and allows the firm to cover some of its average fixed costs as well as covering its average variable costs entirely

Question 47

What should your shutdown decision be when the market given price is below the minimum point on the AVC curve (below shutdown price)?

Answer 47

When p is less than the shutdown point, it means that the firm is unable to cover its average variable costs and therefore make no contribution to their average fixed costs hence a greater loss is made by the firm producing at q star which is why it is best if the firm were to shutdown

Question 48

How should you present your answer when the market given price is below the minimum point on the AVC curve (shutdown price)?

Answer 48

Look at the profit equation which involves AVC again:
Profit (pi) = q(p - AVC(q)) - FC

Now here p is smaller than AVC … p - AVC is negative and q is positive as always …
Profit (pi) = some negative value - FC

Compare that to a shutdown decision producing 0 output and that would be equal to just taking away your fixed costs

… you can see that by producing at quantity q* your profit is actually smaller than if the firm simply shutdown

This is because the firm here is not able to cover its average variable costs (cost of production per unit) entirely and … isn’t making a contribution to reduce its average fixed costs (fixed costs per unit)
… it is better if the firm was to shutdown

Question 49

Overall, what can you conclude about when a firm should decide to produce and when it should decide to shutdown?

Answer 49

Basically, you should produce the candidate that you got in the output decision (1st of 2 steps) when p=MC as long as it is above the minimum point on the AVC curve or the shutdown point

If the candidate that you got in the output decision is less than the shutdown point (minimum point on the AVC curve) then you shutdown instead of producing

Question 50

What is the supply function?

Answer 50

Tells us how many units of the product the firm is willing to deliver for a given price of this product

Question 51

What is the market supply function?

Answer 51

Tells us how many units all firms on the market are willing to deliver

Question 52

What does the short run supply function look like graphically?

Answer 52

It is the MC curve from the point it straightens and most importantly it is above the shutdown point … needs to be higher than the minimum point on the AVC curve (shutdown point)
Think about it makes sense why- a firm will not be willing to supply anything if price was to fall below the shutdown price- it would simply shutdown

See image in notes

Question 53

How does a firm react to a fall in the market given price?

Answer 53

See diagram in notes to visualise

But basically fall in price means that the marginal cost is now higher than the price which is not where the firm wants to produce at (think back to the 3 situations and how the firm decides on the middle where p=MC) … the firm responds to the fall in price by reducing quantity

If price continues to fall, then the firm will continue to make the same adjustment by reducing quantity (moving down along the MC curve or now short run supply curve) until the price falls below the shutdown price (minimum point on the AVC curve) which is when the firm will simply shutdown and stop producing all together (0 quantity)

REMEMBER because the firm moves down along the MC or short run supply curve it tells us how a firm will react (in terms of quantity produced) to changes in price (supply function definition)

Question 54

How do we assume a firm settles the price at which to produce at?

Answer 54

It takes the market given price and eventually settles on a price such that p=MC and … where profit is maximised

Question 55

How do you derive the short run supply function for an individual firm and why is it definitely the supply function?

Answer 55

Basically use p=MC
In the question you should be given MC or try to work it out if you can and basically make p equal to it

So for example, p=4q (remember the steeper straight line): here the relationship between p and q is the supply function but only when you express q as a function of p … the short run supply function is:

… q (p) = 1/4p

The above is the supply function because it tells us everything that it needs to as the supply function- it tells how a firm will respond in terms of the quantity produced to a change in price in the short run- substitute values in and you will get your answer

Question 56

If the individual short run supply function for a firm is q(p) = 1/4p then what is the market supply function if their are an n number of identical firms like the one mentioned above in the market?

Answer 56

Qs(p) = n(1/4p)

n firms multiplied by the individual firms short run supply function
Capital Q important and also small s too- small s written in bottom right of capital Q

Question 57

Do changes in fixed cost affect marginal cost?

Answer 57

No changes in fixed cost do not affect marginal cost (stays constant)- general rule

Question 58

Do changes in fixed cost affect average cost?

Answer 58

Yes as if fixed cost was to fall then that would lead to a fall in the average fixed cost
… this would effect AC as AC = AFC + AVC
So it would mean a fall in average cost

Question 59

How would a firm react if the government introduced a subsidy to business rates which lowers the rental price of capital?

Answer 59

Assume the subsidy reduced the rental price of capital which led to a fall in fixed costs

The reduction in fixed costs reduces average fixed cost which leads to a fall in average costs

A fall in fixed costs doesn’t affect AVC and … this doesn’t affect the shutdown price
The fall in fixed costs also doesn’t affect marginal cost and … our output decision at p=MC doesn’t change either which means we continue to produce at q* (our candidate solution)

So essentially, the decision of the firm to supply quantity q is not affected by introduction of the government subsidy- some firms are going to shutdown with or without a subsidy- will use the subsidy to offset losses and may even earn a profit but they will not supply a higher quantity

… subsidy does mean that fixed costs fall and … profit goes up but the subsidy does not change the behaviour of the firm in terms of the quantity the firm chooses to produce

See notes image

Question 60

How would a firm react if the government introduced a subsidy to wages?

Answer 60

Now fixed cost isn’t affected as neither the rental price of capital changes and the amount of capital employed is already fixed in the short run anyway

However the variable cost does fall as the wage rate of labour falls as a result of the subsidy

The MC, AC and AVC curves shift down (because they all fall- the marginal cost of producing an extra unit of output will be lower when wage rates fall, the average cost will fall as AC = AFC + AVC and if VC falls then AVC will fall which means AC will fall)

So basically what happens is is that the supply function shifts right (makes sense if the MC curve shifts down which is basically a shift right- supply curve is the straight part of the MC curve above the shutdown point) so that the quantity the firm produces increases (… the firms output decision is affected because MC is affected by the fall in the variable costs)- it is unclear whether the market given price will change but we do know is that the short run firm supply curve will shift right which will lead to an increase in the output by the firm

(See notes image)

Question 61

What do the examples of the introduction of 2 different subsides show?

Answer 61

That 2 subsides can have a dramatically different effect on a firms behaviour depending on where they are focused- the same amount of money can have massively different effects on the reaction of a firm

The subsidy on business rate (charged on non-domestic or non housing properties) to reduce the rental price of capital for firms did not affect the output decision of the firm- the firm continues to produce at the same quantity

The subsidy on wage rates however did affect the output decision of the firm- it caused the supply curve to shift right which meant the individual firm has increased the quantity it produces