2.1 Firms and costs Flashcards
What does Producer theory assume firms objective is?
to maximize profits Profits = Revenue – Costs
More specifically to maximises the present discounted value of profits for
shareholders
What are we going to assume about firms?
we are going to ignore that firms are an organisation run by people who have individual objectives ( firm is a single decision maker)
Why do we assume profit maximisation is the goal?
because in a competitive market, you have to profit maxmise to even stay in business as profit = 0 in this market.
You inherit a 205 square foot shop in covent garden and are considering converting it into a donguhut shop, You estimate that each month: Sales £50000 Staff costs : £20000 iNGREDIENTS: 15000 Marketing:£5000 Utilities, maintenance etc: £5000 Business rates £1500 Should you create the doughut shop?
We have to consider the opportunity cost of the shop, could we get more profit converting into something else, or just renting the shop ( in econ we will assume opp cost = 0, but in practice we take this into consideration)
What is opportunity cost?
What is the opportunity cost of using an input from inventory oil?
1) is defined as the value of an input in its best alternative use
2) If the only alternative is selling now then its it current price.
What is the production function?
What are the marginal product of capital and marginal product of labour definition?
MPK: tells me how much extra output i get from an additionala unit of capital, keeping labour inputs constant.
MPL: tells me how much extra output i get from additional unit of capital keeping capital input constant.
What is the marginal product of capital and labour?
To produce coffee we need labour and capital inputs ( workers and coffee machine) Lets say 1 worker and 1 coffee machine can produce output of 12
Lets say a second worker and 1 coffee machine produce an output of 20 cofees ( so 8 more coffees) Lets say a 3rd worker and 1 coffee machine produces an output of 24 coffees in total ( 4 more coffees) = hence the marginal product of labour is increasing at a diminishing rate.
Same thing when I have 2 coffee machines and 1 worker i produce 18 coffees, when i increase the number of workers, output will increase but at a diminishing rate = the marginal product of capital is increasing at a diminishing rate.
What is another property of the production function?
If i double the inputs i.e workers and cofee machines, my output will double e.g. from 12 to 24. This is called constant returns to scale.
1) The marginal product of labour will be higher if….
2) The marginal product of labour will be lower if…
3) The marginal product of capital will be higher if…
4) The marginal product of capital will be lower if…
1) if we increase capital
2) if we decrease capital
3) if we increase labour
4) if we decrease labour
We said that the marginal product of capital and labour is increasing at a decreasing rate, what is the formula term for this and how do we prove it?
How do we illustrate the marginal product of labour on a diagram.
What is the equivalent in consumer theory to indifference curves, and what is the definition of them, and what does non satiation mean here? Draw a diagram
Isoquants: all combinations of labour and capital that give a particular level of output.
More inputs lead to higher output
(equivalent to non-satiation!)
We said for the indifference curves the numbers didn’t matter ( as utility was ordinal) but here does the numbers matter ?
The numbers matter (unlike utility) and
denote output obtainable from inputs
What is the equivalent of the MRS in consumer theory to producer theory?Give definition and draw the diagram? What assumption do we make here?
MRTS = the rate at which one factor must decrease so that the same level of productivity can be maintained when another factor is increased.
As you move along the isoquant. the MRTS is decreasing ( you are more willing to give up one factor for another and keep the same level of productivity.)
What is the equivalent term for the budget line of consumer theory and what does it mean( how is it derived) rearrange it to get an equation of a line, what is the gradient of the line and interpret the y intercept. What is our cost of production problem? What is the gradient called?
wL + rK = Cost of production W: denotes wage and r is the price of capital ( opportunity cost of putting money into the bank , you earn interest r, or could be rental rate for renting machine.
The y intercept interprets the further out the isocost line, the higher the cost of production.
The gradient is called the relative factor price ( price of labour / price of capital same as basically p1/p2 in CT)
So what again what question are we trying to answer?
We are trying to produce q in the lowest cost way ( cost minimization ( i want to produce 100000 cars, whats the cheapest way to do so)
Minimise cost wL + rK of producing q
What is the cost minimization problem the same as in consumer theory and illustrate it?
Compensated demand.
Y axis is K(r,w,q
So we know that the the gradient is -w/r, if the wage rate goes up what happens?
The isocost line becomes steeper , and we have a substation effect ( substitute away from labour to machines and vice versa)
With the cost minimization problem we know that L ( r,w,q) and K(r,w,q) are optimal input mix, what are they called? Now draw the full diagram of cost minimization ( HINT, REMEMBER THE ITS THE SAME AS CONSUMER THOERY?) Highlight C(r,w,q) is the minimum cost of
producing q. What at the tangency what must be true? Once you have your optimal bundle, you can find cost of production doing what?
Conditional factor demands
Gradient of isoquant = gradient of isocost line.
We can find cost of production by reading the intercept.
How do we check for non sanitation and convexity?
What are the 5 steps for finding conditional factor demands?
We are going to find conditional factor demands and cost function, do steps 1-2
We are going to find conditional factor demands and cost function, do steps 3-4
Remember to write it as K(r,w,q) and L(r,w,q)
Now what is the cost function?
What are 4 properties of the cost function?
1) Increasing in output q
2) Conditional factor demands are homegoenous to degree 0 in r, w and the cost function is homoegeonous of degree 1 in input prices r,w
3) The cost function cannot decrease when the price of an input increases
4) Shepherds lemma
How can we proof that increasing output q increases cost c(r,w,q)?
1) Lets say our original quantity is qA.
2) Now we want to achieve quantity qb for the same factor prices( r and w)
3) our input mix will be at some other tanquency ( B)
4) Keeping r and w constant we see the intercept is higher, meaning it most correspond to higher cost.
5) Thus we are absolutely sure increasing q will increase cost!!!
How can we prove the cost function is homoegeonus to degree 1 ?
We have kept q the same but we scaled up the w and r, the gradient doesn’t change, hence tangency doesn’t change. NOTICE THE COST HAS GONE UP BUT NOTICE ON Y INTERCEPT WE HAVE SCALED UP COST OF CAPITAL BY SAME PROPORTION.
What will happen to cost when the price of an input rises? Proof of second property of the cost function. ( HINT suppose we keep wage fixed but the cost of capital rises)
Suppose we keep wage fixed but the cost of capital rises, originally the optimal production mix is at A where the gradient is -w/ra.
If r rises to rb, then the isocost line becomes less steep ( shallower), hence input mix changes from A to B, hence we got new intercepts.( new costs divided by individual factor prices, to find q). How do we deduce costs has increased?
1) The y intercept not useful because costs may be changing but r is also changing.
2) The intercept on x axis is far more useful, because i have kept r constant so denominator hasn’t changed, so if the intercept has increased it must be driven by the cost.
SO THEREFORE IF ONE OF THE FACTOR PRICES GO UP WE SHOULD GO TO THE AXIS IN WHICH THE FACTOR PRICE DIDNT CHANGE AND DEDUCE FROM THERE
What are the exceptions to the cost increasing when the price of an input rises? ( will the cost always increase)
The cost may not always increase, lets think about it an increase in Ra to Rb, means we have a subistuiton effect, capital is more expensive and you substitute away from capital towards labour but your still employing capital, which is more expensive than before and overall cost has increased. So the only exception is if the firm does not employ the factor whose price rose ( cost is unchanged
Now that we have a cost function( minimum cost assuming firm wants be efficient as possible, how would be work out total cost, average cost and marginal cost)?
How do MC AND AC relate to each other?
1) MC > AC average cost is increasing ( if a tall person walks in a room and he is taller than average height, then the average height is raised
2) If MC< Ac average cost is falling ( if a short person walks into the room and he is shorter than average, then the average will be falling.
What is constant returns to scale?
If i double my inputs = double my outputs.
What is increasing returns to scale and what is decreasing returns to scale?
IRTS ( IF I DOUBLE MY INPUTS I GET MORE THAN DOUBLE OUTPUT)
DRTS ( IF I DOUBLE MY INPUTS I GET LESS THAN DOUBLE MY OUTPUT)
I think the signs are wrong here.
In an exam we are likely going to have to demonstrate a function has constant, increasing or decreasing returns to scale. So show the 3 scenarios here of RTS?
now what does Economies of scale, Diseconomies of scale and neither Economies or diseconomies of scale mean?
1) Economies of scale: where AC falls with output
2) Diseconomies of scale: where AC rises with output
3) Neither economies nor diseconomies: where AC does not vary with output
We are going to diagrammatically show how RTS link to EOS?, so show Constant returns to scale on a K as function of L diagram? What is the link to cost here?
I want to scale my inputs to double, this means i double my quantity = CRTS
Y intercept goes up so must mean cost has doubled, so total cost is proportional to output.
As we know total cost is proportional to output, draw a diagram showing cost on y axis and quantity of x axis, for constant returns to scale.
As you know that costs are linear with CTS, what must it mean for mc=ac? ( HINT make up a equation for this line), hence is their EOS?
If we make up an equation of c=5q because this line is linear, when we differentiate it the mc = 5 and the ac = 5, hence MC=AC and do not vary with output.
How do we draw increasing returns to scale? ( HINT think about it in terms of cost)? What is the shape of the function on diagram?
Doubling inputs more than doubles output; doubling output less than doubles cost.
The function is concave.
We are going to look at AC and MC for IRTS, how do we find AC and MC?
How does this look on diagram?
1)To find AC, we draw a chord between origin and q, and gradient of this line is the average cost ( TC/q), if i increase my quantity we can see that the AC is falling( as gradient getting shallower, hence EOS.
2) To find MC we look at gradient at each particulate level of output and we see the gradient is falling too.
SO both are positive but AC AND MC both falling
So we know that both Ac and Mc are falling but which is bigger than the other?
MC less than AC (must be for AC to be falling!) - think about short person, if he comes into a room and less than average, he must bring the average down. so hence MC< AC
How do we draw Decreasing returns to scale? ( HINT think about it in terms of cost)? What is the shape of the function on diagram?
Shape is convex to origin.
Doubling inputs less than doubles output and more than doubles cost
We are going to look at AC and MC for DRTS, how do we find AC and MC?
How does this look on diagram?
1) To find AC, we draw a chord between origin and q, and gradient of this line is the average cost ( TC/q), if i increase my quantity we can see that the AC is rising ( as gradient getting steeper, hence DOS.
2) To find MC we look at gradient at each particulate level of output and we see the gradient is rising too.
SO both are negative but AC AND MC both rising
So we know that both Ac and Mc are rising but which is bigger than the other?(Draw it)
MC more than AC (must be for AC to be rising!) - If a man walks into the room and is taller than average, hence the average must be increasing.
So we established that we commonly see EOS AND DOS in same firm for Perfectly competitive markets so, For small q there are economies of scale, so AC falls For large q there are diseconomies of scale and AC rises. WHAT MUST THE COST FUNCTION LOOK LIKE?
how do we know that a firm that experiences EOS AND DOS, has this cost function( HINT PART A show me how AC changes over quantity)
So remember to denote AC, we find gradient from origin to different production levels, and see the gradient is falling ( getting shallower so this shows EOS) to a point. Until you hit point b, when you move beyond b, average costs start to rise. So b would be the minimum on a u shape cost function.
how do we know that a firm that experiences EOS AND DOS, has this cost function( HINT PART B show me how MC changes over quantity)
To look at MC, we look at gradient at each quantity, we see that it starts falling as quantity increases before A. so MC< AC.
Then at A MC = AC.
After A, the gradient at each quantity is increasing so MC increasing, so MC> AC.
Show U-shaped MC and AC
What is the difference between Long run total cost ( LRTC) and Short run total cost ( SRTC) ? What is higher LRTC ( When everything is flexible) or STRC( when capital is fixed)
LRTC can never be higher than SRTC
• Can often do better and never worse with more flexibility ( you can reoptimise in the long run or short run and long run can be the exact same)
What are the formulas for these ?
We are going to show finding SRTC, from the cobb-douglas function we solved earlier. Again this was the lRTC that was optimal.As you can see for any given w and r this is a constant. Firstly what is this firm facing CRS IRTS OR DRTS and what about MC AND AC?
1) Constant returns to scale ( linear cost function, if i double my inputs i get double my outputs)
2) MC AND AC are equal and constant
Suppose in the production ( think it might be planning still) period we fix capital so K = K*, how can we find SRTC? ( PART 1)
1) Take my production function and rearrange it to get L as a function of L and q ( So i know i will produce q in the short run and K is a fixed number, i can find the level of labour to achieve that q supposing capital is fixed.
2) so we use the question then sub in K* which is fixed.
So for example if i had one unit of capital and i wanted to produce 1 unit of output, i would need 1 unit of labour.
So we have found how much labour i would need to achieve quantity q, given fixed capital, now what is my SRTC?
My cost is always 2 parts, cost of labour + cost capital.
1) We sub in the w x labour to find cos of labour with fixed K* + cost of capital rK*( this is just the equivalent of wL + rK with optimal quantities).
I know that this is short run total costs because in the long run we only have a variable costs, but in the short run we can have both.
So we know this is short run total cost? now work out SRAC AND SRMC?
What does this diagram show and why are they same at q1?
rk is your fixed cost and then you have increasing variable cost.
In the long run its just linear.
At q1 this shows optimal planning, correctly anticipating the quantity, the capital you choose in the short run was the right one.
If you are too the left of q1 you installed too much capital, if you are too the right of q1 you have installed too little capital.
Problem set 1i and ii)
Problem set 1iii)
Problem set 2i)
2ii part i check for NS and Convexity
2ii part b) find conditional factor demands
2ii part c ) cost function
2iii)
