Long Run Profit Maximisation & Competitive Markets Flashcards
LR PM equation
π = py - w₁x₁ -w₂x₂
(Same as short run except x₂ no longer fixed)
How solve the LRPM problem
differentiate with respect to both x₁,x₂ since LR both factors are variable
P (δf/δx₁) - w₁ = 0
P (δf/δx₂) - w₂ = 0
to get
pMP₁= w₁
pMP₂=w₂
Use CD function to replace f in the first order conditions just worked out.
CD = x₁ to the a x₂ to the b
pax₁ to the a-1 x₂ to the b - w₁ = 0
pbx₁ to the a x₂ to the b-1 - w₂ = 0
then times first one by X₁ and second one by x₂
pax₁ to the a x₂ to the b - w₁ = 0
pbx₁ to the a x₂ to the b - w₂ = 0
then denoting output ax1 to the a and x2 to the b as Y (output), we get…
pay - w₁x₁ = 0
pby - w₂x₂ = 0
rearrange to make optimial x1 and x2.
x1 = pay/w1
x2=pby/w2
then sub back into CD function, then we can solve to find y.
Constant returns to scale is the case where ouptut is undefined. Why, and what assumptions do we have to make (2)
CRS means doubling input doubles output. Assuming prices of the good, and the prices of the two factors don’t change, profit must double. This means one of 3 things must be true….
If CRS exists… 1/3 things must be true
1. If any one positive level of output is profitable…
- If any one positive level of output is profitable… increasing output willl always increase profits.
- If any one positive level of output leads to a loss…increasing output will always increase losses
- If any one positive level of output means the firm breaks even, this will be true at every output level.
If any one positive level of output leads to a loss
increasing output will always increase losses
- If any one positive level of output means the firm breaks even,
this will be true at every output level.
This means the only feasible outcome with constant returns to scale appears to be zero profits. Why is this unrealistic (4)
CRS may not apply for all output levels
Large firms may have price-setting power (reject fixed p assumption)
High output may lead to lower price (reject fixed p assumption)
Factor demand may affect factor prices (reject fixed factor p assumption)
Why may CRS not apply for all output levels
Producing very small or large inputs can be inefficient. i.e diminshing marginal product.
2nd reason why CRS may not create zero profits:
Large firms may have price setting power
If producing a huge amount, firm may be so big it has price setting power, and so the assumption of fixed P might not hold.
3rd reason why CRS may not create zero profits:
High output may lead to lower price
May need to drop price, so again assumption of fixed P may not hold.
4th reason why CRS may not create zero profits:
Factor demand may affect factor prices
If producing a lot, firm may need to pay more to acquire more of the F.O.P. So rejects assumption of prices of the 2 factors being constant.
Next subtopic:
Competitive markets - key feature
Firms are price takers.
Why? (3)
many small firms
identical products
perfect information so cannot sell above the market price
Demand curve in a competitive market
Horizontal since price takers so no firm can sell anything above the market price - firm can sell as much as it wants to at that price
Competitive firm’s supply decision
Deciding how much to sell at the given price.
Competitive firms supply decision : how does it maximise profit
FOC gives us
P=MC
What must be considered also in this choice?
If MC is U shaped- if U shaped there may be 2 points of output for a single price so need to choose between them.
(look at pg 10)
at output slighty from y1, p>mc so revenue is increasing, so clearly not maximised profits yet.
at t right of y2, p<mc, so profit falls, showing that y2 is the maximised point.
Where does a firm not want to produce (same as alevel)
Where is the supply curve?
If price < AVC
Shown by supply curve being the part of the MC curve above the lowest point of AVC. (Since will only supply above the AVC point)
Producer surplus for a competitive firm (pg12)
1 diagram for a normal linear supply curve, and other with the supply curve starting at the short run shutdown output
In between pL and p*
Producer surplus vs profit difference.
- how can we express profit as a function of producer surplus
Producer surplus only considers variable costs.
Profit= PY - Cv(y) - F
Producer surplus = PY - Cv(y)
- Profit = Producer surplus - fixed cost.
On cost revenue diagram, where is profit, PS, variable costs and fixed costs.
(Draw a diagram of a competitive firm making profit)
(pg13)
Profit is blue rectange (difference between P and AC x Y)
Producer surplus is difference between P and AVC x Y (sum of blue and orange rectangles)
Variable costs is AVC x Y (white rectangle)
So fixed costs is orange area (difference between AC and AVC x Y)
Long run supply - what is important to note about the supply curve
Since all costs are variable, a firms long run supply curve is part of the LMC above LAC.
(i.e will only produce if above average cost - same intuition as short run where supply curve is the MC curve above the AVC, except this time LMC above LAC)
Whereas in the short run the supply curve is part of the SMC that is above AVC (it will continue to produce as long as P>AVC since it is still contributing to fixed costs)
Diagram to show LR and SR supply. (pg15)
What is important to note
LR supply curve (part of LMC above LAC) is flatter than SR supply curve (part of SMC above AVC)
Because supply can be more responsive (elastic) to change in price.
Why is LR supply curve (LMC above LAC) flatter than SR supply curve (SMC> AVC)
(i.e costs go up proportionally slower following a rise in output)
Easier to change F.O.P e.g increase factories and labour.
In short run restricted, perhaps only be able to increase workers into a factory.
Industry supply - how do we find?
Sum our supply curves horizontally.
i.e add together the quantities the firms are willing to sell at that price.
we will use 2 examples:
Industry with 2 firms with different supply curves
Industry with 2 or more firms with identifical supply curves
1st scenario: (top graph pg16)
Industry with 2 firms with different supply curves
Firm 1 produces output y1.
Firm 2 produces output y2.
And to find industry supply we just add them together. so = y1+y2
2nd scenario: (bottom graph pg16)
2 or more firms with identical supply curves
if firms have identical supply curves, industry supply is just one firms output x no. of firms
So with identical supply curves, what does free entry/exit imply:
and what profit is made in equilibrium?
Firms are responsive to profit incentives.
Firms leave if making losses, enter if profit exists.
In equilibrium we say firms earn 0 profits. (In reality it is slightly above 0 profits as shown later)
IN THE LONG RUN:
With identical supply curves (competitive market), what is the lowest price they will supply at?
And what if the price is below this?
The lowest price they will take is the bottom of LAC curve, which we call p*.
If p<p*, at least one firm will leave in the long run.
(rmb this is for long run - may stay in short run if.. pto)
Now consider demand side
Pg 17 - 4 firms example with demand curve - where would the price be, and how many would operate?
Price would be where demand curve and s(3) intersect, which is slightly above p*. So profits made.
4th firm wouldn’t enter since it anticipates price falling below P* if it were to join and increase output further, thus explaining the price fall, and so would make a loss.
so therefore in this example, 3 firms would operate in this market
What if we started with 4 firms?
The price would be where D=s(4)
They may all stay in the market in the short run if the price where D intersects S(4) is above avc. (so they can contribute to their fixed costs)
But the first firm able to vary its (short-run) fixed factor would leave the market, and three firms would remain.
So, in the long run, this market would support three firms.
What is the number of firms in a market with free entry/exit determined by? (Pg 18)
Demand conditions: we can see through the diagram a shift in demand can change the number of firms in the market.
At original demand curve, only 3 firms are profitable.
At new demand curve D’, 4 firms are now profitable (p>p*).
So how how is the number of firms in a competitive market defined?
It is highest number of firms that makes non-negative profits.
(p slightly above p* as demonstrated in our examples)
(so its not exactly when profit is zero, just a very good approximiation)
Now we can see the LONG RUN supply curve in a competitive market.
How is this represented
LRAS is the highest number of firms where supply curve lies above p*.
We mark this by bold sections for each supply curve.
As we add more firms and their supply curves, each curve gets flatter. (Pg19 diag shows this)
Gets closer to horizontal, so we just assume a horizontal LRAS. (Pg20)
So, in a competitive market profits are approximately 0.
Whats if there is something that limits free entry?
e.g a license to enter an industry, issued to the highest bidders.
How much will license cost, and will the successful bidders earn profits?
License cost r, and we treat it as a fixed cost that not everyone is able to pay (since have to bid for finite licenses - essentially a long run constraint on firms entry)
What is economic rent
The amount a F.O.P is paid in excess of the minimum payment required for it to be supplied.
E.g worker willling to work for a low wage but gets paid more.
What do we assume
We assume it is constless to produce/administer licences (0 cost), and all other costs are variable costs
Profit of firm obtaining a licence expression
π= py - cv(y) - r
(Remember cost of licenses is treated as a fixed cost.
How is cost of the license determined
Since licnences are finite and competed for, the cost (r) is determined by firm’s WTP.
What would the cost of the license be, and what is significant to note about this expression??
The cost that results in firms making 0 profit.
so
π = py - Cv(y) - r = 0
which can be rearranged as
r=py* - Cv(y*) WHICH IS PRODUCER SURPLUS!!
The amount firms would pay for the licence r would be equal to their producer surplus
Pg 21 licences diagram + explain shaded sections
P=MC=AC as competition for licenses competes profits down to 0.
Rent seeking and example
When factors are fixed in supply, some PS is lost as economic rent. This can lead to artificially creating scarcity.
e.g licensing goods to restrict supply without good reason, just for the licence issuer to gain rent
