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.