Profit maximisation Flashcards
Short run total cost formula
STC(q)= SFC + SVC (q)
- FC: fixed costs
- VC: variable costs
Short run average cost (formula)
SAC(q) = SAFC(q) + SAVC(q)
Short run marginal cost (formula)
SMC = STC’(q)
For SFC we assume
that fixed costs are sunk. They are incurred even if output level is 0
Profit formula
Profit = total revenue - total cost
= p * q - STC(q)
Profit analysis
at q= 0, profit = - STC(q)
at q> 0, profit> - SFC only if p> SAVC (q)
As a result, a profit maximising firm produces a positive output only if p>= min SAVC
If p> min SAVC, then we can find the optimal quantity q* w the first order condition
price = marginal cost
p = SMC(q*)
The firm either produces
q* as above (interior solution) or 0 (corner solution)
So the firm produces either q* as above (interior solution) or zero (corner solution). Therefore
the supply curve has 2 parts given by
- q=0 , when p< min SAVC
- SMC (q) when p>= min SAVC
For any q>= 0
profit = (p - SAC(q))q >= 0
- if and only if p>= min SAC
A competitive firm can operate when its economic profit is negative
happens if price is above min SAVC (shut-down price) but below SAC (break-even price)
SR curve shows
how the optimal production varies with the market price
In the SR
nb of producers is fixed
market supply at a given price equals the sum of quantities produced by each firm that is operating
Difference SR & LR
firms can adjust their capital levels (capacity adjustment)
firms may enter or exit the industry
Long run formula Profit
total revenue - total cost
= p * q - LTC(q)
Long run first order condition
price = LR marginal cost
p = LMC(q*)
In the long run, the firm either produces
q* (interior solution) as above or zero (corner solution)
In the LR any cost
is variable (no need to distinguish variable and fixed costs)
LR supply has
2 parts as well
- when p < min LAC, it’s the y axis
- when p >= min LAC, it’s LMC curve (portion above the long run AC curve)
LR market w a fixed
nb of firms
- no entry/exit
- the market supply is the horizontal sum of the supply curves of all firms operating
