Download 2. Non-Sunk Costs

Review of Producer Choice
1. Production function
- Types of production functions
- Marginal productivity
- Return to Scale
2. The cost minimization problem
- Solution: MPL(K,L)/w = MPK(K,L)/r
- What happens when price of an input changes?
3. Deriving the cost function
- Types of costs (Fixed and Variable)
- Short-run costs and long-run costs
- Properties of the cost function (marginal and average costs)
Economies Of Scale
Definitions
We say that a cost function exhibits economies of scale, if the average cost
decreases as output rises, all else equal.
We say that a cost function exhibits diseconomies of scale, if the average cost
increases as output rises, all else equal.
The smallest quantity at which the long run average cost curve attains its
minimum point is called the minimum efficient scale.
Economies Of Scale
Economies of scale, diseconomies of scale, minimum efficient scale.
AC ($/yr)
AC(Q)
Q (units/yr)
0
Q* = MES
Economies Of Scale
Why are there economies of Scale?
1. Increase returns to scale- Fixed costs
- Larger scale of production permits more specialized inputs.
2. Decreasing return to scale- Organizational structure and managerial costs
- Adding software engineers increases communication costs: If there are n engineers, there
are ½n*(n – 1) pairs, so that communication costs rise at the square of the project size
- “The Peter Principle”: Workers move up until they become incompetent
- System slack: it is easier to hide inefficiencies in a large organization than in a small one
Economies Of Scale
Economies of Scale and Returns to scale
-
When the production function exhibits decreasing returns to scale, the long
run average cost function exhibits diseconomies of scale
-
When the production function exhibits increasing returns to scale, the long
run average cost function exhibits economies of scale
-
When the production function exhibits constant returns to scale, the long
run average cost function is flat: it neither increases nor decreases with
output.
Economies Of Scope
External economy of scale, or an industry economy of scale: Industry demand
can effect the price of inputs
A firm has Economies of Scope if production of various related goods, decreases
the average costs
Example: Boeing produces both commercial and military jets. Even though
production is separate, there are various externalities that may reduce costs
When there are Economies of Scope producing other goods decreases average
costs
When there are Economies of scale producing more decreases the average costs
Economic Costs
Definition: the Economic Profit is the between total revenue and the economic
costs
Difference between economic profit and accounting profit: The economic profit
includes the opportunity costs
Example: Suppose you start a business:
- the expected revenue is $50,000 per year.
- the total costs of supplies and labor are $35,000.
- Instead of opening the business you can also work in the bank and earn
$25,000 per year.
- The opportunity costs are 35,000+20,000=55,0000
- The economic profit is -$5,000
- The accounting profit is $15,000
Main Goal: Derive the Firm’s Supply
Definition: the Economic Profit is the different between total revenue and the
economic costs
A firm takes the price as given and chooses Q to maximize profit.
When the firm sells Q units, it’s profit is given by
  pQ  TC (Q)
or
  TR (Q)  TC (Q)
The Firm’s Problem: Profit Maximization
The single firm’s problem:
max  (Q)  TR (Q)  TC (Q)
Q
- The Marginal Revenue is the rate which Total Revenue changes with output.
TR(Q)
MR(Q) 
Q
“When the firm increases output by an additional “small” unit, the
marginal revenue is the additional revenue generated”
- The Marginal Cost is the rate which Total Cost change with output.
TC (Q)
MC (Q) 
Q
“When the firm increases output by an additional “small” unit, the marginal cost
is the additional cost incurred generated”
Profit Maximization
The single firm’s problem:
max  (Q)  TR (Q)  TC (Q)
Q
Optimality condition:
If MR> MC then profit rises if output is increased
If MR < MC then profit falls if output is increased.
Therefore, the profit maximization condition for a price-taking firm is MR = MC
What is the marginal revenue? the price as given, therefore marginal revenue is just
TR
the price
MR 
p
Q
Optimality condition:
And the firm chooses quantity such that:
P = MC(Q)
Profit Maximization
Optimality condition:
1. P = MC(Q)
2. MC(Q) increases
Short Run Supply
In the Short Run there are some fixed inputs:
1.There are fixed costs
2.Total Costs of producing Q units: Total variable costs + total fixed costs
What are the firm’s Costs when producing 0? Fixed costs consist of
1. Sunk costs are unavoidable- for example patent licensing cost
2. Non-Sunk Costs can be avoided- for example if the firm can rent out
some of the capital.
The key difference is Sunk costs are incurred when the firm produces
nothing, and non-sunk costs can be avoided
Short Run Supply
Example: Off-shore drilling
Independent contractors are hired by a petroleum company to drill wells in
the sea , using oil rigs:
Short Run Supply
Example: Off-shore drilling
What are the costs of a contractor who runs
an off-shore oil rig?
- Personnel: Crew managers, engineers,
marine personnel, drilling workers….
- Drilling supplies such as drills and fuel
- Maintenance costs, food, medical care
- Insurance
Key point: personnel costs are fixed because
the contractor commits to hiring the workers,
before she knows whether there are wells to
drill
- Drilling supplies and fuel are variable costs
Short Run Supply
Example: Off-shore drilling
When there are no wells to drill, the output is
zero. What are the costs to the contractor in
this case?
There are several options:
1. A “Hot Stacked” rig is taken out of service but remains fully stacked with workers and
ready to operate- in this case all fixed costs are sunk, but variable costs are avoided.
2. A “Cold Stacked” rig is taken out of service for a long period of time, the crew is laid off
and the doors are welded shut. In this case the only sunk cost is the insurance, while
the other fixed costs are non-sunk
Short Run Supply
Question: When does the firm choose to produce, and when does the firm prefer to shut down?
Assume all fixed costs are sunk: P*Q – TVC(Q) – TFC > -TFC 
P*Q – TVC(Q) > 0  P > AVC(Q)
Key definition:
If the price drops below the shut down price the firm prefers to produces
nothing than any positive amount.
Note: A firm may choose to operate in the short run even if economic profit is negative.
Important to remember: if the firm produces output Q and sells it for a price p then;
1. When p>ATC(Q) the firm makes a profit. When p<ATC(Q) the firm loses money
2. When p>AVC(Q) the firm produces Q>0, when p<AVC(Q) the firm shuts down
3. When AVC(Q)<p<ATC(Q) the firm operates at a loss
Short Run Supply
Key Definition: A single firm’s Short run supply curve specifies the profit maximizing
output for each market price.
The firm’s short run supply curve is give by:
1. When P < Ps the firm chooses to produce nothing, Q=0
2. When P > Ps the firm chooses to produce Q>0 such that MC(Q)=p
$
SMC
ATC
AVC
Ps
Quantity
In this case all fixed costs are sunk:
At prices below ATC but above AVC,
Even though profits are negative , the
firm is better off producing than
shutting down because of sunk costs.
Short Run Supply when all fixed costs are sunk
What if some fixed costs are not sunk?
When does the firm choose to produce, and when does the firm prefer to shut down?
Now, TFC = SC + NSC, and when the firm produces it incurs the NSC and the variable
costs
P*Q – TVC(Q) – NSC-SC > -SC 
P*Q – TVC(Q) -NS> 0  P > AVC(Q)+NS/Q
ANSC = AVC + NSFC/Q
Now, the shut down price, Ps is the
minimum of the ANSC curve.
.
Short Run Supply when some fixed costs are not sunk
The firm’s short run supply curve is give by:
1. When P < Ps = the firm chooses to produce nothing, Q=0
2. When P > Ps the firm chooses to produce Q>0 such that MC(Q)=p
Short Run Supply
Example: all fixed costs are sunk
Suppose a firm has the following cost function TC(Q) = 100 + 30Q -10 Q2 + Q3
What is the supply curve?
Solution in two steps:
i. Figure out the shutdown price
ii. Figure out how much the firm produces
TFC = 100 (sunk)
ATC(Q)=100/Q+30-10Q+ Q2
TVC(q) = 30Q -10 Q2 + Q3
AVC(q) = 30-10Q+ Q2
MC(q) = 30 -20Q+3 Q2
Shutdown price: p=MC(Q)>AVC(Q)
- When q=5: mc(q)=AVC(q), shutdown price p=mc(5)=5
The firm’s short run supply curve is:
- If the price is P < 5: then the firm produces nothing Q = 0
- If price is P > 5: then P = MC(Q)  P = 30 -20Q+3 Q2
Short Run Supply
Example: all fixed costs are not sunk
Suppose a firm has the following cost function if Q>0
TC(Q) = 100 + 20Q + Q2 and if Q=0 TC(Q)=0. What is the supply curve?
Solution in two steps:
i. Figure out the shutdown price
ii. Figure out how much the firm produces
TFC = 100 (non- sunk)
TVC(Q) = 20Q + Q2
ATC(Q) = 100/Q+20 + Q
MC(Q) = 20 + 2Q
When all fixed costs are non sunk the firm produces only if P>ATC, Why?
Shutdown when p=MC(q)=ATC(Q) or when q=10. Therefore the shutdown price is p=40.
The Firm’s demand is:
- If the price is P < 40: then Q = 0
- If price is P > 40: then P = MC(Q)  P = 20+2q  Q = 10 + ½P
Short Run Market Supply Curve
Definition: The short run market supply is the sum of the quantities each firm
supplies at that price.
Example: suppose 3 types of firms with different marginal costs and different shut down
prices. Each firm has a different