Download Production and Costs

TR, MR and Demand
TR= PQ,
MR=D(TR)/DQ
|E|=1
D
Production and Costs
an Economist’s view
Q = f ( L, K,….)
Short-Run (production): K – fixed
Long-Run (planning): everything is flexible
Measures of productivity
• Total product (TP)
TP = Q (L, K) = L1/2 K1/2
Fixed vs variable proportion functions
- Average Product (AP)
APL = Q/L
APK = Q/K
- Marginal Product (MP)
MPL = DQ/DL
Law of Diminishing Marginal Product
– Seen in the slope of the MP curve
– More intense usage of fixed input by the
variable inputs may initially increase Q;
however, after a certain point inputs are less
productive and produce less output for each
additional input added
– Can employ additional inputs when MP is
decreasing. Do not employ additional inputs
when MP is negative
• Relationships between MP, AP, and TP
If MP>0 then TP is rising
If MP<0 then TP is falling
If MP is rising then the output function is
convex
If MP is falling then the output function is
concave
MP as the slope of the production function
If MP>AP then AP is rising
If MP<AP then AP is falling
Costs of Production
fixed vs. variable vs. sunk
Opportunity cost (explicit + implicit)
Cost of Labor: wage bill
User Cost of Capital: Economic Depreciation
+ Interest Rate * Value of Capital
costs
TC = w L + r K
Variable (w L), fixed (r K)
Averages:
ATC = TC/Q AVC = TVC/Q AFC = TFC/Q
Marginal: MC = DTC/DQ = DTVC/DQ
Some cost identities and profit
maximization in the short-run
•
•
•
•
MC=MR
MC = w / MPL
W = VMPL=MR*MPL
AVC = w / APL
Long-run costs
Everything is variable
Isoquant and Isocost analysis
&
Input substitution
Isocost
wL+rK=C
K
C/r
-(slope) = (C/r)/(C/w) = w/r
C/w
L
Isoquant
Q = f ( L, K ) = constant
K
-(slope) = (dK/dL)
dQ = MPL dL + MPK dK
dK/dL = MPL/MPK
dK/dL – MRTS of labor for capital
Set dL =1
L
Equilibrium
cost minimization
K
MPL/MPK = w/r
w/MPL = r/MPK
the last $ spent on capital brings the same
change in output as the last $ spent on labor
L
returns to scale
% change in inputs => % change in output
(%D output) > (%D inputs) increasing returns
Q = Ka Lb if a + b > 1 then we have increasing returns to
scale.
economies of scale and the LRAC
specialization and technology
economies of scope
sharing of inputs
scope 
c ( x ) + c ( y )  c ( x, y )
c( x, y )
Cost minimization
MPL/MPK = w/r
w/MPL = r/MPK
the last $ spent on capital brings the same
change in output as the last $ spent on labor
Profit maximization
Profit = total revenues – total costs
Profits are maximized when MC = MR
MC = W/MPL => W = MR * MPL
market structure
oligopoly
monopoly
mc
Perfect
competition
Perfect competition and the
internet
Assumptions:
-
number of firms
Ease of entry and exit
Perfect information
Identical transaction costs
Homogeneous good
Horizontal demand and MR.
Shut down and break even price levels
Long-run and cost structure of the industry
monopoly
• Market power & MR
• What is Monopoly and why do they exist?
natural monopoly
barriers to entry (legal, brand loyalty….)
is Microsoft a monopoly?
Measures of monopoly power
- elasticity approach
- Learner index (P-MC)/P
Monopolistic competition
Large number of firms and heterogeneous goods
oligopoly
Few players and strategic behavior
Oligopolies arise because of the same reasons as
monopolies.
Models for studying Oligopoly
Kinked Demand Model (discontinuous MR)
Cournot Duopoly Model
Game Theory
Bertrand and Stackelberg Models
Game theory
Cooperative vs non-cooperative games
Basic 2X2 game framework analysis
Price leadership models, airlines
Tacit collusion (explicit)
Implicit collusions and the MIT case
Tree form games and entry deterrence
Multi-plant production
obtaining total MC
Multi-market marketing
price discrimination vs price differentiation
obtaining total marginal cost curve