TR, MR and Demand TR= PQ,MR= (TR)/ Q D MR |E|=1

TR, MR and Demand

TR= PQ, MR=(TR)/Q

D

MR

|E|=1

Production and Costsan 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 = Q/L

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 lessproductive 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 = TC/Q = TVC/Q

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

Isocostw L + r K = C

L

K

C/w

C/r-(slope) = (C/r)/(C/w) = w/r

IsoquantQ = f ( L, K ) = constant

K

L

-(slope) = (dK/dL)dQ = MPL dL + MPK dK

dK/dL = MPL/MPKdK/dL – MRTS of labor for capitalSet dL =1

Equilibriumcost minimization

MPL/MPK = w/rw/MPL = r/MPK

the last $ spent on capital brings the samechange in output as the last $ spent on labor

K

L

returns to scale% change in inputs => % change in output

(% output) > (%inputs) increasing returns

Q = KL if > 1 then we have increasing returns to scale.

economies of scale and the LRACspecialization and technology

economies of scopesharing of inputs

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yxc

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Cost minimization

MPL/MPK = w/rw/MPL = r/MPK

the last $ spent on capital brings the samechange 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

monopoly Perfectcompetition

oligopoly mc

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 monopolybarriers 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 behaviorOligopolies arise because of the same reasons as

monopolies.

Models for studying OligopolyKinked Demand Model (discontinuous MR)Cournot Duopoly ModelGame 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 productionobtaining total MC

Multi-market marketingprice discrimination vs price differentiationobtaining total marginal cost curve