Ch. 28. Oligopoly - Summary - Intermediate Microeconomics - Varian

28. Oligopoly

Oligopoly
A. Oligopoly is the study of the interaction of a small number of
firms
1. duopoly is simplest case
2. unlikely to have a general solution; depends on market struc-
ture and specific details of how firms interact

28.1 Choosing a Strategy
B. Classification of theories
1. non-collusive
a) sequential moves
1) quantity setting — Stackelberg
2) price setting — price leader
b) simultaneous moves
1) quantity setting — Cournot
2) price setting — Bertrand
2. collusive

28.2 Quantity Leadership

C. Stackelberg behavior
1. asymmetry — one firm, quantity leader, gets to set quantity
first
2. maximize profits, given the reaction behavior of the other
firm
3. take into response that the other firm will follow my lead
4. analyze in reverse
5. firm 2
a) maxy2 P(y1 + y2)y2 − c(y2)
b) FOC: P(y1 + y2) + P′(y1 + y2)y2 = c′(y2)
c) solution gives reaction function, f2(y1)
6. firm 1
a) maxy1 P(y1 + f2(y1))y1 − c(y1)
b) FOC: P(y1 + f2(y1)) + P′(y1 + f2(y1))y1 = c′(y1)
c) see Figure 26.2.
7. graphical solution in Figure 28.4.
D. Price-setting behavior
1. leader sets price, follower takes it as given
2. given p1, firm 2 supplies S2(p1)
3. if demand is D(p), this leaves D(p1) − S2(p1) for leader
4. hence leader wants to maximize p1y1 − c(y1) such that y1 =
D(p1) − S2(p1)
5. leader faces “residual demand curve”

28.5 Simultaneous Quantity Setting

E. Cournot equilibrium — simultaneous quantity setting
1. each firm makes a choice of output, given its forecast of the
other firm’s output
2. let y1 be the output choice of firm 1 and ye
2 be firm 1’s beliefs
about firm 2’s output choice
3. maximization problem maxy1 p(y1 + ye
2)y1 − c(y1)
4. let Y = y1 + ye
2
5. first-order condition is
p(Y ) + p′(Y )y1 = c′(y1)
6. this gives firm 1’s reaction curve — how it chooses output
given its beliefs about firm 2’s output
8. look for Cournot equilibrium — where each firm finds its
expectations confirmed in equilibrium
9. so y1 = ye
1 and y2 = ye
2

28.6. Example of Cournot
1. assume zero costs
2. linear demand function p(Y ) = a − bY
3. profit function: [a − b(y1 + y2)]y1 = ay1 − by2
1 − by1y2
4. derive reaction curve
a) maximize profits
b) a − 2by1 − by2 = 0
c) calculate to get y1 = (a − by2)/2b
d) do same sort of thing to get reaction curve for other firm
5. look for intersection of reaction curves

28.9 . Bertrand – simultaneous price setting
1. consider case with constant identical marginal cost
2. if firm 1 thinks that other firm will set p2, what should it set?
3. if I think p2 is greater than my MC, set p1 slightly smaller
than p2
4. I get all the customers and make positive profits
5. only consistent (equilibrium) beliefs are p1 = p2 = MC


28.10 . Collusion
1. firms get together to maximize joint profits
2. marginal impact on joint profits from selling output of either
firm must be the same
3. max p(y1 + y2)[y1 + y2] − c(y1) − c(y2)
4. P(y1 + y2) + P′(y1 + y2)[y1 + y2] = c′(y1) = c′(y2)
5. note instability — if firm 1 believes firm 2 will keep its output
fixed, it will always pay it to increase its own output
6. problems with OPEC
7. if it doesn’t believe other firm will keep its output fixed, it
will cheat first!

Ch. 24: INDUSTRY SUPPLY - Summary - Intermediate Microeconomics - Varian

Ch. 24: INDUSTRY SUPPLY


In Ch. 23, We have seen how to derive a firm’s supply curve from its marginal cost curve. In a market,  there will typically be many firms. So the supply curve the industry presents to the market will be the sum of the supplies of all the individual firms. In this chapter,  we learn how develop the
industry supply curve and make decisions based on it.

23.1 Short Run Industry Supply


A. Industry supply: Sum of the MC curves

(1) S(p) =



(2) Example:

Firm 1:            Firm 2:

c(y)= 2y2 +3          c(y)= 3y2 +3

MC= 4y                 MC=6y

P=4y                 P=6y

S1(p)= p/4         S2(p)= p/6

Market Supply: S(p) = S1+ S2= p/4 + p/6 = (10/24)p





B. Equilibrium in the short run



(1) Look for point where D(p) = S(p)



(2) can then measure profits ()of firms





C. Short run and long run supply



(1) If profits > 0, entry of new firms in the long run



(2) If any firm have identical cost structure, then

      Price in long run = minimum of AC-curve







D. Economic rent



(1) If no factors are scarce: Long run supply curve: Horisontal



P= minAC



All firms have Zero Profits

(no factors of production are "paid" more than its value,

i.e. the opportunity cost of the factor)



(2) What if some factors (of identical quality) are scarce in the long run? Because:

(a) licences/patents

(b) raw materials, land



(3) Entrants (new firms) will have higher costs



(4) "Old" firms will still have economic rents, because price won’t be as low as their minimum AC.

Ch. 23: FIRM SUPPLY - Summary - Intermediate Microeconomics - Varian

Ch. 23: FIRM SUPPLY

 In this chapter we derive the supply curve of a competitive firm from its cost function using the model of profit maximization.

We first  describe the alternative market environments in which a firm has to operate. But in this chapter we concentrate on pure competitive market only.


23.1 Market Environments

A. Firms face two sorts of constraints



(1) Technological - summarized in cost function



(2) Market constraints - how will

consumers and
other firms
react to a given firm’s choice



B. Assumption: Pure/perfect competition



(1) Price takers - takes market prices as given,

i.e. outside of any particular firms control

Example - if many "relatively" small firms


Demand curve facing a competitive firm




C. Supply decision of competitive firm



(1) maxy py- c(y)





(2) first order condition: Price = MC

p = c’(y)



(3) second order condition: c’’(y)  0

i.e. only upward-sloping part of MC-curve matters



(4) check that it is profitable to operate at all

revenue > Variabel Costs

py > cv(y)



p > cv(y)/y

price > Average Variable Costs



D. Example

c(y) = 2y2 + 3

cv(y) + F



[ Supply: Si(p) = 0.25p ]





E. Producer’s Surplus (PS)



(1) PS is defined to be Revenue - Variabel costs

py - cv(y)



(2) Since cv(y) = area under MC-curve



(3) PS = area above MC-curve





F. Long run supply



(1) L= Long Run



(2) LAVC = LAC Why?



No costs are fixed in the long run

i.e.  All costs are variable in the long run



(3) Long Run Supply more elastic than Short Run Supply



Demand Supply



ED =  ES =

[ES,L > ES,S]

Hal R. Varian - Intermediate Microeconomics A MODERN APPROACH - 9th Edition - Book Information and Chapter Summaries

Contents

1. The Market - Summary

2. Budget Constraint

3. Preferences

4. Utility

5. Choice

6. Demand

7. Revealed Preference

8. Slutsky Equation

9. Buying and Selling

10. Intertemporal Choice

11. Asset Markets

12. Uncertainty

13. Risky Assets

14. Consumer’s Surplus

15. Market Demand - Summary

16. Equilibrium

17. Econometrics

18. Auctions

19. Technology - Summary

20. Profit Maximization

21. Cost Minimization

22. Cost Curves

23. Firm Supply

24. Industry Supply

25. Monopoly

26. Monopoly Behavior

27. Factor Markets

28. Oligopoly

29. Game Theory

30. Game Applications

31. Behavioral Economics

32. Exchange

33. Production

34. Welfare

35. Externalities

36. Information Technology

37. Public Goods

38. Asymmetric Information

Mathematical Appendix

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Ch. 21. COST MINIMIZATION - Summary - Intermediate Microeconomics - Varian

Ch. 21.  COST MINIMIZATION

The profit-maximization problem can be split into two pieces.

First step in the problem is how to minimize the costs of producing any given level of output.
Second step is to choose the most profitable level of output.

In this chapter the first step—minimizing the costs of producing any given level of output is discussed.


A. Max profits require minimize costs

1. Minimize w1x1 +w2x2 s.t. f(x1, x2)=y

2. Geometric solution

    Isocost curves and isoquant for f(x1, x2)=y

    w1/w2=MP1/MP2



3. Optimal choice (X1*) is the conditional factor demand function

Function of input-prices

Conditional of level of production (y)



4. Examples

Perfect susbstitutes
Fixed proportions
Cobb-Douglas


B. Returns to scale and the cost function

(1) Increasing returns (to scale) - decreasing AC

(2) Constant returns - constant AC

(3) Decreasng returns - increasing AC



C. Long run and short run costs

(1) Long run: all inputs variable

(2) Short run: some inputs fixed



D. Fixed and quasi-fixed costs

(1) Fixed: must be paid, whatever the output level

(2) Quasi-fixed: only paid when output is positive




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Ch. 20 Profit Maximization - Summary - Intermediate Microeconomics - Varian

Ch. 20: PROFIT MAXIMIZATION


In this chapter,  a model of how the firm chooses the amount to produce and the method of production to employ based on the criterion of profit maximization is described.

We  assume that the firm faces fixed prices for its inputs and outputs. Where the individual purchasers have no effect on the prices is a competitive market. Hence we are studying the profit-maximization problem of a firm that faces competitive markets for the factors of production
it uses and the output goods it produces.


20.1 Profits

A. Profit: Revenues - costs

Each output and input valued at its market price: Opportunity cost
Measure in terms of flows


B. Short-run and long run maximization

Fixed factors
Quasi-fixed factors - eliminated at zero output


C. Short-run profit maximization

(1) max pf(x)-wx

(2) optimum when value of marginal product = price of (variable) input



D. Long run profit maximization

All factors are variable



E. Profit max and returns to scale



(1) Constant returns implies profits are zero

        But - all factors are rewarded at opportunity cost



(2) Increasing returns to scale:

        Competitive model doesn't make sense

Ch. 19 Technology Summary - Intermediate Microeconomics - Varian

Ch. 19: TECHNOLOGY

19.1 Inputs and Outputs

 Inputs to production are called factors of production. Factors of production are often classified into broad categories such as land, labor, capital, and raw materials. The input capital may require some more explanation.  Capital goods are those inputs to production that are themselves produced goods. Basically capital goods are machines of one sort or another: tractors, boiler, computer etc. that do certain jobs more efficiently than men.

Inputs and outputs of a production process are measured in flow units: a certain amount of labor per week and a certain number of machine hours per week will produce a certain amount of output a week.


19.2 Technological Constraints

A. Technology: What patterns of inputs and outputs are feasible













C. Technological constraints

(1) Production set - combinations of inputs and outputs that are feasible

(2) Production function: Upper bondary

(3) Isoquants: All possible combinations of inputs which yield the same level of output



D. Examples of isoquants

(1) Fixed proportions - Leontieff

(2) Perfect substitutes

(3) Cobb-Douglas

(4) Can't take monotonic transformations



E. Well-behaved technologies



(1) Montonic - more inputs produce more output

(2) Convex - averages produce more than extremes



 F. Marginal product



(1)  MP1: How much extra output you get from increasing input 1 - holding input 2 fixed

(2) MP1= d f(x1, x2)/ d x1



G. Technical rate of substitution (TRS)

(1)  Like MRS



(2) TRS= dx2/dx1= - = ¶ f/¶ x1/ ¶ f /¶ x1



H. Diminishing marginal product



(1) Law of diminishing return





I. Diminishing technical rate of substitution



(1) Equivalent to convexity

(2) Diminishing TRS is not the same as diminishing MP



J. Long run and short run



(1) Some factors fixed: Short run

(2) All factors varied: Long run



H. Returns to scale



(1) Constant returns

(2) Increasing returns

(3) Decreasing returns


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