1.9.1 Monopolistic/Game theory

Question 1

Assumptions

Answer 1

• Sellers price makers
• Buyers price takers
• Free entry and exit in long run

Difference to perfect/monopoly:
- Perfect price takers
- Monopoly single firm and no entry

Question 2

What are likely causes?

Answer 2

• Few firms in market
  Firms produce heterogenous/differentiated goods
  Sufficiently different from competitiors to make price maker, but similar enough to be affected by actions of other firms

examples: barbers (location), pubs, corner shops, magazines, chocolate

• Imperfect information and transaction costs present - important reason for market power
• Raise price to some extent before consumers switch

Question 3

What is profit max in short/long run

Answer 3

In short run make supernormal profits

In long run entrants shift the AR inwards until firms make normal profits (p = AC)
- Firms produce where MC = MR = p

Firms produce where AC > min(AC) - it is to the left of the bottom - excess capacity problem.
- Consumers value variety - fewer firms could operate at higher scale and lower AC but this would reduce variety
- In general, no guarantee equilibrium number of firms optimal

The number of firms in the long run depends on the fixed cost - high fixed cost mean fewer firms

Question 4

Calculus example of monopolistic

Answer 4

Q = q1+q2
p = 339 - Q
MC = 147
Fixed cost of F
Total cost C(q) = 147 + F

Short run:
Number of firms fixed, each firm maximises profit

Two firms:
- Each firm produces 64 units
- If a rival produces 64, remaining firms face residual demand:
P = 339 - Q = 339 - (64 + q) = 275 - q

TR = (275-q)q
MR = 275 - 2q
MR = MC when 275 - 2q = 147 and so q* = 64

As such when both firms produce 64 units maximising profit given output of rival firm: SR equilibrium

Since p = 339 - 128 = 211
Profit = TR - TC = (211 x 64) - (147 x 64) - F = 4096 - F
F = 4096, in SR equilibrium each firm makes 0 profits so also LR equilibrium

Question 5

What is a dominant strategy?

Answer 5

In game theory, dominant strategy produces a higher payoff than any other strategy the player can use for every possible combination
- A rational player must play a dominant strategy

Pretty simple

                qA =64         qB = 48

qB = 64 4.1/4.1 5.1/3.8
qB = 48 3.8/5.1 4.6/4.6

If B chooses 64, As best quantity is 64
If B chooses 48, As best quantity is 64

Thus the best strategy is qA = 64 for A

Question 6

What is Nash equilibrium

Answer 6

Many games do not have dominant strategy so use nash equilbrium

If both players use this, no player can obtain a higher payoff - all games have at least one nash equilibrium - it is the primary solution concept in game theory

To find it, look for strategies where each player uses the best response to rivals strategies:

Best response: identifying optimal strategy for every possible combination of strategies of other players
- IF player has dominant strategy this is her best response (since dominant strategy maximises payoff whatever rivals use)
- In general, best response varies with rival strategy choice