# L1 - Refresher of Microeconomics Flashcards

How to find the equilibrium price and quantity under a monopoly?

Ex. inverse demand curve ==> P = 9 - 0.5Q and Monopolist total cost function is TC(Q) = 0.5Q^{2}

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How to find the equilibrium price and quantity under perfect competition?

Ex. inverse demand curve ==> P = 9 - 0.5Q

How will we be measuring welfare in this module?

- Consumer surplus ==> area below demand curve but above price ‘p’
- producer surplus ==> area above marginal costs line but below price ‘p’
- if p > MC there will always be some deadweight loss in the market

It is normally assumed that firms are big enough to look after themselves whereas consumers are quite small –> so policymakers tend to like to look after consumers more

How do you calculate consumer surplus under a monopoly and perfect competition?

- Monopoly produces Q at point MR = MC
- Then gets price from the demand curve

- Under Perfect Competition
- P = MC so sub into the demand curve to find Q

Core things you need to remember about game theory?

- A game consists of PLAYERS, STRATEGIES, INFORMATION, TIMING, PAYOFFS
- There is a Nash equilibrium when: no player can do better than their chosen strategy, given their beliefs of how other players will play
- we use backwards induction to solve sequential games

What are the model and assumptions of Cournot’s model?

What would a Nash equilibrium mean in Cournot’s model?

- by maximising the differential of the profit function we get the best response function

Cournot’s model: What does the best response function of each firm look like on a graph?

How do we find the equilibrium quantities under Cournot’s model?

- We have sub in the nash equilibrium quantity in for both firms and then rearrange
- Equally can sub one quantity for first ‘i’ into the other firm’s best response function to derive the same answer

- profit function is for firm ‘i’ only!!!!
- CS formula is the area of the triangle above the price (would be easier to see from a diagram)

What is the model and assumptions of Bertrand’s model?

- As products as homogenous consumers will only pay the lowest price in the market for it

How can we derive the Nash Equilibrium in Bertrand’s model?

- Formally the profit I get from setting the price at the NE level greater than or equal to the profit I would get by setting the price at any other level

What does the Bertrand-Nash equilibrium look like on a graph?

- looking at the orange line which is firm ‘i’s best response function
- if firm j charges a high price ==> firm i will set its price at the monopoly level p
^{M}(to a straight line) - in the middle firm j will always set its price equal to firm ‘i’s, so there is always an incentive to slightly undercut them and take the total market share of demand (hence the downwards slope towards MC)
- if firm J prices are too low ==> firm ‘i’ will set their price at MC and won’t go any lower

- if firm j charges a high price ==> firm i will set its price at the monopoly level p

What is the Bertrand Paradox?

- The result of the Bertrand model is known as the Bertrand paradox Why?
- Consider the implications of the Bertrand-Nash equilibrium:
- 1) Suppose there was only one firm in the market: this firm would be a monopolist and would charge a high price
- 2) Suppose another firm enters the market that sells an identical product: the firms set the price that would be set under perfect competition…

The paradox is that, by adding only one firm, we go from:

- the extreme of monopoly power to the other extreme of no market power!
- In reality, we do not observe this, so there must be something wrong - but what?
- something is wrong with Bertrand’s assumptions e.g. don’t have the same costs, production capability and scale ( maybe cant serve the whole market)

What would happen under Bertrand’s model if firm j’s marginal cost were less than firm i’s?

- Firm i’s best response function would shift upwards
- firm j can now set their price lower than firm i (marginally undercutting even though this is both firm’s best responses)
- this would mean firm j takes the whole market, and earns positive profits as p
_{j}* > MC_{j}–> this breaks the Bertrand Paradox