question
Static Oligopoly Model
answer
n firms, each firm chooses an action once
choices are simultaneous
no scope for any firm to react to rivals choices or influence each other
each firm chooses its action to maximize its own payoff taking as given the choices it expects by other firms
choices are simultaneous
no scope for any firm to react to rivals choices or influence each other
each firm chooses its action to maximize its own payoff taking as given the choices it expects by other firms
question
Cournot Model
answer
each firm chooses a quantity it offers for sale, a=q
question
Bertrand
answer
each firm chooses a price at which its willing to sell any quantity, a=p
question
Examples of Markets
answer
Cournot: oil or other commodity markets
Bertrand: differentiated products with constant marginal costs
Bertrand: differentiated products with constant marginal costs
question
Nash Equilibrium
answer
A firm's payoff can depend on its action a and the vector of all other firms actions --> under differentiated products Bertrand competition
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Homogenous Products Cournot
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profits of any firm i depend only on its output q and the total of other firms outputs
question
Non-Cooperative Nash Equilibrium
answer
A set of actions, one for each firm, such that for each firm i, taking as given the equilibrium choices of others, its own choice a is at least as good for it any other feasible choice
The action is the best response function of i to expected choices of others
The action is the best response function of i to expected choices of others
question
Cournot Competition Linear Case
answer
firms sell homogenous products
price determined when total quantity by all firms is given to an auctioneer who sets market clearing price
we can see how price varies as a function of our own choice of q
each firm behaves as a monopolist on its own inverse residual demand -- residual demand depends on the given choices of other firms, which are correctly expected by each firm
price determined when total quantity by all firms is given to an auctioneer who sets market clearing price
we can see how price varies as a function of our own choice of q
each firm behaves as a monopolist on its own inverse residual demand -- residual demand depends on the given choices of other firms, which are correctly expected by each firm
question
Best Response Function Cournot
answer
monopoly output minus 1/2 the output it expects of others, because increasing rivals output by Δ shifts i's residual demand left by Δ, so its MR shifts left by Δ/2. With constant MC, its optimal output decreases by Δ/2
question
Duopoly Equilibrium
answer
simultaneously solving the two FOCs, which gives the cournot equilibrium outputs as functions of only the demand and cost parameters
firms output increases if its own marginal cost falls or if the rivals rises, and (a) effect is stronger than (b)
q=(a-2c1+c2)/3b
firms output increases if its own marginal cost falls or if the rivals rises, and (a) effect is stronger than (b)
q=(a-2c1+c2)/3b
question
n symmetric firms
answer
if all have identical marginal costs
q=1/(n+1)*Qpc
Qc=n/(n+1)Qpc
Qpc=(a-c)/b
q=1/(n+1)*Qpc
Qc=n/(n+1)Qpc
Qpc=(a-c)/b
question
Under Supply Socially
answer
cournot industry output is below the optimal level for society
any active firm has price above MC, so expanding its output would raise welfare
any active firm has price above MC, so expanding its output would raise welfare
question
Over-Supply Privately
answer
industry output is above the optimal level for the industry
expansion by firm j harms any other firm i by depressing price which reduces i's revenue in proportion to i's output
expansion by firm j harms any other firm i by depressing price which reduces i's revenue in proportion to i's output
question
Misallocation of production across firms if MCs differ
answer
equilibrium industry output could be produced at lower cost by shifting output from firms with higher MCs to firms with lower MCs
in cournot, firms with lower MCs do have higher ouputs, but higher MC firms still survive despite selling homogenous products, so industry cost could be reduced by shifting additional output away from them
in cournot, firms with lower MCs do have higher ouputs, but higher MC firms still survive despite selling homogenous products, so industry cost could be reduced by shifting additional output away from them
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