# Bertrand Competition - help! watch

1. If anyone could explain at least part of this i would be very grateful!!

asymmetric costs --> c1 < c2

The high-cost firm will never set a price below its marginal cost c2
For prices greater than c2, undercutting as in the symmetric case
When prices arrive at c2, the low cost-firm can still undercut the rival’s
price by a small amount, and steal all market

NE -> p1 ≈ c2, profit1 ≈ (c2– c1 )Q(c2) > 0

q2 = profit2 = 0

Market power (low-cost firm’s mark-up) ≈(c2-c1)/c2

It can be very small if the difference in costs is small

Concentration --> max degree (only the low-cost firm is active)

thanks
2. (Original post by redkopite)
asymmetric costs --> c1 < c2
basically it costs firm 2 more to make a product than firm 1

The high-cost firm will never set a price below its marginal cost c2
if revenue is less than the cost of making something, you make a loss, no rational firm will do this in the long run

For prices greater than c2, undercutting as in the symmetric case
When prices arrive at c2, the low cost-firm can still undercut the rival’s
price by a small amount, and steal all market
basically say c1=1 and c2=2, and prices start at 10 (p1=p2=10)...then each firm will sell for 10, and get half the market each because consumers are indifferent between them.
If however one of the firms cuts the price to 9, then they will get the WHOLE market as this is more attractive to every consumer, the added quantity sold increases overall profits. this process of undercutting continues until it stops becoming profitable. This happens for firm 2 earlier. At a price of 2 they will simply break even as this is equal to their costs, however firm 1 is still making profit as their costs are lower, and can afford to cut the price even further, say, to 1.99999... at this price they can take the whole market as opposed to half the market at 2 because firm 2 can no longer compete and lower its prices without making a loss, and because of perfect information and all that crap, ALL consumers will buy the SLIGHTLY cheaper product

NE -> p1 ≈ c2, profit1 ≈ (c2– c1 )Q(c2) > 0

NE is nash equilbrium right? basically its firm 1s optimal strategy, to set their price EVER SO SLIGHTLY below the costs of firm 2 (this can be miniscule) so for all intents and purposes it equals costs of firm 2, hence you sub in c2 for p1. profit is just total revenue - total cost.

q2 = profit2 = 0

Market power (low-cost firm’s mark-up) ≈(c2-c1)/c2

It can be very small if the difference in costs is small

Concentration --> max degree (only the low-cost firm is active)
dunno about the rest, doesnt seem too important, lol

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