S2W6

The market demand curve for plumbing services offered by Mario and Luigi is given by P =
48 − 4Q, where Q = QM + QL. QL is the quantity of plumbing services supplied by Luigi, and
QM is the quantity of plumbing services supplied by Mario. The constant per-unit marginal cost
is £12 for both Mario and Luigi. Find the equilibrium price, quantities and profits if Mario and
Luigi act as Bertrand duopolists in the market for plumbing services

Suppose that Nintendo and PlayStation are suppliers in the market for game consoles, and the
market is characterised by monopolistic competition. If the competition follows the Cournot
model:

• Nintendo and PlayStation choose prices simultaneously

• Nintendo and PlayStation choose quantities simultaneously

• Nintendo chooses their quantity first, followed by PlayStation

• PlayStation chooses their quantity first, followed by Nintendo

Papa’s Pizzeria and Papa’s Burgeria are right next to each other on a busy street. Both currently
earn £200 profit. They both have the option of running an advertising campaign. If Papa’s
Pizzeria advertises and the Burgeria does not, then Pizzeria earns £220, and Burgeria earns
£210. If Papa’s Burgeria advertises and the Pizzeria does not, then Burgeria earns £202, and
Pizzeria earns £230. If they both advertise, they each get £208. If both decide simultaneously
whether to advertise, what are the Nash Equilibrium outcomes?

Sonic and Shadow the Hedgehogs work together and have a monopoly over the market for rings
in Green Hill Zone. The annual demand for rings P = 200 − Q. The marginal cost of a ring is
constant at M C = 20. Sonic and Shadow had a fall out, and now Sonic runs one firm and Shadow
runs another. They still have the same marginal costs, but now they are Cournot duopolists.
How much profit have the Hedgehogs lost?

One night, Steve runs into a creeper, a zombie, and an enderman discussing duopolies. They are
all trying to understand how two of them could behave in different ways to gain market power
and set up duopolies. The creeper explains to the rest that any good duopolists must be good
game theorists. The zombie and the enderman cannot understand why this is the case. The
creeper explains that duopolies can collude and then cheat, but the enderman and zombie still
fail to see the resemblance.
How should the creeper explain to the enderman and the zombie why game theory and Duopoly
behavior go hand in hand?

Answer explanation

Oligopoly collusion creates options for the firms to “cheat” on the other. They will both be better off if no one cheats (for example by lowering prices) but if they do cheat and the other doesn’t, this is best for them and therefore this is their dominant strategy and their Nash equilibrium. To circumvent this, firms could play a tit-for-tat strategy, but the tat move can be very costly for firms. A Cournot model allows for the nash equilibrium for both firms to not cheat as they take the quantity as a given.

Two villagers have all the iron pickaxes in the village and are therefore the only ones with access
to diamonds. They don’t know how to make a profit on this until Steve (an economist) comes
along to guide them. He explains to them that they have two options, a shared monopoly, or,
to prevent cheating, a cournot duopoly, he also helps them by working out the demand curve for
diamonds and the marginal cost of extracting it. These are P = 10 − Q and M C = 2.
Which model has higher profits? Which option should they pick?

• Cournot has higher profits, pick this model

• Shared Monopoly has higher profits, pick this model

• Shared monopoly has higher profits, but they don't necessarly pick it

• Cournot has higher profits, but they don't necessarly pick it

Answer explanation

Team of the Year (TOTY) Messi is one of the rarest cards in the game FIFA. KSI was able to
pack him this year but wants to figure out at what price he wants to sell him to buy all the
other TOTYs. He understands that since there is Qn output there are n “firms” in cournout
equilibrium. He comes across the equation: P = 1 + 1/(ε/si) = M C. Where si is his market
share of TOTY Messis, and ε= elasticity. Since he packed Messi within a minute of him being
released, at first he has si = 1 but after a few days, enough Messi’s are on the market for his
market share to be very close to 0.
True or False: He will begin pricing by perfect competition first and then as a
monopolist.

• True

• False

Answer explanation

With a market share close to 0, even in a cournout equilibrium, he prices at P=MC, so he will do this after a few days. He should price as a monopolist only when he is the only person in the game with TOTY Messi.

In the world of Bang Dream! Girls Band Party, two bands decide to settle their rivalry by competing in a chocolate-making contest. Kasumi's ChocoHarmony and Tae's MelodySweets are the contenders, each striving to win over fans with their delicious creations. They pay their helpers a wage of 10 notes (the currency) and aim to price their chocolates competitively in LiveStreet, a town that adores music and sweets equally.

Given that labor (paid at 10 notes per helper with a productivity of 1 chocolate per note) is their only cost, at what price will ChocoHarmony and MelodySweets likely set for their chocolates to capture the hearts of LiveStreet?

• 10

• 15

• 5

In the diverse world of Pokémon, trainers often find themselves at PokéMarts looking to purchase a variety of Poké Balls. Each type of Poké Ball—be it a standard Poké Ball, a Great Ball, an Ultra Ball, or a specialized ball like the Net Ball or Dusk Ball—offers unique advantages tailored to different Pokémon catching scenarios. This variety allows trainers to optimize their catching strategy based on the specific Pokémon they encounter in the wild.

Describe the trade-off between cost and variety within the context of PokéMart's offerings

In a group of 4 friends, two win every single time without fail. They want to make sure they
keep winning. However, 1 friend is better than the other so they make a deal to make sure their
other two friends don’t win. They identify the demand curve for a win as P = 50 − 4Q and
Q = Q1 + Q2 Because Friend 1 has more skill, his MC of winning = 0 but for friend 2 his MC is
20.
What is the equilibrium price of a win, the number of wins, and the profits for each friend?

Answer explanation