State whether the following statements are TRUE, FALSE, or UNCERTAIN,
and in brief sentences, possibly using diagrams, mathematical formulas, or an example, give the reason for your answers. The reasoning is more important than the correct classification.
a) Consider a simultaneous game in which both players have a
dominant strategy. In this case the Nash equilibrium is always Pareto-effcient.
b) In a game where the two players have no dominant strategies,
a Nash equilibrium cannot exist.
c) Two firms with the same marginal costs and competing à la Stackelberg, in equilibrium produce the same quantity.
d) In the Cournot model, firms always share the market equally
(produce the same quantity).
e) The Pearl Theater is a local monopolist in the town of Redcats.
Pearl’s marginal cost is constant and equal to $6. Thus, if it is optimal for Pearl to charge $12 per ticket, then the elasticity of demand at this price must be equal
to 1/2.
f) The cost structure of firms active in an industry is such that
the average cost is always higher than the marginal cost. Then, this industry is a natural monopoly.
g)A dominant strategy equilibrium is always a Nash equilibrium.
h) In a duopoly, with identical firms and homogeneous product,
total surplus does not depend on the type of competition, i.e. quantity (Cournot) vs. price (Bertrand) competition
i) Two firms A and B compete in a duopoly à la Bertrand. Their cost functions are cA(y) = 10yAe cB(y) = 5yB, respectively (where yAand yB are the quantities produced). In equilibrium B will be the only supplier in the market and will set the price equal to the monopoly price pM= 15.
k) In a monopoly situation the equilibrium will never correspond to a quantity on the inelastic section of the demand curve.
l)The market quantity supplied in a monopoly is always smaller than the quantity under perfect competition.